# Akshat Rk

EconomistGMATTutor posted a reply to The product P of two prime numbers is between 9 and 55. in the Problem Solving forum
“Hello M7MBA. Let''s take a look at your question. We have one prime number "a" that is greater than 2 and less than 6. Hence a=3, 5. The other primer number "b" is greater than 13 and less than 25. Hence b=17, 19, 23. Hence, the possible products are: If a=3 then ...”
February 26, 2018
EconomistGMATTutor posted a reply to Which of the following has the same value as 5^6? in the Problem Solving forum
“Hello M7MBA. Let''s see. How you asked, we have to rewrite the expression as follows: $$5^6=5^{3\cdot2}=\left(\left(5\right)^3\right)^2=125^2.$$ Therefore, the correct answer is the option D. I hope this answer can help you. I''m available if you''d like a follow-up. Regards.”
February 26, 2018
EconomistGMATTutor posted a reply to Which one of the following is the minimum value of in the Problem Solving forum
“Hello M7MBA. Let''s take a look at your question. We have two numbers which product is 36, that is to say, $$a\cdot b=36.$$ The options for a and b are: a=1, b=36 --------a+b=37. a=2, b=18 --------a+b=20. a=3, b=12 --------a+b=15. a=4, b=9 ----------a+b=13. a=6, b=6-----------a+b=12. ...”
February 26, 2018
EconomistGMATTutor posted a reply to If the surface area of a certain cube is 2400, what is... in the Problem Solving forum
“Hi LUANDATO. Your answer is good. This is the correct way to solve this PS question. Since a cube is formed by 6 faces that are squares, then 6L^2=2400 and therefore L=20. And the volume of a cube is L^3, hence the volume is (20)^3=8000. Therefore, the correct answer is the option C. I ...”
February 24, 2018
EconomistGMATTutor posted a reply to If a merchant makes a profit of 20% based on the selling... in the Problem Solving forum
“Hello LUANDATO. We have to look at this question carefully. Let''s say that the selling price is $100. Then, 20% profit means that the cost price is$80 and $20 is the profit obtained. Now we need to find what percent of$80 represents $20:$80--------------100% $20---------------x% ...” February 24, 2018 EconomistGMATTutor posted a reply to Jerry and Ross decide to have a footrace. They run 1,000... in the Problem Solving forum “Hello LUANDATO. Your answer is great and very fast. Another way you can do it (but is a bit longer than yours) is the following: Jerry ran at 5 mts/sec during 500 meters, then they ran during $$t=\frac{500}{5}=100\ \text{seconds}$$ On the other hand, in 100 secs Ross ran $$d=4\cdot100=400\ ...” February 24, 2018 EconomistGMATTutor posted a reply to Peter and Jacob are at the northwest corner of a field... in the Problem Solving forum “Hello AAPL. Let''s take a look at your question. The following image shows how the walked. https://s10.postimg.org/5wsl1g0et/Rectangle.png Now, we can see that the distance walked by Peter is:$$\sqrt{160^2+300^2}=\sqrt{25600+90000}=\sqrt{115600}=340\ ft$$On the other hand, the ...” February 20, 2018 EconomistGMATTutor posted a reply to In a certain candy store in New York in the Problem Solving forum “Hello Roland. Let''s take a look at your question. There is something that is not clear in the wording. Watching the answers, this PS should be solved like this: In each case, the orange candy is the cheapest, therefore in both cases, the discount will be 30 cents. Hence, the difference is ...” February 20, 2018 EconomistGMATTutor posted a reply to The area of one square is x^2 + 10x + 25 and the area in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. We will first find the length of side for both the squares and then find the perimeters of both.$$Area\ of\ first\ square\ =\ x^2+10x+25$$Let length of side of the square is ''a'', then,$$a\times a=\ x^2+10x+25a^2=\ x^2+10x+25$$...” February 19, 2018 EconomistGMATTutor posted a reply to Dawn chases her young brother Paul. She runs at a... in the Problem Solving forum “Hello AAPL. Let''s take a look at your question. Let''s assume Dawn speed is 6mts/sec and Paul speed= 1mts/sec. The combined speed is 5 mts/sec. If she ran for 2 minutes, then their distance is (5mts/sec)*(120sec)=600mts. Paul running at 1m/sec covers 600 meters in 600 secs = ...” February 18, 2018 EconomistGMATTutor posted a reply to A telephone company charges x cents for the in the Problem Solving forum “Hello Roland. Let''s take a look. Let''s suppose that the call lasts t minutes. Now, let''s write 5.55 as 555 cents, then for the first minute = x cents. for the rest of the call = y(t-1). Hence, 555 cents = x+y(t-1). This implies$$x+y\left(t-1\right)=555\ \Leftrightarrow\ \ \ ...” February 18, 2018 EconomistGMATTutor posted a reply to Four people are to be selected to receive a modeling in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. We have to select 2 men from 10 (10C2), one woman form 5 (5C2) and one child form 2 (2C1). Hence, the number of ways is $$10C\ 2=\frac{10!}{8!\cdot2!}=\frac{10\cdot9\cdot8!}{8!\cdot2}=\frac{90}{2}=45$$ $$5C\ ...” February 17, 2018 EconomistGMATTutor posted a reply to In how many ways can the letters of word "EDUCATION&quo in the Problem Solving forum “Hello Vjesus12. Let''s take a look at the question. EDUCATION has 5 vowels and 4 consonants. Hence, there are 5! ways of arranged the vowels and there are 4! ways to arrange the consonants. Now, let''s call A to all the vowels and B all the consonants together. Hence, we have two ways to ...” February 17, 2018 EconomistGMATTutor posted a reply to Which of the following best approximates in the Problem Solving forum “Hi Vjesus12. Let''s take a look at your question. Let''s rewrite the numbers as follows: 0.2 = 2*10^(-1) 0.3 = 3*10^(-1) 0.4 = 4*10^(-1) 0.5 = 5*10^(-1) Now, ...” February 17, 2018 EconomistGMATTutor posted a reply to If Tom goes y miles in x hours, how many miles does he go in the Problem Solving forum “Hi Vjesus12. Let''s take a look at your question. If Tom goes y miles in x hours, it implies that his speed is$$\frac{y}{x}\ \frac{\text{miles}}{\text{hours}}.$$Now, we want the speed per in minutes. Hence, we have to divide by 60 (since 1 hour=60 minutes). Therefore, Tom does ...” February 17, 2018 EconomistGMATTutor posted a reply to If 8^(-x) < 1/32^3, what is the smallest integer value of in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. We have to rewrite the power and then we just have to take a look at the exponents. The calculation is:$$8^{-x}<\frac{1}{32^3}\ \Leftrightarrow\ \ \ \frac{1}{8^x}<\frac{1}{32^3}\ \Leftrightarrow\ \ 32^3<8^x$$...” February 17, 2018 EconomistGMATTutor posted a reply to In a certain quiz that consists of 10 questions, each questi in the Problem Solving forum “Hi ardz24, Let''s take a look at your question. Each question after the first is worth 4 points more than the preceding question, so we can write the sequence of points as: x, x+4, x+8, x+12, ... x+36 (10 questions total) This seems to be an arithmetic sequence with:$$n=10,\ d=4$$The ...” February 15, 2018 EconomistGMATTutor posted a reply to Cindy paddles her kayak upstream at m kilometers per hour... in the Problem Solving forum “Hi AAPL, You have followed the correctly perfect approach to solve the problem.” February 15, 2018 EconomistGMATTutor posted a reply to The length and width of a certain rectangle are in the rati in the Problem Solving forum “Hi Max@Math Revolution, Let''s take a look at your question. Since, the length and width of a certain rectangle are in the ratio 4 to 5, therefore, Length = 5x Width = 4x Area = 2000 sq units$$Area\ =\ Length\ \times\ Width2000\ =\ \left(5x\right)\left(4x\right)2000\ =\ ...” February 15, 2018 EconomistGMATTutor posted a reply to What is the area of the lot in square meters? in the Problem Solving forum “Hi AAPL, The approach you followed is perfectly correct.” February 13, 2018 EconomistGMATTutor posted a reply to If 9 - x^2 ≥ 0, which of the following describes... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. First of all let me clarify that $$9-x^2\ can\ not\ be\ written\ like\ \left(3-x\right)^2.$$ $$We\ will\ write\ 9-x^2\ as\ difference\ of\ squares\ like:$$ $$\left(3\right)^2-\left(x\right)^2\ge0 ... (i)$$ $$Using\ difference\ of\ square\ ...” February 13, 2018 EconomistGMATTutor posted a reply to If 4x-12 >= x + 9, which of the following must be true? in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question.$$4x-12\ge x+94x-12+12\ge x+9+124x\ge x+214x-x\ge x+21-x3x\ge21\frac{3x}{3}\ge\frac{21}{3}x\ge7$$The answer is x is greater than or equal to 7. We can see that option B, C, D and E does not ...” February 13, 2018 EconomistGMATTutor posted a reply to What is the least common multiple of 39, 91, 93 and 217? in the Problem Solving forum “Hi Max@Math Revolution, Let''s take a look at your question. To find the least common multiples of given numbers, we need to write the numbers a product of their prime factors. 39 = 3 x 13 91 = 7 x 13 93 = 3 x 31 217 = 7 x 31 Common Factors = 3, 13, 7, 31 Least Common Multiple = 3 x ...” February 13, 2018 EconomistGMATTutor posted a reply to If 5n/(4n - x) = (0.788)^(-1) , then x/n = in the Problem Solving forum “Hi Brent@GMATPrepNow, Let''s take a look at your question.$$\frac{5n}{\left(4n-x\right)}=\left(0.788\right)^{-1}\frac{5n}{\left(4n-x\right)}=\frac{1}{0.788}\frac{5n}{\left(4n-x\right)}=\frac{1000}{788}\frac{5n}{\left(4n-x\right)}=\frac{250}{197}$$...” February 13, 2018 EconomistGMATTutor posted a reply to At a certain carpet factory, if carpeting of width 10... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. Carpeting of width 10 feet is moving continuously through a dryer at a constant speed of 2160 feet per hour, therefore, 10 * 2160 = 21,600 sq ft of carpeting moved through the dryer in one hour. We know that 1 hour = 3600 seconds, hence To ...” February 13, 2018 EconomistGMATTutor posted a reply to If 2^{(x+y)^2} / 2^{(x-y)^2} = 2, what is the value of xy? in the Problem Solving forum “Hi swerve, Let''s take a look at your question.$$\frac{2^{\left(x+y\right)^2}}{2^{\left(x-y\right)^2}}=2 ... (i)$$Let''s evaluate the square of binomials in the exponent of 2, using polynomial identities:$$\left(x+y\right)^2=x^2+2xy+y^2\left(x-y\right)^2=x^2-2xy+y^2$$Eq(i) ...” February 13, 2018 EconomistGMATTutor posted a reply to If the amount of federal estate tax due on an estate valued in the Problem Solving forum “Hi ardz24. Let''s take a look at your question. The value of the state is 1,350,000. Hence, it exceeds by 100,000 (because 1,350,000 - 1,250,000 = 100,000). Now, the state has to pay$$437,000+100,000*43\%=437,000+100,000\cdot\frac{43}{100}=437,000+43,000=480,000.$$Finally, the ...” February 13, 2018 EconomistGMATTutor posted a reply to If the amount of federal estate tax due on an estate valued in the Problem Solving forum “Hi ardz24. Let''s take a look at your question. The value of the state is 1,350,000. Hence, it exceeds by 100,000 (because 1,350,000 - 1,250,000 = 100,000). Now, the state has to pay$$437,000+100,000*43\%=437,000+100,000\cdot\frac{43}{100}=437,000+43,000=480,000.$$Finally, the ...” February 13, 2018 EconomistGMATTutor posted a reply to When a person aged 39 is added to a group of n people in the Problem Solving forum “Hello Mo2men. Let''s see your question. In the first case we have the following:$$\frac{39+x}{n+1}=\frac{x}{n}+2\ -----\left(1\right)$$and in the second case we have:$$\frac{15+x}{n+1}=\frac{x}{n}-1\ -----\left(2\right)$$where x represents the sum of the ages of all n people in the ...” February 13, 2018 EconomistGMATTutor posted a reply to For integers a, b, and c, if ab = bc in the Problem Solving forum “Hi lheiannie07. Let''s take a look at your question. First, the question is which of the options listed MUST be true. Hence, it has to be true always. If we choose a=1, b=0 and c=2, then ab=bc=0. Now (A) a=c is FALSE. (B) a^2*b=b*c^2=0 is true, but it has to be true always. (C) a/c = 1 ...” February 13, 2018 EconomistGMATTutor posted a reply to Problem Solving in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. After 6 games, team B had an average of 61.5 points per game. We can find the total points scored in these 6 games using average formula.$$Average\ =\ \frac{Sum\ of\ points\ }{Number\ of\ games}61.5\ =\ \frac{Sum\ of\ points\ }{6}$$...” February 11, 2018 EconomistGMATTutor posted a reply to A certain type of siding for a house costs 10.50... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. Since the cost is given according to per square yard, therefore we will convert the length in yards as well. We know that:$$1\ ft=\frac{1}{3}yards60\ ft=60\times\frac{1}{3}yards=20\ yardsLength=20\ yardsWidth=4\ yards$$...” February 11, 2018 EconomistGMATTutor posted a reply to In a certain sequence, the first term is 1, and each... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question.$$First\ term\ =\ 1$$Each successive term is 1 more than the reciprocal of the term that immediately precedes it, therefore, we can find the next term as: Reciprocal of 1 is 1.$$Second\ term=\ 1+\frac{1}{1}=1+1=2$$Reciprocal of 2 is 1/2. ...” February 11, 2018 EconomistGMATTutor posted a reply to If sum of the roots of the equation x^2 -5x+6 = 0 is in the Problem Solving forum “Hi GMATinsight, Let''s take a look at your question. The quadratic equation given is:$$x^2-5x+6=0$$We know that, for a quadratic equation ax^2+bx+c=0, Sum of roots = -b/a Product of roots = c/a We can find the sum and product of roots of given quadratic equation as:$$Sum\ of\ ...” February 11, 2018 EconomistGMATTutor posted a reply to The area of square ABCD is x^ 2 + 18 √ 3 x + 243 . What is in the Problem Solving forum “Hi ardz24, Let''s take a look at your question. We know that the area of a square is always the square of the length of side. So we can find the length of side using the area. $$Area=x^2+18\sqrt{3}x+243$$ If s represents the length of side of square, then, $$s^2=x^2+18\sqrt{3}x+243$$ ...” February 11, 2018 EconomistGMATTutor posted a reply to Every trading day in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. The price of CF Corp stock either goes up by$1 or goes down by $1 with equal likelihood, it means that, $$p\left(Up\right)=\frac{1}{2}$$ $$p\left(Down\right)=\frac{1}{2}$$ We need to find the probability that the price of CF Corp ...” February 11, 2018 EconomistGMATTutor posted a reply to Donna has a 60 miles drive to a work conference... in the Problem Solving forum “Hi AAPL. Let''s take a look. We know she has to drive 60 miles in 90 minutes. Now, we are asked for miles per HOUR. Hence, let''s make the conversion from minutes to hours. Therefore, 90 minutes = 90/60 = 1.5 hours. Now, Donna drove halfway at 30 miles per hour, this implies that she ...” February 11, 2018 EconomistGMATTutor posted a reply to Set S = {1, 2, 3, 4, 5, 6, 7, x} If x is an integer in the Problem Solving forum “Hello Vjesus12. Let''s see your questions. Since all the numbers are sorted, we can assume that x>7. Now, as the set S has an even number of elements (8), the median is given by (a+b)/2, where "a" and "b" are the numbers on the middle of the set. In our case, a=4 ...” February 11, 2018 EconomistGMATTutor posted a reply to Problem Solving in the Problem Solving forum “Hello Roland. There is a mistake with the answer. Let''s see why. Let''s call the sides of the rectangle "x" and "y". Hence the area is A=x*y. Now, if each side is increased by 15%, the measure of the sides will be $$X=x+15\%\cdot x=x+0.15\cdot x=1.15\cdot x$$ ...” February 11, 2018 EconomistGMATTutor posted a reply to John and Jane went out for a dinner and they ordered... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. Assume that the original price of the dish is x, then, the 10% discount on the dish can be calculated as: $$Discount=\left(10\%\right)\times x$$ $$Discount=\left(\frac{10}{100}\right)\times x=0.1x$$ $$Discounted\ price\ of\ the\ ...” February 10, 2018 EconomistGMATTutor posted a reply to Four friends, Charles, Mike, Brian, and John, went on a... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. The approach you used is absolutely correct. But we can solve it Just by adding up all three equations.$$M=B+400\ ...\left(i\right)J=C-1200\ ...\left(ii\right)C=M+400...\left(iii\right)$$Adding Eq(i), (ii) and (iii), we ...” February 10, 2018 EconomistGMATTutor posted a reply to Tom found a box of 220 baseball cards. Begin a thoughtful... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. Tom had a total of 220 baseball cards. He wanted to save at least 50 percent of the cards for himself.$$50\%\ of\ \ 220\ card=\left(\frac{50}{100}\right)\times220=110$$Lets see if the remaining 110 cards can be distributed evenly among his ...” February 10, 2018 EconomistGMATTutor posted a reply to A plane traveled k miles in its first 96 minutes of flight.. in the Problem Solving forum “Hello AAPL. The way you solve it is perfect. Another way you could solve it is making the conversion from minutes to hours from the beginning. That is to say,$$96\ \text{minutes}\ =\ \frac{96}{60}\text{hours}$$and$$t\ \text{minutes}\ =\ \frac{t}{60}\text{hours}.$$Hence, ...” February 9, 2018 EconomistGMATTutor posted a reply to Drill Press M can bore 3000 holes an hour and Drill Press... in the Problem Solving forum “Hello LUANDATO. There is a mistake with the option C. The correct answer should be 36/5. Let''s see why. We know that Drill Press M has to operate for 9 hours (in this way, the number of hours that has to operate Drill Press N will be minimum). Hence, Drill Press M will bore 3000*9 = 27.000 ...” February 9, 2018 EconomistGMATTutor posted a reply to Each day Linda spends 6 hours at her baby-sitting job... in the Problem Solving forum “Hello LUANDATO. Let''s see. Your answer is perfect. She spends 7.5 hours each day of job, but she only earns 6*15=90 each day. Then, her rate per day is 90 / 7.5 = 12. Hence, the correct answer is the option E=12. I hope this may help you. If you have any doubt, just let me ...” February 9, 2018 EconomistGMATTutor posted a reply to Walking at 60% of his usual speed a man takes... in the Problem Solving forum “Hi Swerve. Let''s take a look at your question. Let''s consider the following variables:$$V_u\ -\ \text{usual}\ \text{speed}T_u\ -\ \text{Usual}\ \text{time}$$Hence, we have th following$$V_u\cdot T_u\ =\ 60\%\cdot V_u\cdot\left(T_u+24\right)\ \Leftrightarrow\ \ ...” February 9, 2018 EconomistGMATTutor posted a reply to On a 20 mile course, Pat bicycled at an average rate of 30 in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Pat bicycled at an average rate of 30 miles per hour for the first 12 minutes. We can find the distance covered by Pat in the first 12 minutes by first converting 12 minutes to hours. We need to be in same units. ...” February 8, 2018 EconomistGMATTutor posted a reply to A conference room in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. The North clock loses 30 sec/hr and the South clock gains 15 sec/hr. The ratio between the North clock loss and South clock gain is: $$North\ Clock\ :\ South\ Clock$$ $$30:15$$ $$2:1$$ We can use these ratios to find when these ...” February 8, 2018 EconomistGMATTutor posted a reply to David covers a total of 240 miles journey, of which in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Let the first half of 120 miles journey is covered at a constant speed of x miles/hr. Then the second half of 120 miles journey will be covered in (x+10) miles/hr. Let the time taken to cover the first half of journey is y hours. Then the time ...” February 8, 2018 EconomistGMATTutor posted a reply to At Supersonic Corporation, the time required for a machine.. in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The time required to complete a job is: $$=\sqrt{w}+\sqrt{\left(w-1\right)}$$ The rate is inverse of time, therefore we can find the rate as: $$Rate\ =\frac{1}{\sqrt{w}+\sqrt{\left(w-1\right)}}$$ Rationalizing the denominator: $$Rate\ ...” February 8, 2018 EconomistGMATTutor posted a reply to A truck travelling at 70 MPH uses 30% more gasoline... in the Problem Solving forum “Hi LUANDATO, You are following the correct approach. Yes, at 70MPH it uses 30% more gasoline, which means that it will consume 1.3L to travel 19.5 miles. Now we will calculate, how long will it travel at 70MPH in 1 liter as:$$=\frac{19.5\ miles}{1.3\ L}=15miles/L$$Now we can calculate ...” February 8, 2018 EconomistGMATTutor posted a reply to Two taps can fill a cistern in 20 minutes and 30 minutes... in the Problem Solving forum “Hi LUANDATO. Let''s continue your explanation. The first tap rate is 1/20 per minute. The second tap rate is 1/30 per minute. Now, we have to set the following equation:$$rate\ tap\ 1\ during\ x\ \text{minutes}\ +\ \left(time\ both\ taps\ worked\ together\right)\left(rate\ tap\ 1\ +\ ...” February 8, 2018 EconomistGMATTutor posted a reply to A train travels from Albany to Syracuse, a distance of... in the Problem Solving forum “Hi swerve. The way you did it is perfect. Another way that we could do here is the following (but I rather the way you did it): The total distance is 120*2=240 miles. The total time is 5 hours and 24 minutes = 5.4 hours. The average speed is: ( 50 m/h + v_2 m/h ) / 2. We have to ...” February 8, 2018 EconomistGMATTutor posted a reply to If (1+x)y=y, which of the following must be true? in the Problem Solving forum “Hi vinni.k, xy=0 itself indicates that one of the variables either x or y or both should be zero, only then this equation will be true. So we can say that either x = 0 or y = 0.” February 8, 2018 EconomistGMATTutor posted a reply to Which of the following inequalities holds if 3.24<x<5. in the Problem Solving forum “Hi Max@Math Revolution, Let''s take a look at your question. We have to check the inequalities that hold if 3.24 < x < 5.36 The open interval given includes all the values between 3.24 and 5.36 exclusive. We will check all the given inequalities for at least two random values of the ...” February 8, 2018 EconomistGMATTutor posted a reply to An automobile's gasoline millage varies, depending... in the Problem Solving forum “Hi AAPL, You followed the correct approach.” February 7, 2018 EconomistGMATTutor posted a reply to Java invests in a new mutual fund. The fund averages 10%... in the Problem Solving forum “Hi swerve, You used the correct approach.” February 7, 2018 EconomistGMATTutor posted a reply to Car X and Car Y traveled the same 80-mile route. If Car X in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. Car X traveled 80 miles in 2 hours. $$Speed\ =\ \frac{Distance}{Time}$$ $$Speed\ =\ \frac{80}{2}=40 miles/hr\$$ Car Y traveled at an average speed that was 50 percent faster than the average speed of Car X. 50% of 40 = (50/100)*40 = 20 ...” February 4, 2018 EconomistGMATTutor posted a reply to A boy's club, which is trying to raise money by having... in the Problem Solving forum “Hi AAPL, Yes. You have used the correct logic. Perfectly worked out.” February 4, 2018 EconomistGMATTutor posted a reply to If 7x – y in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. $$7x-y=23\ ...\ \left(i\right)$$ $$7y-x=31\ ...\ \left(ii\right)$$ Adding Eq(i) and (ii), $$7x-y+7y-x=23+31\$$ $$6x+6y=54\$$ $$6\left(x+y\right)=54\$$ $$x+y=\frac{54}{6}=9$$ Therefore, Option E is correct. Hope it ...” February 4, 2018 EconomistGMATTutor posted a reply to A box of balls originally contained 2 blue balls for every r in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. Let b represents blue balls, r represents red balls and x represents the total balls originally in the box. A box of balls originally contained 2 blue balls for every red ball can be represented as: $$r+2b=x\ ...\ \left(i\right)$$ After 12 ...” February 3, 2018 EconomistGMATTutor posted a reply to Last year, Company X paid out a total of$1,05,000... in the Problem Solving forum
“Hi swerve, Can you please recheck the question statement? It seems that there is some information missing or incomplete.”
February 3, 2018
EconomistGMATTutor posted a reply to A school is comprised of 400 people both teachers and... in the Problem Solving forum
“Hi LUANDATO, You have used the correct approach. The right answer is 60. I am available if you''d like any follow up.”
February 3, 2018
EconomistGMATTutor posted a reply to In a two-pound box of nuts and bolts that costs $2.34... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. A two pound box of nuts and bolts cost$2.34. The statement says that the weight in the box due to bolts is equal to the weight due to nuts, which means that the weight of nuts is equal to the weight of bolts. So a 2 pound box will contain 1 ...”
February 3, 2018
EconomistGMATTutor posted a reply to A wire is cut into three equal parts. The resulting... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. Suppose that the minimum length of wire be 3x. If it is cut into three equal pieces, length of each piece will be x. The resulting segments are then cut in 4, 6 and 8 equal parts respectively. 4 pieces will be of length x/4 each. 6 pieces ...”
February 3, 2018
EconomistGMATTutor posted a reply to If the positive integer y is divisible by 3, 8, and 12, in the Problem Solving forum
“Hello M7MBA. Now, since y is divisible by 3, 8 and 12, we get that y has, on its prime factorization, three 2''s and one 3. This is becuase 3 = 3*1 8 = 2*2*2 12 = 2*2*3 LCM(3,8,12) = 3*2*2*2 = 24. Hence, y is divisible by 24. Now, y is not divisible by 36 because 36 = 2*2*3*3, and y ...”
February 3, 2018
EconomistGMATTutor posted a reply to What is the probability of getting only 1 head in a single in the Problem Solving forum
“Hi M7MBA. Let''s take a look at your question. First, we have _ _ _ (3) places, and each place has 2 possibilities (H or T). Hence, there are a total of 2*2*2=8 possibilities. Now, we want to obtain ONLY one head, this implies that we have the next cases: HTT THT TTH Therefore, ...”
February 3, 2018
EconomistGMATTutor posted a reply to There are 4 more women than men on Centerville's board of ed in the Problem Solving forum
“Hello M7MBA. Let''s take a look at your question. Since it says 4 women more, it implies that W=M+4 (M=W-4). The case that you wrote is when is 4 times. Now, since there are 10 members on the board, we have that 10 = M + W = W-4+W = 2W-4 -------------- 2W = 14 -------- W=7. ...”
February 3, 2018
EconomistGMATTutor posted a reply to Rhonda runs at an average speed of 12 kilometers per hour, a in the Problem Solving forum
“Hello ardz24. Let''s take a look at your question. First, we have to convert the speed from kilometers per hour to kilometers per minute. V_R----Runs----- 12 km/h ------- 12km/h * 1/60 (h/min) --------1/5 km/min= 0.2 k/min. V_B---Bicycles ---- 30 km/h ------ 30km/h * 1/60 (h/min) ...”
February 3, 2018
EconomistGMATTutor posted a reply to If 2^n+2^n-2=5120, then n=? in the Problem Solving forum
“Hi Max@Math Revolution, Let''s take a look at your question. $$2^n+2^{n-2}=5120$$ $$2^n+2^n.2^{-2}=5120$$ Taking 2^n as a common factor: $$2^n\left(1+2^{-2}\right)=5120$$ $$2^n\left(1+\frac{1}{2^2}\right)=5120$$ $$2^n\left(1+\frac{1}{4}\right)=5120$$ ...”
February 2, 2018
EconomistGMATTutor posted a reply to Eight friends in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. Total bill of the restaurant = $480 discount coupon = 25% off The discount on the total bill can be calculated as: $$Discount\ =\ 480\ \times25\%$$ $$Discount\ =\ 480\ \times\frac{25}{100}=120$$ $$\text{Remaining amount they have ...” February 2, 2018 EconomistGMATTutor posted a reply to what is the area of the un-grazed, un-shaded region? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. In the rectangle ABCD, Let BC =AD = x Then BG = AG = x because these are the radii of the circular area. Hence we can write the dimensions of the rectangular area as: Width = BC = x Length = AB = x + x = 2x The area equation can be ...” February 2, 2018 EconomistGMATTutor posted a reply to In the diagram, what is the value of x? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. We will solve this problem using Cosine law. Cosine law is$$a^2=b^2+c^2-2bc\ Cos\ A$$Where a, b and c are the side lengths of a triangle and A is the angle between the sides b and c. Apply Cosine law on the triangle give, we get: ...” February 2, 2018 EconomistGMATTutor posted a reply to If (1+x)y=y, which of the following must be true? in the Problem Solving forum “Hi vinni.k, Let''s take a look at your question.$$\left(1+x\right)y=y\left(1+x\right)=\frac{y}{y}\left(1+x\right)=1x=1-1=0$$To find y let''s evaluate the equation:$$\left(1+x\right)y=yy+xy=yxy=y-yxy=0y=0$$Therefore, Option B is ...” February 2, 2018 EconomistGMATTutor posted a reply to Derek can read x pages in 5 minutes. At this rate, how . . . in the Problem Solving forum “Hello vjesus12. Let''s take a look at your question. Derek can read x pages in 5 minutes, this implies that Derek can read$$\frac{x}{5}\ \text{pages}\ \text{per}\ \text{minute}.$$Therefore, to read p pages will take him$$\frac{p}{\frac{x}{5}}=\frac{5p}{x}\ \text{minutes}.$$Hence, the ...” February 1, 2018 EconomistGMATTutor posted a reply to If the perimeter of a rectangular property is 46 meters in the Problem Solving forum “Hello vjesus12. Let''s take a look at your question. You are correct, you have to use the formulas$$2X+2Y=46\ \ and\ \ \ \ \ X\cdot Y=76 .$$Hence,$$X+Y=23\ \ and\ \ \ \ \ X=\frac{76}{Y}.$$Replacing X on the first equation we get$$\frac{76}{Y}+Y=23\ \Leftrightarrow\ \ \ 76+Y^2=23Y\ ...” February 1, 2018 EconomistGMATTutor posted a reply to If the charge of staying in a student youth hostel in the Problem Solving forum “Hi vjesus12. Let''s take a look at your question. We are interested in the cost of 23 days. We have to divide this 23 days as follows: 7 days (a week) + 16 days. Then, the equation that gives us the cost total is: $$Cost=18\cdot\left(7\right)+10\cdot\left(16\right)=126+160=286\ ...” February 1, 2018 EconomistGMATTutor posted a reply to The length of each side of square A is increased by in the Problem Solving forum “Hello vjesus12. Let''s take a look at your question. Let''s suppose that the length of each side of A is equal to 10cm. Then, the area of A is equal to 10*10=100. Now: each side of square A is increased by 100 percent to make square B implies that the length of each side of B is equal to ...” February 1, 2018 EconomistGMATTutor posted a reply to In a basketball game, Tim scored 10 points more...... in the Problem Solving forum “Hello vjesus12. Let''s take a look at your question. Let be T= Tim, J=Joe and K=Ken. Then: Tim scored 10 points more than Joe implies that T=J+10. (J=T-10) but only half as many points as Ken implies that T=K/2. (2T=K) the three players scored a combined total of 50 points implies ...” February 1, 2018 EconomistGMATTutor posted a reply to Find the remainder of 2^100/12 in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. We need to find the remainder of$$\frac{2^{100}}{12}=\frac{2^{2\times50}}{12}=\frac{4^{50}}{12}$$Let''s check what happens when powers of 4 is divided by 12, starting from 4^2.$$4^2=16\frac{16}{12}=1\ remainder\ ...” January 31, 2018 EconomistGMATTutor posted a reply to If 5 dollars and 35 crowns is equivalent to 7 pounds...... in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Suupose that d represents the dollars, c represents the crowns and p represents the pounds, then according to the question statement, we can write the following equations. 5 dollars and 35 crowns is equivalent to 7 pounds: $$5d+35c=7p$$ ...” January 31, 2018 EconomistGMATTutor posted a reply to If a person purchases 15 of the 3,000 tickets sold in a... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. We know that we can find the probability of an event by dividing the number of successful outcomes divided by the total number of outcomes. Number of tickets purchased by a person = 15 Total number of tickets = 3000 We will first find the ...” January 31, 2018 EconomistGMATTutor posted a reply to A factory has a fixed cost of$45,000 a month, and a cost in the Problem Solving forum
“Hello vjesus12. Let''s see your question. The fixed cost is $45,000. The cost of each item is$2.5. The price of each item is $5. So, when an item is sold the profit is$5-$2.5 =$2.5. Now, we have to divide the fixed cost by the profit for each item, that is to say, ...”
January 27, 2018
EconomistGMATTutor posted a reply to A merchant gets a 5% discount on each meter . . . . in the Problem Solving forum
“Hi vjesus12. Let''s take a look at your question. For the first 2000 meters, there is no discount. Hence the cost is $2*2000 =$4000. For the next 1500 meters, there is a discount of 5%. Hence the cost is 2$*(1500)*95% =$3000*95/100 = $2850. For the next 1000 meters, there is a discount ...” January 27, 2018 EconomistGMATTutor posted a reply to What is the probability that you get a pair . . . . in the Problem Solving forum “hi vjesus12. Let''s take a look at your question. You can not use the equation (52C1)*(3C1) because you can not choose the cards. You just have to pick them from the top. Hence first, you pick the top card. Then, there are 51 cards and there are only 3 cards that can form a pair with the ...” January 27, 2018 EconomistGMATTutor posted a reply to If the curve represented by y = x^2 – 5x + t intersects .. in the Problem Solving forum “Hi Vjesus12. Let''s take a look at your question. Option 1: Since $$y=x^2-5x+t$$ intersects with the x-axis at (-1,0) we have that $$0=\left(-1\right)^2-5\left(-1\right)+t\ \Leftrightarrow\ 0=1+5+t\ \Leftrightarrow\ t=-6.$$ Hence, the curve is represented by $$y=x^2-5x-6,$$ and this ...” January 27, 2018 EconomistGMATTutor posted a reply to Z is the set of the first n positive odd numbers, where .... in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. We will solve this question by assuming some random values for the set Z. Let n = 5, therefore, the set Z has first 5 positive odd numbers. i.e. $$Z=\left\{1,\ 3,\ 5,\ 7,\ 9\right\}$$ Let k = 2, then x is the is the maximum value of the ...” January 26, 2018 EconomistGMATTutor posted a reply to A circle has center at origin and radius 1...... in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Center of the circle is (0, 0). Radius = 1 https://s19.postimg.org/nl8jmatqr/Untitled.png We will use the angle XOZ first using the arc length formula. $$S=\ r\left(theta\right)$$ $$\frac{2\pi}{3}=1\left(theta\right)$$ ...” January 26, 2018 EconomistGMATTutor posted a reply to Four brothers Adam, Bill, Charles and David... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. Your answer is right. We have to set four equations with four variables. Your equations are great: $$(1) A+B+C+D=9900$$ $$(2) A=\frac{1}{2}\cdot\left(B+C+D\right)$$ $$(3) B=\frac{1}{4}\cdot\left(A+C+D\right)$$ $$(4) ...” January 24, 2018 EconomistGMATTutor posted a reply to Two trains are heading toward each other on a 750-kilometer in the Problem Solving forum “Hello swerve. Let''s take a look at your question. If we calculate the combine speed we will get 80+70= 150 km/h. Now, the will collide in$$\frac{750km}{150\ \frac{km}{h}}=5\ h.$$Hence, the correct answer is the option C=15. I hope this answer can help you. I''m available if you''d ...” January 24, 2018 EconomistGMATTutor posted a reply to On a certain track and field team, a sprinter runs 120... in the Problem Solving forum “Hi swerve. Your answer is perfectly ok. Because the sentence a sprinter runs 120 meters per minute, which is 4 times as fast as the speed of a distance runner, implies that the runner distance speed is 120/4 = 30 mts/min. And the distance runner can run 120 meters (in 4 minutes) twice as ...” January 24, 2018 EconomistGMATTutor posted a reply to If the probability of Sita getting selected to a school... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The probability of Sita getting selected to a school = 20% = 20/100 = 1/5 This question can easily be solved by calculating the probability of opposite event. The probability of Sita not getting selected to a school = 1 - 1/5 = 4/5 ...” January 21, 2018 EconomistGMATTutor posted a reply to If the figure below is a square with a side of 4 units... in the Problem Solving forum “Hi LUANDATO, You have followed the perfectly right approach.” January 21, 2018 EconomistGMATTutor posted a reply to Problem Solving in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. We will compare each fraction with 1/4 to check which one is greater than 1/4. Let''s start with option A, 12/50 To compare fractions, we make the denominators of the fraction same. ...” January 20, 2018 EconomistGMATTutor posted a reply to Probability in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Total people = 2500 35% people invest in municipal bonds, therefore, Number of people who invest in municipal bonds = 2500 * 35/100 = 875 Number of people who invest in oil stocks = 2500*18/100 = 450 Number of people who do not invest in ...” January 20, 2018 EconomistGMATTutor posted a reply to There are 7 players in a bowling team with an average... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. We have three numbers, one is 85, average of 7 numbers and other two are 110 and 60. We can find average of these three numbers as:$$Average\ =\ \frac{85+110+60}{3}=\frac{255}{3}=85$$Therefore, option B is correct. Hope it helps. I am ...” January 20, 2018 EconomistGMATTutor posted a reply to Arnold and Danny are two twin brothers that are... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. Let age of twin brothers be x today then after a year their age will be x + 1. The product of their ages today is smaller by 9 from the product of their ages a year from today. It can be written as:$$\left(x+1\right)^2-9=x^2$$...” January 20, 2018 EconomistGMATTutor posted a reply to What is the value of x? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. We know that the in a circle when two chords of a circle make an angle at the circumference of the circle, the arc subtended by that angle is always twice the angle. Therefore, in the circle given,$$2x\ =\ arclength\ \left(BAD\right) ... (i)$$...” January 20, 2018 EconomistGMATTutor posted a reply to Sentence Correction in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Let P, K and M represents the number of hours Pat, Kate and Mark charged to the project respectively. Then the total number of hours can be represented as:$$P+K+M=162...\left(i\right)$$Also, Pat charged twice as much time to the ...” January 20, 2018 EconomistGMATTutor posted a reply to Which of the following is always true in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. We will take some random values to check each statement. Let''s start from statement (I). Let 5 negative consecutive integers be -1, -2, -3, -4, -5. Average of five numbers = (-1-2-3-4-5)/5 = -15/5 = -3 Average of largest and smallest ...” January 20, 2018 EconomistGMATTutor posted a reply to What is the area of an equilateral triangle... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. Area of equilateral triangle can be calculated as:$$Area=\frac{s^2\sqrt{3}}{4}$$, where s is the side length of the equilateral triangle.$$Area=\frac{\left(60\right)^2\sqrt{3}}{4}Area=\frac{3600\sqrt{3}}{4}Area=900\sqrt{3}$$...” January 18, 2018 EconomistGMATTutor posted a reply to The perimeter of a polygon with sides of integer... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. The perimeter of the polygon is 45 and 2 sides, the smallest and longest are 5 and 10. Therefore the sum of the rest of the sides will be 45 - 10 - 5 = 30 Also, length of the remaining sides will be between the smallest and the longest side, i.e. ...” January 18, 2018 EconomistGMATTutor posted a reply to The distance between Omaha and Lincoln... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The distance between Omaha and Lincoln is 50 miles, therefore, to take a round trip Justin and Kayla have to cover a distance of 100 miles. Justin drives a car that gets 30 miles per gallon of gas, Let''s find the number of gallons it consumes ...” January 18, 2018 EconomistGMATTutor posted a reply to How many real roots does the equation . . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question.$$x^2y+16xy+64y=0y\left(x^2+16x+64\right)=0x^2+16x+64=0$$To find the number of roots of a quadratic equation, we use the discriminant. If Discriminant < 0, there are two distinct complex roots of the quadratic equation. ...” January 18, 2018 EconomistGMATTutor posted a reply to How many integers are there between 51 and 107, inclusive in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. To find the number of integers between any two given integers, inclusive, we use the formula: Highest Number - Lowest Number + 1 = 107 - 51 + 1 = 57 Therefore, Option D is correct. Hope it helps. I am available if you''d like any ...” January 18, 2018 EconomistGMATTutor posted a reply to Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. TV1= x , TV2= x+200 , TV3= x+400 and TV4= x+600 . We now that$$3400=x+\left(x+200\right)+\left(x+400\right)+\left(x+600\right)=4x+1200 3400=4x+1200\ \Leftrightarrow\ 4x=2200\ \Leftrightarrow\ x=550.$$Therefore, the 28 inch Tv ...” January 18, 2018 EconomistGMATTutor posted a reply to For all real numbers, [x] = the greatest integer less . . . in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. , it implies that - E=56. I hope this answer can help you. Feel free to ask me again if you have a doubt. Regards.” January 18, 2018 EconomistGMATTutor posted a reply to in how many ways 5 different chocolates be distributed . . . in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. Let the 5 cholcolates be : C1 , C2 , C3 , C4 and C5. And there be 4 Students : S1 , S2, S3 and S4. Now, The first Chocolate can be given in 4 ways (Either to S1 or S2 or S3 or S4). The Second Chocolate can be given in 4 ways (Either ...” January 18, 2018 EconomistGMATTutor posted a reply to A computer appliance dealer bought a computer in the Problem Solving forum “Hello lheiannie07. Let''s take a look at your question. A computer appliance dealer bought a computer at a wholesale price of 500 and then sold it at a 20 percent discount off the suggested retail price. If the dealer made a 12 percent profit on the wholesale price, it implies that he sold ...” January 17, 2018 EconomistGMATTutor posted a reply to The sum of the mean, the median, and the range of . . . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Let''s first find the mean of the set {1, 2, 6}.$$Mean\ =\ \frac{Sum}{\text{Number of quantities}}Mean\ =\ \frac{1+2+6}{3}=\frac{9}{3}=3$$Median is the middle value of the data when it is arranged in ascending or descending order. ...” January 16, 2018 EconomistGMATTutor posted a reply to The length of a rope, by which a cow is tied... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. The rope was originally 22m long, therefore we will find the grazed area using 22m. The cow can graze in a circular area and the rope will act as the radius of the circle, therefore,$$Area_1=\pi r_1^2Area_1=\pi\left(22\right)^2$$...” January 16, 2018 EconomistGMATTutor posted a reply to During a spring season, a certain glacier surged at . . . . in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. glacier surged at the rate of 1 mile per 100 days, it implies that his rate is$$\frac{1}{100}\ \frac{miles}{days}.$$Now, we have to convert from miles to feet and from days to hours. Now, 1 mile = 5,280 feet and 1 day = 24 hours. Hence, ...” January 16, 2018 EconomistGMATTutor posted a reply to If a and b are negative integers, which of the . . . . in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. If we choose a = -2 and b = -3, we will have I. (-a)^b = (2)^(-3) = 1/(2^3) --> Positive II. (-a)^(-b) = 2^3 --> Positive III. a^(-b) = -2^3 --> Negative Then, the correct answer is the option C. I hope this answer can ...” January 16, 2018 EconomistGMATTutor posted a reply to An athlete runs R miles in H hours... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. R miles in H hours implies R/H miles per hour. Q miles in H hours implies Q/H miles per hour. Then, the combined average speed is equal to$$\frac{\frac{R}{H}+\frac{Q}{H}}{2}=\frac{R+Q}{2H}.$$This is why the correct answer is the ...” January 14, 2018 EconomistGMATTutor posted a reply to If paint costs 3.20 per quart, and a quart covers 20... in the Problem Solving forum “Hello LUANDATO. Let''s see your question. If paint costs 3.20 per quart, and a quart covers 20 square feet, it implies that$$20\ ft^2\ per\ 3.20\ dollars$$. A cube of 10 feet on each edge, has 6 faces with area 10*10=100 feet square. Then we have to paint 6*100=600 feet square. ...” January 14, 2018 EconomistGMATTutor posted a reply to Working alone, pump A can empty a pool in 3 hours... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. Working alone, pump A can empty a pool in 3 hours, it implies that pump A wor at a rate 1/3 pool/hour. Working alone, pump B can empty a pool in 2 hours, it implies that pump A wor at a rate 1/2 pool/hour. Working together the rate will ...” January 13, 2018 EconomistGMATTutor posted a reply to Let f(x)= (x-p)(x-q). If f(11)=f(20)=0, then f(10)=? in the Problem Solving forum “Hi Max@Math Revolution, Let''s take a look at your question.$$f\left(x\right)=\left(x-p\right)\left(x-q\right)f\left(11\right)=\left(11-p\right)\left(11-q\right)\text{Since,} f\left(11\right)=0\left(11-p\right)\left(11-q\right)=0\text{Either ...” January 13, 2018 EconomistGMATTutor posted a reply to If the number 892,132,24x is divisible by 11, what must . . in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. First, let''s remember the multiplication rule of 11: (Sum of digits at odd places - Sum of digits at even places) should be divisible by 11. We have the number 892,132,24x, then: ...” January 13, 2018 EconomistGMATTutor posted a reply to Which of the following is equal to in the Problem Solving forum “Hi Max@Math Revolution, Let''s take a look at your question. $$\left(\sqrt{16+4\sqrt{15}}+\sqrt{16-4\sqrt{15}}\right)^2$$ Evaluating the square, $$=\left(\sqrt{16+4\sqrt{15}}\right)^2+2\left(\sqrt{16+4\sqrt{15}}\right)\left(\sqrt{16-4\sqrt{15}}\right)+\left(\sqrt{16-4\sqrt{15}}\right)^2$$ ...” January 11, 2018 EconomistGMATTutor posted a reply to A large research project was scheduled over the course... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. A large reaserch project was scheduled over the course of 28-month period, and a budget of$84,000 was alloted for the course of the entire project , it implies that $$\frac{84000}{28}=3000\ \ \text{dollars}\ \text{per}\ \text{month}.$$ ...”
January 11, 2018
EconomistGMATTutor posted a reply to A fruit salad mixture consists of apples, peaches, and grape in the Problem Solving forum
“The fruit salad mixture consists of three fruits; apples, peaches and grapes. The mixture has an average of 13 pounds per fruit, therefore, total weight of the salad will be: $$=13\times3=39\ pounds$$ Let the grapes be x pounds, then, apples = 3x peaches = 5x/2 $$x+3x+\frac{5}{2}x=39$$ ...”
January 11, 2018
EconomistGMATTutor posted a reply to Water is leaking out from a cylinder container... in the Problem Solving forum
“Hello LUANDATO. Let''s take a look at your question. The volume of a cylinder container is $$V=\pi\cdot r^2\cdot h .$$ Now, we know that after 10 minutes it has been leaked out $$0.31\cdot10=3.1\ m^3\ of\ water.$$ On the other hand the water has decreased 0.25 meter. We now can build a ...”
January 11, 2018
EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum
“Hello Roland2rule. Let''s take a look at your question. Let a, b, c and d the number of chocolates that have A, B, C and D respectively. First, we know that A had 80 more chocolates then B initially, that is to say, $$\left(1\right)\ \ \ \ \ \ a=80+b\ .$$ Now, A gave 1/3rd of the ...”
January 9, 2018
EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum
“Hello Roland2rule. Let''s take a look at your question. Let a, b, c and d the number of chocolates that have A, B, C and D respectively. First, we know that A had 80 more chocolates then B initially, that is to say, $$\left(1\right)\ \ \ \ \ \ a=80+b\ .$$ Now, A gave 1/3rd of the ...”
January 9, 2018
EconomistGMATTutor posted a reply to A large solid cube is assembled by gluing together... in the Problem Solving forum
“Hello LUANDATO. Let''s see. We have that 27 of the small cubic blocks have not red paint on them. It implies that they were under the last layer of cubic blocks. So, we have that a cube of 3x3x3 was inside of the larger cube. Therefore, the dimensions of the larger cube were 5x5x5. It implies ...”
January 9, 2018
EconomistGMATTutor posted a reply to A large solid cube is assembled by gluing together... in the Problem Solving forum
“Hello LUANDATO. Let''s see. We have that 27 of the small cubic blocks have not red paint on them. It implies that they were under the last layer of cubic blocks. So, we have that a cube of 3x3x3 was inside of the larger cube. Therefore, the dimensions of the larger cube were 5x5x5. It implies ...”
January 9, 2018
EconomistGMATTutor posted a reply to For how many integers n is 1^n = n^1? in the Problem Solving forum
“Hi M7MBA, Let''s take a look at your question. We are asked to find, for how many integers, $$1^n=n^1$$ Let''s try out some random values. For n = -1 $$1^{(-1)}=(-1)^1$$ $$\frac{1}{1}=-1$$ $$1\ne-1$$ For n = 0 $$1^0=(0)^1$$ $$1\ne0$$ For n = 1 $$1^1=(1)^1$$ $$1=1$$ ...”
January 7, 2018
EconomistGMATTutor posted a reply to Sara is an avid lottery player. In the certain game... in the Problem Solving forum
“Hello LUANDATO. Let''s take a look at your question. We have to find all the prime factors of each option. Option A: $$32=2^5\ \ \ -\ \ \ 48=2^4\cdot3\ \ \ -\ \ \ 52=2^2\cdot13.$$ Option B: $$33=3\cdot11\ \ \ -\ \ \ 42=2\cdot3\cdot7\ \ \ -\ \ \ 56=2^3\cdot7.$$ Option C: $$39=3\cdot13\ \ \ ...” January 7, 2018 EconomistGMATTutor posted a reply to What is the smallest positive integer that can be multiply.. in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. One easy way to solve this PS question is trying number by number. Option 1: 2*1,008 = 2016, is not a perfect square. Option 2: 3*1,008 = 3024, is not a perfect square. Option 3: 5*1,008 = 5040, is not a perfect square. ...” January 7, 2018 EconomistGMATTutor posted a reply to Points J (3, 1) and K (-1, -3) are two vertices of an... in the Problem Solving forum “Hello AAPL. Let''s take a look at your question. You are right. We have to use the formula$$d\left(P_1,P_2\right)=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}.$$We have that J=(3,1), K=(-1,-3) and L=(x,6). Then$$d\left(J,\ ...”
January 7, 2018
EconomistGMATTutor posted a reply to Sequence and Series in the Problem Solving forum
“Hello Roland2rule. Let''s take a look at your question. First of all, there is a mistake. B is NOT the correct answer. Let''s see which one is the correct option. We have 4 men with different heights. We can set the following sequence with the height of each man: $$m_1,\ \ m_1+2\ ,\ \ m_1\ ...” January 5, 2018 EconomistGMATTutor posted a reply to If the radius of the circle circumscribing a triangle is... in the Problem Solving forum “https://s17.postimg.org/5bn2tkmyz/Sin_t_tulo.png Hello AAPL. Let''s take a look at your question. The image represents the problem. All the red lines have the same length (equal to the radius). Then, the red triangle is equilateral. Therefore, its angles have the same measure 60º. Now, ...” January 5, 2018 EconomistGMATTutor posted a reply to Geometry in the Problem Solving forum “Hello Roland2rule. Let''s take a look at your question. We know that the cylindrical tank contains 36π cubic feet of water and is filled to half its capacity, it implies that its capacity is 72π cubic feet. On the other hand, the volume of the cylindrical tank is$$V=\pi r^2h$$where r is ...” January 5, 2018 EconomistGMATTutor posted a reply to If 298=256L+N298=256L+N, where LL and NN are . . . . . . in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. If we divide both sides by 2^8 we can get$$\frac{2^{98}}{2^8}\ =\ \frac{256}{2^8}\cdot L\ +\ \frac{N}{2^8}\ \Leftrightarrow\ 2^{90}\ =\ L\ +\ \frac{N}{2^8}.$$Now, we have that L+N/(2^8) must be an interger. The only option that satisfy this ...” January 3, 2018 EconomistGMATTutor posted a reply to Bob wants to run a mile in the same time as his sister. in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. First of all, let''s convert the time to seconds. Bob''s time = 640 secs. His sister''s time = 576 secs. Now, if we improve the time of Bob by 10% we can get that the new time is: 640 - 64 = 576 secs. So, the correct answer is the ...” January 3, 2018 EconomistGMATTutor posted a reply to For positive integer values of n, the operation . . . . . in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. We have to solve 15#-14#=k#. But, we have to notice that 15# = 15 + 14#. Now, we can rewrite 15#-14#=k# as follows:$$ k\# = 15\#-14\#\ =\ 15\ +\ 14\#\ -\ 14\#\ =\ 15 .$$Therefore, the correct answer is E. I hope this explanation may ...” January 3, 2018 EconomistGMATTutor posted a reply to Which of the following MUST yield an integer when . . . . in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. The sum of five consecutive positive integers is: n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 = 5(n+2). So, it is multiple of 5. Therefore, it MUST yield an integer when divided by 5. Hence, there is no need to try the rest of the ...” January 3, 2018 EconomistGMATTutor posted a reply to What is the value of x? in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The length of the square is (2x+1), therefore the area of the bigger square is:$$\text{Area of Big Square}=\left(2x+1\right)^2 $$Area of the shaded region and areas of two smaller squares add up to the area of the bigger square. Hence, ...” January 3, 2018 EconomistGMATTutor posted a reply to A bakery sold an average (arithmetic mean) of 820... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. Let G be the number of good days and F be the number of fair days during the operating period, then Sum of Cookies during Good days + Sum of Cookies during Fair days = Sum of Cookies during the operating period ... (i) We know that, ...” January 3, 2018 EconomistGMATTutor posted a reply to If the radius of a cylinder is doubled and so... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. If radius if a cylinder is r and height is h, the volume of the cylinder is:$$V=\pi r^2h$$If the radius of the cylinder is doubled and so is the height, the volume of the cylinder can be calculated as, ...” January 3, 2018 EconomistGMATTutor posted a reply to The surface of a cylinder of radius r and height h... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. The red area is the area of two circular bases of the cylinder.$$\text{Red Area}=2\pi r^2$$The green area if equal to the curved surface of the cylinder, i.e.$$\text{Green Area}=2\pi rh$$If the red area is equal to the green area ...” January 3, 2018 EconomistGMATTutor posted a reply to Point (x, y) is a point within the triangle... in the Problem Solving forum “Hi AAPL, Lets take a look at your question. We will first find the equation of the line connecting the two points (0, 10) and (5, 0).$$Slope\ =\ \frac{0-10}{5-0}=-\frac{10}{5}=-2$$Equation of line can be written as:$$y-0=-2\left(x-5\right)y=-2x+10$$Now we will find the ...” January 3, 2018 EconomistGMATTutor posted a reply to The ‘moving walkway’ is a 300-foot long conveyor . . . in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. Time Bill takes to reach the group = Distance / Speed = 120/6 = 20 sec During these 20 seconds the group of people covered some distance at a speed of belt i.e. 3 feet per second. To calculate that distance: Distance = Speed * Time Distance = 3 * ...” January 1, 2018 EconomistGMATTutor posted a reply to Integers in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. N is a positive integer less than 200, and 14N/60 is an integer.$$\frac{14N}{60}=\frac{7N}{30}$$N must be a multiple of 30 for 7N/30 to be an integer. Also N<200, therefore, we can only consider multiples of 300 less than 200, ...” December 31, 2017 EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Let ''x'' be the total chocolates in the can. After eating half of the chocolate mini bars in a can, remaining chocolates will be:$$x-\frac{1}{2}x=\frac{1}{2}x$$Clayton gave one fourth of the remaining mini bar chocolates to his ...” December 31, 2017 EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Voilet and Veruca have a combined total of 15. Each Wonka bar cost 1. Therefore, they can get 15 wonka bars. Now, 15 Wonka bars will generate 15 wrappers. 3 wrappers can be exchanged with 1 Wonka bar. Therefore, using 15 wrappers they ...” December 31, 2017 EconomistGMATTutor posted a reply to Interest Rates in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. To find the greatest possible value in the given month, we will be using the greatest interest rate i.e. 9%. Base payment = 250$$\text{Interest on base payment}\ =\ 250\times9\%\text{Interest on base payment}\ =\ ...”
December 31, 2017
EconomistGMATTutor posted a reply to Sabrina is contemplating a job switch. She is . . . . in the Problem Solving forum
“Hi M7MBA, Let''s take a look at your question. Old job paid Sabrina annually = $85,000 New job pays$45,000 plus 15% commission of each sale. If each sale is for $15,000, then commission earned by each sale will be: $$=15000\times15\%$$ $$=15000\times\frac{15}{100}=225$$ Let Sabrina ...” December 31, 2017 EconomistGMATTutor posted a reply to A car traveled 462 miles per tankful of gasoline on the... in the Problem Solving forum “Hi swerve, Let''s take a look at your question. On Highway, using a tank full of gasoline a car traveled = 462 miles In city, using a tank full of gasoline a car traveled = 336 miles Let, On Highway, miles per gallon the car traveled = x miles, then In city, miles per gallon the car ...” December 31, 2017 EconomistGMATTutor posted a reply to If one root of the equation 2x^2 + 3x – k = 0 is 6... in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. 6 is the root of the quadratic equation 2x² + 3x - k = 0, therefore, $$2\left(6\right)^2+3\left(6\right)-k=0$$ $$2\left(36\right)+3\left(6\right)-k=0$$ $$72+18-k=0$$ $$90-k=0$$ $$k=90$$ Therefore, Option A is correct. Hope it ...” December 31, 2017 EconomistGMATTutor posted a reply to The contents of a bag of marbles consist of 9 green... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. There are 9 green and 16 blue marbles in a bag. Let the 9 green marbles are 60% of a total of ''x'' marbles. Then $$x\times60\%=9$$ $$x\times\frac{60}{100}=9$$ $$x=9\times\frac{100}{60}$$ $$x=15$$ It means that if there are a ...” December 31, 2017 EconomistGMATTutor posted a reply to Marion rented a car for$18.00 in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. Marion rented a car for $18.00 plus$0.10 per mile driven. If ''c'' represents the amount charges and ''d'' represents the miles driven, we can write: $$c=18+0.10d$$ Craig rented a car for $25.00 plus$0.05 per mile driven. We can write ...”
December 30, 2017
EconomistGMATTutor posted a reply to what is a in terms of b? in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. If we look at the bigger triangle, the top angle is a+26. Base angles are 60 and b. Since, sum of all three angles of a triangle is 180 degrees, hence, $$\left(a+26\right)+b+60=180$$ $$a+26+b+60=180$$ $$a+b+86=180$$ $$a+b=180-86$$ ...”
December 30, 2017
EconomistGMATTutor posted a reply to What is the measure of angle E? in the Problem Solving forum
“Hi swerve, Let''s take a look at your question. In triangle ABC, $$\angle BCA=180-\angle BAC-\angle ABC$$ $$\angle BCA=180-75-65$$ $$\angle BCA=40$$ Since, segment BC is parallel to the line AD, therefore, alternate interior angles are congruent. $$\angle CAD=\angle BCA$$ ...”
December 30, 2017
EconomistGMATTutor posted a reply to what is the area of quadrilateral ABOC? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. We know that the tangents are perpendicular to the radius at the point where the tangent is intersecting the circle. Therefore, triangles ABO and ACO are right triangles. In Triangle ABO, $$OB=1$$ $$OA=\sqrt{10}$$ We can find AB using ...”
December 30, 2017
EconomistGMATTutor posted a reply to what is the area of semicircle Z (in square feet)? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. Radius of the semi circle X = 6 ft Diameter of the semi circle X = 12ft Radius of the semi circle Y = 8 ft Diameter of the semi circle Y = 16 ft We can find the diameter of the semi circle Z using Pythagoras Theorem, ...”
December 30, 2017
EconomistGMATTutor posted a reply to Coordinate plane in the Problem Solving forum
“Hello Roland2rule. Let''s take a look. The equation of the parabola is $$x=2y^2+5y-17.$$ The equation of the line L is $$L:\ y-y_0=m\left(x-x_0\right)\Leftrightarrow\ \ y-y_0=3\left(x-x_0\right).$$ We just have to find a point that is on the line. In order to find it we have to solve the ...”
December 30, 2017
EconomistGMATTutor posted a reply to Percents in the Problem Solving forum
“Hello Roland2rule. Let''s take a look at your question. If Sam buys 10 pcs, without the promo discount he should pay 100$. Since he brought "at least 3" he won the first promo discount, hence he had to pay 88% of the total price. So, he should pay 88%*100$ = 88$. Now, since he ...” December 30, 2017 EconomistGMATTutor posted a reply to A computer store originally bought 1,000 modems at a total.. in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. If the store bought 1,000 modems for d dollars, it implies that the individual price is given by $$p=\frac{d}{1,000}\ \text{dollars}.$$ Since each modem was sold for 25 percent more than its original cost, then the price of each modem sold ...” December 30, 2017 EconomistGMATTutor posted a reply to What is the length of AD? in the Problem Solving forum “Hi swerve, Let''s take a look at your question. Draw a horizontal line parallel to CB, from point D that intersects the line Ab at point E, such that AED is a right triangle. Since, $$DE=CB$$ Therefore, $$DE=6$$ Now, let''s find AE. $$AE=AB-EB$$ $$AE=AB-DC$$ $$AE=12-10$$ ...” December 29, 2017 EconomistGMATTutor posted a reply to Percents in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. 7.5 litre mixture of water and sugar is 60% sugar. Amount of sugar in 7.5 litre mixture is: $$=7.5\times\frac{60}{100}$$ $$=\frac{75}{10}\times\frac{3}{5}$$ $$=\frac{15}{10}\times3$$ $$=\frac{45}{10}=4.5$$ It means, in 7.5 ...” December 29, 2017 EconomistGMATTutor posted a reply to Fraction/Ratio in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. If C denotes cats and D denotes dogs, then, $$\frac{C}{D}=\frac{5}{6}$$ $$6C=5D...(i)$$ If there are 18 fewer cats then dogs, we can write it as, $$C=D-18$$ Substitute C in eq(i), $$6\left(D-18\right)=5D$$ $$6D-108=5D$$ ...” December 29, 2017 EconomistGMATTutor posted a reply to Fraction/Ratio in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Let S denotes the spinsters and C denotes the cats, then $$\frac{S}{C}=\frac{2}{7}$$ $$7S=2C ... (i)$$ If there are 25 more cats then spinsters, we can write it as, $$C=S+25$$ Substitute C in eq(i), we get, ...” December 29, 2017 EconomistGMATTutor posted a reply to If x is positive, which of the following in the Problem Solving forum “Hello Vjesus12. First of all, I want to comment that the third option is not displayed. The third option is: $$(III)\ \ \ 2x<x^2<\frac{1}{x}$$ Let''s try with x=1/2. Then $$\frac{1}{x}=\frac{1}{\frac{1}{2}}=2\ \ \ \ \ \ \ \ \ 2x=2\cdot\frac{1}{2}=1\ \ \ \ \ \ \ \ \ \ ...” December 28, 2017 EconomistGMATTutor posted a reply to What is the average of 1/2, 2/5 and 3/10? in the Problem Solving forum “Hello Vjesus12. Let''s see your question. We can rewrite this numbers to get an easy way to find the average. We can rewrite and reorder the numbers as follows:$$\frac{3}{10}\ \ \ ,\ \ \ \ \ \frac{2}{5}=\frac{4}{10}\ \ \ ,\ \ \ \ \frac{1}{2}=\frac{5}{10}\ .$$Therefore, the average is given ...” December 28, 2017 EconomistGMATTutor posted a reply to G(x) is the greatest integer less in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. Let''s suppose that x=5.2. Then$$G\left(x\right)=G\left(5.2\right)=5\ ;\ \ and\ \ \ \ L\left(x\right)=L\left(5.2\right)=6.$$Therefore,$$L\left(x\right)-G\left(x\right)=1.$$This situation happens every time that x is not an integer. ...” December 28, 2017 EconomistGMATTutor posted a reply to What is the smallest positive integer in the Problem Solving forum “Hello Vjesus12. Let''s see your question. You could try number by number or solve it as follows:$$\sqrt{n\cdot7!}=\sqrt{n\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}=2\sqrt{n\cdot7\cdot(3\cdot2)\cdot5\cdot3\cdot2}$$...” December 28, 2017 EconomistGMATTutor posted a reply to A man in a car observes that he can count 41 electric poles in the Problem Solving forum “Hello ardz24. Let''s see your question. The man saw 41 electric poles and each consecutive electric pole is known to be 50 meter apart, it implies that the man droves for$$d=41\cdot50=2050\ meters.$$On the other hand, the man droves during 2 minutes. Now using the formula$$d=v\cdot t\ ...” December 26, 2017 EconomistGMATTutor posted a reply to If b=a+4, then for which of the following . . . in the Problem Solving forum “Hello M7MBA. Let''s take a look at your question. If b=a+4 then $$\left(x-a\right)^2+\left(x-b\right)^2=\left(x-a\right)^2+\left(\left(x-a\right)-4\right)^2=\left(x-a\right)^2+\left(x-a\right)^2-8\left(x-a\right)+16$$ ...” December 25, 2017 EconomistGMATTutor posted a reply to The variables a and b are non-zero integers... in the Problem Solving forum “Hello LUANDATO. Let''s see your question. We have that $$a=\frac{2b^3}{c},\ \ \ \text{then}\ \ c=\frac{2b^3}{a}.$$ Now, if we write "a/2" instead of "a" and "2b" instead of "b", we will get: ...” December 25, 2017 EconomistGMATTutor posted a reply to Two members of a certain club are selected to speak... in the Problem Solving forum “Hello AAPL. Your answer is very well. Another way you could try it is: we have to choose 2 people (the order doesn''t matter), we have two places: _____ _____. For the first place we have n options and for the second place we have n-1 options. So, we have n*(n-1) options. But, we have ...” December 23, 2017 EconomistGMATTutor posted a reply to In triangle PQR, QS and SR are angle bisectors... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. As QS and RS are bisectors, we can say that PQS=SQR=x and PRS=SRQ=y. Now, we can set the following equation: $$80º+x+x+y+y=180º\ \Leftrightarrow\ \ 2x+2y=100º=x+y=50º.$$ Now, if we look at the triangle QSR we can see that ...” December 23, 2017 EconomistGMATTutor posted a reply to In the figure, KLMN is a square and angle KJN=45°... in the Problem Solving forum “Hello AAPL. Let''s take a look at your question. We have a right triangle JKN, with hypotenuse 6 and angle KJN=45º. We have then $$\sin\left(45º\right)=\frac{KN}{6}\ \Leftrightarrow\ \ KN=\frac{6\sqrt{2}}{2}=3\sqrt{2}$$ and $$\cos\left(45º\right)=\frac{JN}{6}\ \Leftrightarrow\ \ ...” December 23, 2017 EconomistGMATTutor posted a reply to If b < e < y+k and b-1 < w < k, then which of th in the Problem Solving forum “Hello Vjsesus12. Let''s take a look at your question. We have the following inequality:$$b<e<y+k\ \ and\ \ b-1<w<k\ .$$Adding both inequalities we will get$$2b-1<e+w<y+2k.$$Hence, I is true.. Now we cannot subtract the inequalities, so II is not true. Let''s ...” December 23, 2017 EconomistGMATTutor posted a reply to A company accountant estimates in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. Train fares for business trips this year = 7,500 10% increase in train fares business trips next year = 7,500 * 10% = 7500 * 0.1 = 750 Total Train fares for business trips next year = 7,500 + 750 = 8,250 Air fares for business trips ...” December 21, 2017 EconomistGMATTutor posted a reply to What is the area of the triangle? in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. Since the given triangle is an isosceles triangle, therefore, two of the sides of the triangle are congruent. We can see that the base angles are the same i.e. y degrees, hence sides opposite to these two angles will be the same in length. ...” December 21, 2017 EconomistGMATTutor posted a reply to In the rectangular coordinate system above... in the Problem Solving forum “Hello LUANDATO. You have to calculate each area. You''re right about what you''re thinking. The triangle P.$$Base=4,\ Height=1\ \ \ then\ \ \ Area=\frac{4\cdot1}{2}=2.$$The rectangle Q.$$Length\ =1,\ Width=2\ \ \ then\ \ \ Area=1\cdot2=2.$$The scuare R. The side is the hypotenuse of ...” December 21, 2017 EconomistGMATTutor posted a reply to A bullet train leaves Kyoto for in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. After the first 10 minutes, the bullet train will have traveled$$240\cdot\left(\frac{10}{60}\right)\ =\ 40\ \ \ miles.$$Therefore, at 12:10, the distance between the bullet train and the other train is 300 - 40 = 260 miles. The combined ...” December 21, 2017 EconomistGMATTutor posted a reply to If n is the product of the integers from 1 to 8... in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. n is the product of the integers from 1 to 8, inclusive.$$n=1\times2\times3\times4\times5\times6\times7\times8n=1\times2\times3\times\left(2\times2\right)\times5\times\left(2\times3\right)\times7\times\left(2\times2\times2\right)$$...” December 19, 2017 EconomistGMATTutor posted a reply to A merchant prices a television at 60 percent above . . . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Let the wholesale price of the television be ''x", then,$$\text{Price of television with 60% increase}=x+60\%x=x+0.6x=1.6x$$At Presidents’ Day sale, the television is marked down by 20%. Let''s first calculate the discount offered ...” December 19, 2017 EconomistGMATTutor posted a reply to The average of 25 values is equal to product. . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Out of 25 values, one is 0. Hence, Product of all 25 values = 0 Since average and product of these 25 values are equal. Therefore, Average of 25 values = 0 For average to be equal to zero, the sum of 25 values should be equal to zero. ...” December 19, 2017 EconomistGMATTutor posted a reply to A company accountant estimates . . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question.$$\text{Total train fares for business trips}\ =\ 7,500\text{Total air fares for business trips}\ =\ 11,200\text{10% increase in train fares}\ =\ 7,500\times\frac{10}{100}=750\text{Total train fares for business trips ...” December 19, 2017 EconomistGMATTutor posted a reply to A certain auto manufacturer sold 3% fewer vehicles in 2007.. in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. The manufactured sold 3% fewer vehicles in 2007 than in 2006, and he sold 2,100,000 million in 2016. So, in 2007 he sold 97%*2,100,000 vehicles, that is to say, $$\frac{97}{100}\cdot2,100,000\ =\ 97\cdot21,000\ =\ 2,037,000\ vehicles.$$ ...” December 19, 2017 EconomistGMATTutor posted a reply to If a town of 25,000 people is growing in the Problem Solving forum “Hello lheiannie07. Let''s take a look at your question. The population at the beginning is 25,000. After 1 year the population would be equal to 25,000*0.01+25,000 = 25,000*1.01= 25,250. After 2 years the population would be equal to 25,250*0.01 + 25,250 = 25,250*1.01 = 25,502.5. ...” December 19, 2017 EconomistGMATTutor posted a reply to After taking N tests, each containing 100 questions, John... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. The first time John got 70% correct answers, that is to say, $$100\cdot N\cdot70\%\ =\ 100\cdot N\cdot\frac{70}{100}=70\cdot N\ correct\ answers.$$ Now, by the other hand, ...” December 19, 2017 EconomistGMATTutor posted a reply to ABCD is a quadrilateral, with AB parallel to CD... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. First of all, the area of ABCD is $$\frac{\left(AB+CD\right)\cdot AE}{2}=\frac{\left(4+CD\right)\cdot5}{2}=\frac{\left(4+2\cdot DE\right)\cdot5}{2}.$$ So we just need to find the value of DE. We know that the area of the right triangle ...” December 19, 2017 EconomistGMATTutor posted a reply to Jim can assemble b crates in an hour and Robert in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. $$\text{Jim''s rate }\ =\ \frac{b}{1}=b$$ $$\text{Robert''s rate}\ =\ \frac{2b}{1}=2b$$ $$\text{Jim and Robert''s combined rate}\ = b+2b=3b$$ Working together number of crates they assemble in 1 hour = 3b Working together number of ...” December 17, 2017 EconomistGMATTutor posted a reply to Given a spinner with four sections of equal size labeled in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. Probability of Not Getting an A after spinning the spinner two times can be calculated as: $$P\left(\text{Not getting an A}\right)\times P\left(\text{Not getting an A}\right)$$ $$=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$$ Therefore, ...” December 17, 2017 EconomistGMATTutor posted a reply to The monthly rainfall for the first eight months of 2008. . . in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. The monthly rainfall for the first eight months of 2008 in inches was 2, 4, 4, 5, 7, 9, 10, 11. $$Mean=\frac{\text{Sum of Quantities}}{\text{Number of Quantities}}$$ $$Mean=\frac{2+4+4+5+7+9+10+11}{8}$$ $$Mean=\frac{52}{8}=6.5$$ The data ...” December 17, 2017 EconomistGMATTutor posted a reply to The average (arithmetic mean) of 6 numbers is 8.5. in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. The average (arithmetic mean) of 6 numbers is 8.5. We know that, $$Average\ =\ \frac{\text{Sum of Quantities}}{\text{Number of Quantities}}$$ $$8.5=\ \frac{\text{Sum of 6 numbers}}{6}$$ $$\text{Sum of 6 numbers}=6\times8.5$$ $$\text{Sum ...” December 17, 2017 EconomistGMATTutor posted a reply to Speed and Distance. in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. There are some mistakes in the question. The first one is that 1 mile = 1,760 yards not 1,160 and the options are listed incorrectly as well. Let''s solve the problem using 1 mile = 1,760 yards The car is traveling at a constant rate ...” December 17, 2017 EconomistGMATTutor posted a reply to Algebra in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. If 4 is divided into the positive integer x, it leaves a remainder of 3. If p represents the quotient, then,$$4p+3=x...(i)$$If 9 is divided into x, it leaves a remainder of 4. If q represents the quotient, then,$$9q+4=x...(ii)$$...” December 17, 2017 EconomistGMATTutor posted a reply to The figure attached shows the dimensions of a semicircular.. in the Problem Solving forum “Hello LUANDATO. Let''s take a look at this image. https://s7.postimg.org/cbbgkkjqv/untitled.png The red line represents the way for the vehicles inside the tunnel. And we have a right triangle whose green cathetus represents the greatest height of the vehicles that can use the tunnel. It is ...” December 17, 2017 EconomistGMATTutor posted a reply to James and Henry are at the northwest corner of their... in the Problem Solving forum “Hello LUANDATO. What you said is correct. James walked$$\sqrt{\left(300\right)^2+\left(160\right)^2}=340\ ft.$$Henry walked 180 ft down and then walked in a straight line directly to the southeast corner. We have a right triangle with cathetus a=300-180=120 and b=160. So, the length of the ...” December 17, 2017 EconomistGMATTutor posted a reply to In a certain state, gasoline stations compute the price.... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. It tells us that the price "p" is computed adding the 4% of the price per gallon "d" and then adding 0.18. That is to say,$$p=d+d\cdot4\%\ +0.18\ \leftrightarrow\ \ \ p-0.18=d\left(1+0.04\right)\ \leftrightarrow\ \ ...” December 17, 2017 EconomistGMATTutor posted a reply to Richard receives an increment in his salary.... in the Problem Solving forum “Hi Luandato, Let''s take a look at your question. Let ''x'' be the total family income then, Before the increment Richard''s salary = (20%)(x) = 0.2 x After increment Richard''s salary = (30%)(x) = 0.3 x The percentage points of the salary of Richard as a percentage of his family''s total ...” December 17, 2017 EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum “Hello Roland2rule. Let''s see your question. We have that $$2\cdot n+5\cdot m=50.$$ The possible options are: $$\left(1\right)\ \ \ \ n=0\ and\ m=10.\ Then\ \left|m-n\right|=10.\$$ $$\left(2\right)\ \ \ \ n=5\ and\ m=8.\ Then\ \left|m-n\right|=3.\$$ $$\left(3\right)\ \ \ \ n=10\ and\ ...” December 17, 2017 EconomistGMATTutor posted a reply to Increasing the original price in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. If the original price of the item is ''100''. 15% increase means:$$=\left(15\%\right)100=\left(\frac{15}{100}\right)100=15$$Total price of the item after 15% increase is:$$=100+15=115$$15% increase in the new price: ...” December 17, 2017 EconomistGMATTutor posted a reply to Permutations and Combination in the Problem Solving forum “Hello Roland2rule. Let''s see your question. We have to arrange 4 woman and 4 men. We have 8 places: _ _ _ _ _ _ _ _. The possible arrangements are MWMWMWMW or WMWMWMWM. The total possibles options are: 1) for MWMWMWMW = 4*4*3*3*2*2*1*1 = 4!*4! = 576. 2) for WMWMWMWM = ...” December 15, 2017 EconomistGMATTutor posted a reply to In the sequence 1, 2, 4, 8, 16, 32, …, in the Problem Solving forum “Hello VJesus12. Let''s take a look at your question. We can rewrite the sequence as follows:$$2^0\ \ ,\ \ \ 2^1\ ,\ \ 2^2\ ,\ 2^3\ ,\ \ 2^4\ ,\ \ \ 2^5\ ,\ \ \ 2^6\ ,\ \dots$$This is equivalent to say that the nth term is$$a_n=2^{n-1}.$$So, we have that$$a_{16}=2^{15},\ \ ...” December 15, 2017 EconomistGMATTutor posted a reply to Bruno and Sacha are running in the same in the Problem Solving forum “Hello Vjesus12. This is a nice question, and it is easier than you think. We have the following: Sacha runs at a constant speed of 6 meters per second Bruno runs at a constant speed of 5 meters per second So, the difference between them is 1 meter per second. If Sacha had to stop 1 ...” December 15, 2017 EconomistGMATTutor posted a reply to Speed and Distance. in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. To find the maximum distance covered by the cyclist, we will use the maximum speed. Speed = 14.0 miles per hour Time = 7 hours Distance = Speed * Time Distance = 14 * 7 = 98 miles. Therefore, Option D is correct. Hope it helps. I ...” December 14, 2017 EconomistGMATTutor posted a reply to Integers in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. Payment for the first book =$21.95 Payment for each additional book after the purchase of first book = $12.99 If the customer purchases 4 books, he will pay$21.95 for the first book and $12.99 for the remaining 3 books. So the total ...” December 14, 2017 EconomistGMATTutor posted a reply to Work/Rate in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. If printer B takes ''x'' minutes to print 40 pages, then printer A will take ''x+4'' minutes to print 40 pages. $$\text{Rate of Printer A}=\frac{40}{x+4}$$ $$\text{Rate of Printer B}=\frac{40}{x}$$ $$\text{Combined Rate of Printer A ...” December 14, 2017 EconomistGMATTutor posted a reply to In a rectangular coordinate syste, what is the are of a... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. The co-ordinates of the rectangle are given as (-4, 1), (1, 1), (1, -3) and (-4, -3) If we take the first two coordinates (-4, 1), (1, 1), We can see that their y coordinate the the same it means that these two points will form a horizontal line, ...” December 13, 2017 EconomistGMATTutor posted a reply to A cylinder is placed inside a cube in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. Volume of the cube = 16 If x represents the side length of the cube then,$$x^3=16x=\sqrtD is correct. Hope it helps. I am available if you''d like any follow up.” December 13, 2017 EconomistGMATTutor posted a reply to In the rectangular coordinate (OG16) in the Problem Solving forum “Hi boomgoesthegmat, Let''s take a look at your question. The coordinates of P are (4, 0), therefore, $$OP=4$$ Area of triangle ORP = 12 We know that: Area of a triangle = (1/2) * (Base) * (Height) $$Area=\frac{1}{2}\cdot OQ\cdot OP$$ $$12=\frac{1}{2}\cdot OQ\cdot4$$ ...” December 13, 2017 EconomistGMATTutor posted a reply to When integer a is divided by 4 . . . in the Problem Solving forum “Hello. Let''s take a careful look at your question. When "a" is divided by 4 the remainder is "2". Possible values for "a": 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, . . . . When "b" is divided by 5 the remainder is "1". Possible values ...” December 12, 2017 EconomistGMATTutor posted a reply to What is the largest possible value of. . . in the Problem Solving forum “Hello Vincen. We have to rewrite the expression to know the possible largest value. $$(x+2)(3-x)(x-3)(2x+4)(2+x)^2\ =\ -2\left(x+2\right)\left(x-3\right)\left(x-3\right)\left(x+2\right)\left(x+2\right)^2$$ That implies that the original expression is equal to ...” December 12, 2017 EconomistGMATTutor posted a reply to A manager must select 2 people from a in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. We have to pick 2 people from a 4 people group. And the order matter. We have 2 places: _____ _____. For the first place we have 4 options and for the second place, we have 3 options. So, there are 4*3=12 different ways to pick the 2 ...” December 12, 2017 EconomistGMATTutor posted a reply to Which of the following is NOT a factor of 20! ? in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. Option 1) 29. This is a prime number and it does not appear in 20! So, this is not be a factor. Option 2) 85. 85=5*17, and 5 and 17 are in 20! So, 85 is a factor. Option 3) 121. 121=11*11, but in 20! there is only ...” December 12, 2017 EconomistGMATTutor posted a reply to What is the value of x in the figure above? in the Problem Solving forum “Hello AAPL. Let''s take a look at your question. For the Inscribed angle theorem, we have that m(EOB)=2*m(EAB)=2*90º=180º. Now, the triangle EAB is equilateral and it has a right angle, so the m(AEB)=m(EBA)=45º. If we consider the line AO, then m(EOA)=m(BOA)=90º. So, xº=90+yº, ...” December 10, 2017 EconomistGMATTutor posted a reply to How many different ways are there to arrange . . . in the Problem Solving forum “Hello M7MBA. We have to arrange 3 adults and 4 children in 7 seats in the following form: A C A C C C A. For the first place, we have 3 options. For the second place, we have 4 options. For the third place, we have 2 options. For the fourth place, we have 3 options. For the fifth place, we ...” December 10, 2017 EconomistGMATTutor posted a reply to Before the regime change, the National Museum regularly... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. Let''s suppose that the museum had 105 artifacts. So, before of the regime change, the museum showed 105/3 = 35 artifacts, and the other 70 artifacts where kept in storage. It says that between 1/7 and 1/5 of the artifacts disappeared, ...” December 10, 2017 EconomistGMATTutor posted a reply to If 2 roots of an equation x^2-3x-3=0 are m and n, what is... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. $$x^2-3x-3=0$$ For a quadratic equation, we know that, Sum of the roots = -b= -(-3) = 3 Product of the roots = c = -3 If roots of the given quadratic equation are m and n, then: $$m+n=3$$ $$mn=-3$$ Using the polynomial identity: ...” December 8, 2017 EconomistGMATTutor posted a reply to If all the faces of pyramid P (including the base) in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. All the faces of pyramid P (including the base) are equilateral triangles of side 2, we need to find the surface area of the pyramid. For that purpose, we will first find the area of one face of the pyramid. Each face is equilateral triangle ...” December 8, 2017 EconomistGMATTutor posted a reply to If all the faces of pyramid P (including the base) in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. If we have a equilateral triangle of side 2, then we can build a right triangle with one cathetus equal to 1, and the hypotenuse equal to 2. Then, using the Pythagoras we have that the other cathetus (the height) is equal to ...” December 8, 2017 EconomistGMATTutor posted a reply to If x^2 + xy - 32 = 0, and x and y are integers, then y . . . in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. If $$x^2+xy-32=0$$ then we could rewrite this as follows: $$x^2+xy-32=0\ \leftrightarrow\ \left(x-a\right)\left(x-b\right)=0$$ where "a" and "b" satisfy $$a+b=y\ \ \ \ \ and\ \ \ \ \ \ a\cdot b=-32.$$ The possible ...” December 8, 2017 EconomistGMATTutor posted a reply to What is the x-intercept of line l? in the Problem Solving forum “Hello swerve. Let''s take a look at your question. The area of the triangle is $$A=\frac{AO\cdot OB}{2}.$$ By the other hand, the y-intercept of line l is 5, it implies that $$OA=5\ and\ OB=x.$$ Replacing this on the area we will get: $$A=\frac{5\cdot x}{2}=30\ \leftrightarrow\ 5x=60\ ...” December 8, 2017 EconomistGMATTutor posted a reply to A cylindrical cup is used to fill a bowl in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question. Volume of cylindrical cup:$$V_{cy}\ =\ \pi\cdot r^2\cdot h.$$Volume of a hemisphere (bowl):$$V_{he}=\frac{2}{3}\cdot\pi\cdot R^3.$$We have$$r=\frac{R}{2}\ \ \ \ and\ \ \ \ h=2\cdot r\ \leftrightarrow\ \ h=R.$$Number of cups ...” December 8, 2017 EconomistGMATTutor posted a reply to If the number of cars in city X this year is 520,800... in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Let the number of cards in city X last year be ''N'', then the number of cars in city X is 24% more than x. This can be represented as:$$N+\ \left(24\%\right)N=520,800N+\ \left(\frac{24}{100}\right)N=520,800N+\ 0.24N=520,800$$...” December 6, 2017 EconomistGMATTutor posted a reply to Given that 1 + 3x > 4 and 2x - 3 < 5, all values of x in the Problem Solving forum “Hi AAPL, Let''s take a look at your question.$$1+3x>43x>4-13x>3x>\frac{3}{3}x>1 ... (i)$$The next inequality is:$$2x-3<52x<5+32x<8x<\frac{8}{2}x<4... (ii)$$Combining (i) and (ii), we ...” December 6, 2017 EconomistGMATTutor posted a reply to A student took five papers in an examination, where the... in the Problem Solving forum “Hi LUANDATO, Lets take a look at your question. The marks of a student in five papers are in the proportion:$$6:7:8:9:10$$Sum of the proportions = 6 + 7 + 8 + 9 + 10 = 40 In all papers together, the candidate obtain 60% of the total marks. Let the total marks be x, then, ...” December 6, 2017 EconomistGMATTutor posted a reply to If x-y+z=-1, -x+y+z=1, and x+y-z=-1, then x+y+z=? in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question.$$x-y+z=-1 ... (i)-x+y+z=1... (ii)x+y-z=-1 ... (iii)x+y+z=?$$Adding equations (i), (ii) and (iii),$$\left(x-y+z\right)+\left(-x+y+z\right)+\left(x+y-z\right)=-1+1-1x-y+z-x+y+z+x+y-z=0-1$$...” December 6, 2017 EconomistGMATTutor posted a reply to Alex deposited x dollars into a new account in the Problem Solving forum “Hi rsarashi, Let''s take a look at your question. Amount Alex deposited in account = x dollars Annual interest earned after one year = (8%) x = 0.08x Total amount in account after one year = (x + 0.08x) = 1.08x After one year, Alex deposited additional x dollars. Total amount after ...” December 6, 2017 EconomistGMATTutor posted a reply to Let P = (x + y)k. If P = 10 and k = 3 in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question.$$P\ =\left(x+y\right)k10\ =\left(x+y\right)3x+y=\frac{10}{3} ... (i)$$We know that average of x and y can be calculated as,$$Average\ =\ \frac{x+y}{2}$$Plugin the value of x+y from eq(i), we get:$$Average\ =\ ...” December 6, 2017 EconomistGMATTutor posted a reply to A cube has a volume of 72. If it is divided into 8 equal cub in the Problem Solving forum “Hi ardz24, Let''s take a look at your question. Volume of original cube = 72 Original cube is divided into 8 equal cubes, therefore, volume of each of the new cube will be: $$=\frac{72}{8}=9$$ Let, edge length of original cube be ''x'' and edge length of each of the new cubes is ''y'', ...” December 6, 2017 EconomistGMATTutor posted a reply to If x >= 0 and x=root(8xy-16y^2), then, in terms of y, x=? in the Problem Solving forum “Hello AAPL. Let''s take a look here. Your first approach is correct. From $$x=\sqrt{8xy-16y^2}$$ we get $$x^2-8xy+16y^2=0.$$ Now, using the quadratic formula we get ...” December 5, 2017 EconomistGMATTutor posted a reply to There are three blue marbles, three red marbles .... in the Problem Solving forum “Hello Vincen. Let''s see what are the formulas here. We have to pick 1 yellow marble from 3 yellow marbles among 9 total marbles. 3/9=1/3. Now, we have to pick another yellow marble from 2 yellow marbles among 8 total marbles. 2/8=1/4. Finally, we have to pick another yellow marble from ...” December 5, 2017 EconomistGMATTutor posted a reply to In the sequence S, the difference between . . . in the Problem Solving forum “Hello Vincen. We have that the difference between any two consecutive terms is equal, that is to say, $$S=a,\ \ a+d,\ \ a+2d,\ \ a+3d,\ \ a+4d,\ \ a+5d,\ \ a+6d\ .\ .\ .\ .$$ Also we have that the sum of the fourth term and the fifth term of the sequence is equal to the seventh term, that is to ...” December 5, 2017 EconomistGMATTutor posted a reply to [x] is the greatest integer less than or equal to the in the Problem Solving forum “Hello Vincen. Let''s see. According to the definition of C. I hope this may help you. Feel free to ask me again if you have a doubt. Regards.” December 5, 2017 EconomistGMATTutor posted a reply to Three machines operating independently, simultaneously, in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. 3 machines ------ 36 hours 4 machines ------- x hours Then x=3*36/4 = 27 hours. But the question says "in how many fewer hours..." Now, if 3 machines spend 36 hours and 4 machines spend 27 hours to do the work, then the work ...” December 5, 2017 EconomistGMATTutor posted a reply to \frac{p+5+p^3\left(-p-5\right)}{-p-5}= in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. $$\frac{p+5+p^3\left(-p-5\right)}{-p-5}$$ Factoring out negative sign from the binomial (-p-5) in the numerator as well as in the denominator. $$=\frac{p+5-p^3\left(p+5\right)}{-\left(p+5\right)}$$ ...” December 2, 2017 EconomistGMATTutor posted a reply to If the sum of the annual salaries of n persons is$x and . . in the Problem Solving forum
“Hi M7MBA, Let''s take a look at your question. The sum of the annual salaries of n persons is $x, so the average annual salary of a person is $$=\frac{x}{n} ... (i)$$ Monthly salary of a person =$y Annual salary of a person = 12y ... (ii) Equation (i) and (ii), both are representing ...”
December 2, 2017
EconomistGMATTutor posted a reply to If 9^y + 3^b=10*3^b, then 2y=? in the Problem Solving forum
“Hi LUANDATO, Lets take a look at your question. $$9^y+3^b=10\times3^b$$ $$\left(3^2\right)^y+3^b=10\times3^b$$ $$\left(3^2\right)^y=10\times3^b-3^b$$ $$3^{2y}=10\times3^b-3^b$$ $$3^{2y}=3^b\left(10-1\right)$$ $$3^{2y}=3^b\left(9\right)$$ $$3^{2y}=3^b\left(3^2\right)$$ ...”
December 2, 2017
EconomistGMATTutor posted a reply to A right cylinder and a cube have the same surface area... in the Problem Solving forum
“Hello AAPL. Let''s see. The surface area of the cylinder is: $$A_{cy}=2\pi\cdot r^2+2\pi\cdot r\cdot h$$ and the surface area of the cube is: $$A_{cu}=6L^2.$$ As the height of the cylinder is equal to its diameter, then $$h=2r,\ so\ A_{cy}=2\pi r^2+2\pi\cdot r\cdot2r=2\pi r^2+4\pi ...” December 2, 2017 EconomistGMATTutor posted a reply to Find the perimeter of the triangle. in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. As CD is perpendicular to AB then AD=DB. Let''s name this lenght as "y". So, the right triangles ADC and BDC has two sides of the same lenght, so BC=AC=5. By the other hand, CO=r=25/8. Let''s name OD as "x". We ...” December 2, 2017 EconomistGMATTutor posted a reply to Of the students at a certain high school, 90 . . . in the Problem Solving forum “Hello Vjesus12. Let''s suppose that there are 100 students. So, we have the following equations: A or G = 90. A and G = 15. A= 2G A without G= ? Now, A or G = A + G - (A and G) 90 = 2G + G - 15 105 = 3G G = 35. A= 70. A without G = A - (A and G) = 70 - 15 = 55. So, the ...” November 30, 2017 EconomistGMATTutor posted a reply to What is the area of shaded region in the figure shown? in the Problem Solving forum “Hello Vjesus12. You have to calculate the slope of the line:$$m=\frac{y_1-y_0}{x_1-x_0}=\frac{1-0}{0-\frac{-8}{3}}=\frac{1}{\frac{8}{3}}=\frac{3}{8}.$$Now, the equation of the line is$$y=mx+b=\frac{3}{8}x+1.$$Finaly, we replace y=4 in the equation of the line:$$4=\frac{3}{8}x+1\ \ ...”
November 30, 2017
EconomistGMATTutor posted a reply to Eight dogs are in a pen when the owner comes... in the Problem Solving forum
“Hello swerve. Let''s take a look at your question. We have to notice that the order is important. So, we are talking about a permutation. The first dog can be chosen from 8 ---------- 8 options. The second dog can be chosen from 7 -------7 options. The third dog can be chosen from 6 ...”
November 30, 2017
EconomistGMATTutor posted a reply to If ax+by=17, 2ax+3by=43, and 3x=2y, in the Problem Solving forum
“Hello Vincen. I will try to explain to you this question in an easy way. $$If\ \ \ ax+by=17\ \rightarrow\ -2ax-2by=-34.$$ Adding this equation to the second given equation we will get $$by=9.$$ Now, replacing this on the first given equation we get $$ax+by=17\ \leftrightarrow\ ax+9=17\ ...” November 28, 2017 EconomistGMATTutor posted a reply to Which of the following is equal to 2^k*5^(k-1)? in the Problem Solving forum “Hello Vincen. Let''s rewrite the expression as follows$$2^k\cdot5^{k-1}=2\cdot2^{k-1}\cdot5^{k-1}=2\cdot\left(2\cdot5\right)^{k-1}=2\cdot10^{k-1}.$$This tell us that the correct answer is A. I hope this can help you to clarify your doubt. I''m available if you''d like a follow up. ...” November 28, 2017 EconomistGMATTutor posted a reply to A bookseller sells his books at a 20% markup in price... in the Problem Solving forum “Hello swerve. Let''s see your question. The bookseller add the 20% to the price he paid for the book. So, if x is the cost price then$$120\%\cdot x\ =\ 12\ dollars,$$it implies that$$120\%\cdot x=\frac{120}{100}\cdot x=\frac{6}{5}\cdot x=12\ dollars\ \leftrightarrow\ ...”
November 28, 2017
EconomistGMATTutor posted a reply to A rectangular with dimensions 24 inches by 42 inches . . . in the Problem Solving forum
“Hello Vincen. Let''s take a look at your question. We need to divide the rectangle in many squares of equal size. The dimensions are 24 by 42 inches. We just need to calculate the greatest common factor of 24 and 42. So $$24=2^3\cdot3\ and\ 42=2\cdot3\cdot7.$$ Then ...”
November 28, 2017
EconomistGMATTutor posted a reply to Authors writing detective stories in the Critical Reasoning forum
“This question asks you to draw a conclusion from the given evidence. The correct choice MUST be true. Choice A: This choice states that there is only one way to construct a "well-written detective story." This cannot be concluded from the argument. Choice B: This one might tempt ...”
November 28, 2017
EconomistGMATTutor posted a reply to Which of the following equivalent to (1/8)^4? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. We will first write the given expression in its simplest form. $$\left(\frac{1}{8}\right)^{^4}=\left(\frac{1}{2\times2\times2}\right)^{^4}$$ $$=\left(\frac{1}{2^3}\right)^{^4}=\left(\frac{1}{2}\right)^{^{12}}$$ Now we will check which of ...”
November 28, 2017
EconomistGMATTutor posted a reply to If the area of a number in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. In the first step we will write as a product of its prime factors. $$100=2\times2\times5\times5$$ Largest prime factor = 5 Smallest prime factor = 2 As defined in the question statement: Area = Largest prime factor - smallest prime ...”
November 28, 2017
EconomistGMATTutor posted a reply to GMATPREP6 - As a trophy property, the price offered for the in the Sentence Correction forum
“Hello! Thank you for your question. I think that richachampion is partly correct - this is an issue of using parallel structure (more about...than about...). There is also an issue with where the modifying phrase "as a trophy property" should go. So let''s break down each answer, and ...”
November 28, 2017
EconomistGMATTutor posted a reply to Sentence Correction in the Sentence Correction forum
“Hello! Thank you for your question. Since you asked mainly about the differences between answers C and D, let''s stick to just those. We know the other three options are wrong because they use phrases like "with such rapidity" and "in such rapidity," which are both over wordy ...”
November 28, 2017
EconomistGMATTutor posted a reply to Sentence Correction in the Sentence Correction forum
“Hello! Thank you for your question. For this example, we''re dealing with a non-essential phrase that I will put in bold for you: For people who have never worked for a living, any job may instill a valuable sense of self-worth and open doors to better jobs in the future. A non-essential ...”
November 28, 2017
EconomistGMATTutor posted a reply to Environmentalists report in the Sentence Correction forum
“Hello! Thank you for your question! Let''s break down each answer, and determine what is right/wrong about each one: Environmentalists report that much of the increase in levels of dangerous mercury ingested by Americans is due to high concentrations of the element in tuna and other fish. A. ...”
November 28, 2017
EconomistGMATTutor posted a reply to The average (arithmetic mean) of y numbers is x. in the Problem Solving forum
“Hi M7MBA, Let''s take a look at your question. The average (arithmetic mean) of y numbers is x, therefore, if the sum of y numbers is Y then it can be represented as: $$\frac{Y}{y}=x$$ $$Y=xy ... (i)$$ If z is added to the numbers, the new average (arithmetic mean) will be z-5, ...”
November 27, 2017
EconomistGMATTutor posted a reply to what is the ratio of the area of the rectangle... in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. In the rectangle ABCD, if AD = 1 then AB = 3 Area of rectangle = Length * Width Area of rectangle = 3 * 1 = 3 Area of circle ca be calculated using formula $$\pi r^2$$ To find the area of circle, we need to find the radius of the circle ...”
November 27, 2017
EconomistGMATTutor posted a reply to What is the radius of the circle? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. We can see that if an altitude is drawn from the vertex A of the triangle to BC, it will represent the radius of the circle. It means to find the radius of the circle, we need to find the length of Altitude of the triangle ABC. Let the altitude ...”
November 25, 2017
EconomistGMATTutor posted a reply to A sphere has a radius of x units. If the length of... in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. We know that a volume of a sphere with radius x can be represented as: $$V=\frac{4}{3}\pi x^3$$ If the length of this radius is doubled, the radius will become 2r and the volume V1 will be: $$V_1=\frac{4}{3}\pi\left(2x\right)^3$$ ...”
November 25, 2017
EconomistGMATTutor posted a reply to Rectangle ABCD has a perimeter of 26. The half circle... in the Problem Solving forum
“Hello LUANDATO. Let''s see your question. The area of the half circle is 8π, so the complete circle would have an area of 16π. It implies that r=AD/2=4. So, AD=8. By the other hand, AB+BC+CD+DA=2AB+2AD=2AB+2*8=2AB + 16 = 26. It implies that 2AB=10, so AB=5. Now, the lenght of the ...”
November 25, 2017
EconomistGMATTutor posted a reply to If 12 cans of soda cost x dollars, then how much will... in the Problem Solving forum
“Hello swerve. We have 12 cans of soda cost x $, that is to say, $$12\cdot s=x\ dollars\ \leftrightarrow\ s=\frac{x\ }{12}dollars.$$ Now, y cans of soda will cost $$y\cdot s=y\cdot\frac{x}{12}dollars\ \leftrightarrow\ y\cdot s=\frac{xy}{12}dollars.$$ Now, we have to convert this to cents. ...” November 25, 2017 EconomistGMATTutor posted a reply to Of the 8 people having a meal... in the Problem Solving forum “Hello LUANDATO. Here, we will use the following formula: $$\left|F\ o\ B\ o\ b\right|=\left|F\right|+\left|B\right|+\left|b\right|-\left(\left|F\ y\ B\right|+\ \left|F\ y\ b\right|+\ \left|B\ y\ b\right|\right)+\left|F\ y\ B\ y\ b\right|$$ where "F" are the people having fries, ...” November 25, 2017 EconomistGMATTutor posted a reply to The graph of the equation xy = k, where k < 0, lies in... in the Problem Solving forum “Hello AAPL. Let''s see your question. As k<0, then "x" and "y" must have differents signs. The cases are: 1- x>0 and y<0, which is the quadrant IV 2- x<0 and y>0, which is the quadrant II So, the correct answer is D . I hope this explanation ...” November 25, 2017 EconomistGMATTutor posted a reply to John spent$25, which is 15 percent of his monthly wage... in the Problem Solving forum
“Hi swerve, Let''s take a look at your question. Let John''s monthly wage is ''$x''. 15 percent of John''s monthly wage is$25, it can be represented as: $$\left(x\right)\left(15\%\right)=25$$ $$\left(x\right)\left(\frac{15}{100}\right)=25$$ $$x=25\times\frac{100}{15}$$ ...”
November 25, 2017
EconomistGMATTutor posted a reply to If a/b=-2/3, then (b-a)/a=? in the Problem Solving forum
“Hi swerve, Let''s take a look at your question. We are given with: $$\frac{a}{b}=-\frac{2}{3}$$ $$a=-\frac{2b}{3}$$ We need to find the value of, $$\frac{b-a}{a}$$ Plugin the value of a in the expression. $$=\frac{b-\left(-\frac{2b}{3}\right)}{-\frac{2b}{3}}$$ ...”
November 25, 2017
EconomistGMATTutor posted a reply to If x = 3y = 4z, which of the following must equal 6x? in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$x=3y=4z$$ We need to check which of the given expressions are equivalent to 6x. Let''s evaluate them one by one. $$I. 18y$$ Let''s rewrite y in terms of x. Since, $$x\ =\ 3y$$ $$y=\frac{x}{3}$$ Replace value of y in 18y, we get, ...”
November 25, 2017
EconomistGMATTutor posted a reply to A bar of gold with dimensions 12 inches by 18 inches by 15 in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. Volume of the bar of gold can be represented as: $$=12\times18\times15inches^3$$ Write it as a product of prime factors. $$=2\times2\times3\times2\times3\times3\times3\times5\ inches^3$$ $$=2^3\times3^4\times5\ inches^3$$ ...”
November 23, 2017
EconomistGMATTutor posted a reply to What is the surface area of the solid right circular... in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. $$Radius=r=3$$ $$Height=h=10$$ We know that the surface area of right circular cylinder can be calculated using the formula: $$=2\pi r\left(r+h\right)$$ $$=2\pi\left(3\right)\left(3+10\right)$$ $$=6\pi\left(13\right)$$ $$=78\pi$$ ...”
November 23, 2017
EconomistGMATTutor posted a reply to What could be the range of a set consisting of odd multiples in the Problem Solving forum
“Hi VJesus12, Let''s take a look at your question. Range of a set is the difference between the largest value and the smallest value of that set. We are asked to find the range of a set consisting of odd multiples of 7. Odd multiples of 7 will be: $$7\times1,\ 7\times3,\ 7\times5,\ ...” November 23, 2017 EconomistGMATTutor posted a reply to There are two boxes A and B. In box A, there are 3 red . . . in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. P(Box A) = 2/6 = 1/3 P(Green marble from Box A) = 5/8 P(Box A) and P(Green marble from Box A)$$=\frac{1}{3}\times\frac{5}{8}=\frac{5}{24}$$P(Box B) = 4/6 = 2/3 P(Green marble from Box B) = 3/5 P(Box B) and P(Green marble from Box ...” November 23, 2017 EconomistGMATTutor posted a reply to A certain sequence is defined by the following rule: in the Problem Solving forum “Hi VJesus12, Lets take a look at your question. The sequence is defined by the rule:$$S_n=k(S_{n-1})$$Then$$S_2=k(S_1)S_3=k(S_2)=k(k(S_1))=k^2(S_1)S_4=k(S_3)=k(k^2(S_1))=k^3(S_1)S_5=k(S_4)=k(k^3(S_1))=k^4(S_1). . . . .. . . . .. . . . .$$...” November 23, 2017 EconomistGMATTutor posted a reply to A clown blows up a spherical balloon such that its... in the Problem Solving forum “Hello AAPL. This is an interesting question. I will try to explain how to solve it. It takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches, so the volume increases from$$V_1=\frac{4\pi\left(1\right)^3}{3}=\frac{4\pi}{3}\ \ \ to\ \ ...”
November 23, 2017
EconomistGMATTutor posted a reply to What is the perimeter of sector ABCD? in the Problem Solving forum
“Hello LUANDATO. Let''s take a look at your question. First, if the area of the circle is 144π, then r=12. Also, If we use that the length of an arc of a circumference is $$L=r\cdot\theta$$ then we got $$L(BD)=12\cdot45º=12\cdot\frac{\pi}{4}=3\pi.$$ So, the perimeter of ABCD is ...”
November 23, 2017
EconomistGMATTutor posted a reply to What is the length of minor arc AC? in the Problem Solving forum
“Hello AAPL. If the area of the circle is 36π then $$A=36\pi\ =\ 6^2\pi,$$ it implies that r=6. By the other hand, as the triangle is equilateral then its angles are equal to 60º. Using the theorem of inscribed angle we got that the central angle in the arc AC is equal to 120º. ...”
November 23, 2017
EconomistGMATTutor posted a reply to In the standard coordinate system, which of the following... in the Problem Solving forum
“Hi Swerve, Let''s take a look at your question. We are given some points and we need to find out which of the points is the greatest distance from the origin. The distance can be calculated using the distance formula as stated below: ...”
November 23, 2017
EconomistGMATTutor posted a reply to The positive integer 200 has how many factors? in the Problem Solving forum
“Hi VJesus12, Let''s take a look at your question. We are asked to find the number of factors of 200. Let''s find the number of factors of 200 step by step. Step 1: To find the number of factors of a number we first write the number as a product of its prime factors. $$200=\ 2\times100$$ ...”
November 23, 2017
EconomistGMATTutor posted a reply to According to public health officials in the Sentence Correction forum
“Hello! I think the best way to understand which answer makes the most sense is to replace the word "it" with what that word is referring to - the age of thirty. So let''s write out each answer after we make this quick change, and see what we have: A. According to public health ...”
November 22, 2017
EconomistGMATTutor posted a reply to SC... Not one in the Sentence Correction forum
“Hello! Thank you for your question. Let''s go through each answer and decide what is good/bad about each: Not one of the potential investors is expected to make an offer to buy First Interstate Bank until a merger agreement is signed that includes a provision for penalties if the deal were not ...”
November 22, 2017
EconomistGMATTutor posted a reply to fractions/ratios/decimal in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. If a big stone broke into three parts in the ratio 1:4:5. Let the weight of the broken stones be 1 unit, 4 unit and 5 unit. Then the weight of the original stone must be 1 + 4 + 5 = 10 units. Since, the value of a precious stone is ...”
November 21, 2017
EconomistGMATTutor posted a reply to If for any number N, f(N) is defined as in the Problem Solving forum
“Hi Vincen, Let''s take a look at your question. The question states: f(N) is defined as the least integer that is greater than or equal to N^2. Therefore, $$f\left(-1.1\right)\ =\ \left(-1.1\right)^2$$ $$f\left(-1.1\right)\ =\ 1.21$$ The least integer that is greater than or equal to ...”
November 21, 2017
EconomistGMATTutor posted a reply to What is the value of x in the figure? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. ABCDE is a regular pentagon. We know that we can calculate the sum of interior angles of a regular polygon using the formula: $$\left(n-2\right)\times180^o$$ Where n is the number of sides of the polygon. For a regular pentagon n = 5. ...”
November 21, 2017
EconomistGMATTutor posted a reply to Anne bought a computer for $2,000 . . . in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. The price of the computer Anne bought =$2,000 Percentage of Sales tax Anne paid = 5% Sales tax Anne paid will be: $$=\ 2,000\times\frac{5}{100}=100$$ Therefore, the total amount Anne paid = 2,000 + 100 = $2,100 The price of the computer ...” November 21, 2017 EconomistGMATTutor posted a reply to Five people, Ada, Ben, Cathy, Dan, and Eliza, are in the Problem Solving forum “Hello Vincen. Let''s take a look at your question. The only option that none of the three girls will stand next to one another is that they stand in the first, third and fifth places. So, they have 3! options to stand. And the boys has 2! options. The total of possible options is 5!. So, ...” November 21, 2017 EconomistGMATTutor posted a reply to If x>y^2>z^4, which of the following statements... in the Problem Solving forum “Hello LUANDATO. We will solve this PS question taking particular numbers. The hypothesis is $$x>y^2>z^4.$$ $$I.\ \ x>y>z$$ Let''s set x=10, y=3 and z=1. Then $$10>3^2>1^4\ and\ 10>3>1.\$$ So, option I could be true. $$II.\ \ z>y>x$$ Let''s set ...” November 21, 2017 EconomistGMATTutor posted a reply to Find the number of integers divisible by 3... in the Problem Solving forum “Hello LUANDATO. We just need to find the first and the last multiple of 3 in that range, that is to say, the value of n such that $$10\le3\cdot n\le200.$$ By inspection we can conclude that $$4\le n\le66.$$ In this range there are $$\left(66-4\right)+1=63\ integers.$$ So, there are 63 numbers ...” November 21, 2017 EconomistGMATTutor posted a reply to The area of an isoceles right triangle is... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at you question. We have an isoceles right triangle with area: $$A=\ 18x^2+6x+\frac{1}{2}=\frac{1}{2}\cdot\left(36x^2+12x+1\right)=\frac{1}{2}\cdot\left(6x+1\right)\cdot\left(6x+1\right).$$ It implies that the length of two cathetus are: 6x+1. So, the ...” November 21, 2017 EconomistGMATTutor posted a reply to The concert this weekend promises in the Sentence Correction forum “Hello! To answer your question, option D says "a number of even larger," but doesn''t say what that''s referring to. A number of even larger what? You could probably make an assumption that the writer means "people" or "audience members," but that''s asking the ...” November 20, 2017 EconomistGMATTutor posted a reply to The majority of the talk in the Sentence Correction forum “Hello! First of all, I totally understand why this one is confusing! Many people use these terms interchangeably, and they really shouldn''t! Here is a breakdown of why each answer is right or wrong: a) The majority of the talk was This one is incorrect because it misuses the word ...” November 20, 2017 EconomistGMATTutor posted a reply to If Sharon's weekly salary increased by 16 percent... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. Let Sharon''s weekly salary be ''x''. If her salary is increased by 16%, she would earn$406 per week. This can be represented as: $$x+x\left(16\%\right)=406$$ $$x+x\left(\frac{16}{100}\right)=406$$ $$x+x\left(0.16\right)=406$$ ...”
November 20, 2017
EconomistGMATTutor posted a reply to If a+b=−8, and a=20/b, what is the value of a^2+b^2? in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. $$a+b=-8$$ $$a=\frac{20}{b}$$ $$a^2+b^2=?$$ Starting from, $$a+b=-8$$ Squaring both sides, $$\left(a+b\right)^2=\left(-8\right)^2$$ Evaluating, $$a^2+b^2+2ab=64...(i)$$ We know that, $$a=\frac{20}{b}$$ Plugging value of ...”
November 20, 2017
EconomistGMATTutor posted a reply to Experimentations on animals in the Critical Reasoning forum
“Susan''s conclusion: The testing of ordinary consumer products on animals is justifiable. Susan''s evidence: Testing on animals is justifiable if it can lead to cures for human ailments. Cleanliness, convenience, and beauty are worthwhile human values deserving of support. Susan''s ...”
November 20, 2017
EconomistGMATTutor posted a reply to What is the value of in the Problem Solving forum
“Hi M7MBA, Let''s take a look at your questions. $$\left(\sqrt{7+\sqrt{29}}-\sqrt{7-\sqrt{29}}\right)^2 ... (i)$$ To evaluate it we will be using the formula: $$\left(a-b\right)^2=a^2-2ab+b^2$$ Using this formula (i) can be written as: ...”
November 19, 2017
EconomistGMATTutor posted a reply to In a recent street fair students were challenged... in the Problem Solving forum
“Hello LUANDATO. Here is the key. Let''s suppose that the length of the side of the large triangle is 3, so each side of the smalls triangles is equal to 1. https://s7.postimg.org/4pdvqqx53/Sin_t_tulo.png By the other hand, the unshaded region is a regular hexagon and it can be splited in 6 ...”
November 19, 2017
EconomistGMATTutor posted a reply to If y and x are numbers such that x + y = 17 . . . . in the Problem Solving forum
“Hello M7MBA. The fastest way to solve this PS question is adding both equations. Adding $$x+y=17\ and\ 2x-y=6$$ you will get $$3x=23,\ so\ x=\frac{23}{3}.$$ Now, we only have to divide by 2. Hence, $$\frac{x}{2}=\frac{\frac{23}{3}}{2}=\frac{23}{6}.$$ Then, the correct answer is A . ...”
November 19, 2017
EconomistGMATTutor posted a reply to Points A, B, C, D lie in this order on the circumference... in the Problem Solving forum
“https://s7.postimg.org/8qqdin56v/Sin_t_tulo.png Hello AAPL. If you look at the image and fill it with the data, you will get the correct answer. The measure of AC=160º and B bisects this arc, so AB=80º and BC=80. As BD=140º and BC=80º, then CD=60º. So, the meause of AD is ...”
November 19, 2017
EconomistGMATTutor posted a reply to Jerry has 3 flavors of ice cream in his parlor... in the Problem Solving forum
“Hi AAPL, Let''s take a look at your question. Jerry has 3 flavors of ice cream in his parlor. Let the flavors be A, B and C. Let''s find out the number of options for George to pick a one flavor ice cream. George can pick any of the three flavors A, B or C. So George has 3 options to choose ...”
November 18, 2017
EconomistGMATTutor posted a reply to ABCD is a square of perimeter 8, If E is the midpoint... in the Problem Solving forum
“Hi swerve, Let''s take a look at your question. The perimeter of square is 8, we know that Perimeter of square = 4 * Length of a side Therefore, 8 = 4 * Length of a side Length of a side = 8/4 = 2 We know that altitude is a perpendicular from a given point to a line. Since E is the ...”
November 18, 2017
EconomistGMATTutor posted a reply to If the price of coffee, p, doubles every week for 4 weeks in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. The price of the coffee is p. It doubles every week for 4 weeks, therefore, After the first week the price of coffee = 2p After the second week the price of coffee = 2(2p) = 2^2 p After the third week the price of coffee = 2(2^2 p) =2^3 p ...”
November 18, 2017
EconomistGMATTutor posted a reply to If the number of units in the circumference of a circle is t in the Problem Solving forum
“Hi ardz24, Let''s take a look at your question. The questions states: "the number of units in the circumference of a circle is the same as the number of square units in its area", which can be written as: Circumference of a Circle = Area of the circle ... (i) We know that, for a ...”
November 18, 2017
EconomistGMATTutor posted a reply to The surface area of a sphere is 4πR^2, and the... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$Area=\ 4\pi R^2$$ $$Volume=\frac{4}{3}\pi R^3$$ The question states: "If the volume of a certain sphere is double the surface area of that sphere", we can write it as: $$Volume=2\times Area$$ $$\frac{4}{3}\pi ...” November 18, 2017 EconomistGMATTutor posted a reply to Idioms in the Sentence Correction forum “Hello! I completely understand your frustration with idioms - they can be a huge pain to deal with! If it helps, try to look at each option from the point of view of a person learning English for the first time. Idioms rarely mean exactly what the words convey. For example, we know in English ...” November 17, 2017 EconomistGMATTutor posted a reply to parallel structure in the Sentence Correction forum “Hello! When looking at questions for problems of parallelism, one easy way to find the right answer is to focus the actions/verbs and see if they all match. So for this question, I''ll take out each of the action verbs in the list so you can see them without all the extra text in the way: (a) ...” November 17, 2017 EconomistGMATTutor posted a reply to style/conscision in the Sentence Correction forum “Hello! To answer your question, B has a subject/verb agreement problem: Clean criminal records of their employees is important to investment banks; hence, a stringent background check are necessary prerequisites for employment. "...a stringent background check..." is singular, but ...” November 17, 2017 EconomistGMATTutor posted a reply to After the Great Depression’s exceptionally high unemployme in the Sentence Correction forum “Hello! To answer your question, the problem with answer D is mainly because it starts with "While," which is a commonly misused conjunction in English! We generally don''t suggest using the word "while" to show contrast - it''s really meant to say that two things were ...” November 17, 2017 EconomistGMATTutor posted a reply to In the United States proven oil reserves in the Critical Reasoning forum “The discrepancy: 1) The amount of oil considered extractable from known fields is at the same level as it was ten years ago, and YET . . . 2) No new oil fields have been discovered, and the annual consumption of oil has increased. We need to show that both of these two statements can be ...” November 17, 2017 EconomistGMATTutor posted a reply to Modifiers in the Sentence Correction forum “Hello! Let''s break down each option to figure out what''s right/wrong about each: An unusually strong cyclist can, it is hoped, provide enough power to set a new distance record for human-powered aircraft in MIT’s diaphanous construction of graphite fiber and plastic. (A) can, it is ...” November 17, 2017 EconomistGMATTutor posted a reply to Modifiers in the Sentence Correction forum “Hello! Let''s go through each option and look at what''s good/bad about them: In the 1970s word leaked that the Tuskegee Institute had performed experiments in which researchers withheld medicine from African American males with syphilis in order to learn how the disease progresses, and in the ...” November 17, 2017 EconomistGMATTutor posted a reply to Awkward construction?? in the Sentence Correction forum “Hello! To answer your question about B: It sound awkward to readers to start a sentence with a coordinating conjunction (for, and, nor, but, or, yet, so). Sometimes, you can get away with starting a sentence with the word "so," but only if it''s being used casually as an interjection ...” November 17, 2017 EconomistGMATTutor posted a reply to The number of tournament games is represented as... in the Problem Solving forum “Hello LUANDATO. In this question we will use the Gauss Sum, which says that the sum of the integers from 1 to n is$$\frac{n\cdot\left(n+1\right)}{2}.$$It tell us$$G\left(n+1\right)=G\left(n\right)+n, and \ G\left(2\right)=1.$$So,$$G\left(3\right)=G\left(2\right)+2=1+2.$$...” November 16, 2017 EconomistGMATTutor posted a reply to Between 1971 and 1975 in the Critical Reasoning forum “The conclusion: The government office was more lax in enforcing drug-promotion laws between 1976 and 1980 than it was between 1971 and 1975. The evidence: Between 1971 and 1975, the government office issued an average of 60 citations a year, and between 1976 and 1980, the annual average for ...” November 16, 2017 EconomistGMATTutor posted a reply to In a mayoral election, Candidate X received 1/3 . . . in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. Votes candidate Z received = 24,000 Candidate Y received 1/4 fewer votes than Candidate Z. Let''s first find 1/4 of Candidate Z votes.$$=\frac{1}{4}\times24,000=6000$$Number of votes Candidate Y received$$=24,000-6000=18,000$$...” November 16, 2017 EconomistGMATTutor posted a reply to Alice and Bruce each bought a refrigerator . . . in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. This question can be solved using system of linear equations. Let Alice paid x dollars and Bruce paid y dollars. The sum of their purchases is 900, therefore,$$x+y=900y=900-x...(i)$$The question states that: "Twice of ...” November 16, 2017 EconomistGMATTutor posted a reply to Powers and roots. in the Problem Solving forum “Hello Vjesus12. Let''s take a look at your question.$$If\ \ \ \sqrt{x}=y,\ then\ x=y^2\ and\ then\ x^4=\left(y^2\right)^4=y^8.$$By the other hand,$$\left(x^{-2}\right)^{-2}=x^4.$$So,$$\frac{1}{\left(x^{-2}\right)^{-2}}=\frac{1}{x^4}=\frac{1}{y^8}=y^{-8}.$$So, the correct answer should ...” November 16, 2017 EconomistGMATTutor posted a reply to If x and y are odd integers in the Problem Solving forum “Hello. The key in this PS question is: "must always" be a non-integer. a) xy, the product of two odd integers is integer. OUT. b) x/y, if x=3 and y=1, then x/y is integer. So, it can be sometimes integer and sometimes not. OUT. c) as above. OUT. d) The product of to odd ...” November 16, 2017 EconomistGMATTutor posted a reply to A car starts from X and moves towards Y. in the Problem Solving forum “Hello Vjesus12. Let''s see: If it took to car B 4 hours to travel 1/3 of the distance, then it will take 8 hours to travel (2/3) of the distance. So, it takes 12 hours (4 hours 1/3, 8 hours 2/3) to travel form X to Y. I hope this explanation may help you. I''m available if you''d like a ...” November 16, 2017 EconomistGMATTutor posted a reply to In response to viral infection, the immune systems of mice t in the Critical Reasoning forum “The conclusion: Keratitis in mice infected with a herpesvirus is caused by antibodies to herpesvirus. The evidence: The immune systems of mice typically produce antibodies that destroy the virus by binding to proteins on its surface. Proteins on the surface of cells in the eye closely ...” November 16, 2017 EconomistGMATTutor posted a reply to 1000SC 203 in the Sentence Correction forum “Hello! Instead of going through each option, I''ll stick to answering your specific question about why answer C is wrong, and A is correct. Answer C states "after there was a bitter dispute over," which, if you read it carefully, isn''t clear as to WHO was arguing. Did Camus break ...” November 16, 2017 EconomistGMATTutor posted a reply to style/conscision in the Sentence Correction forum “Hello! Let''s break this question down, answer by answer, to find the best option: Federal government financing is an essential key in the survival of the interstate rail system. (a) is an essential key in There are two issues with this one. First, saying "an essential key" ...” November 16, 2017 EconomistGMATTutor posted a reply to Like Byron at Missolonghi in the Sentence Correction forum “Hello! Let''s go through this question, answer by answer, to determine why A is the best option: Like Byron at Missolonghi, Jack London was slowly killed by the mistakes of the medical men who treated him. A: Like Byron This one is the best because it clearly shows that the writer is ...” November 16, 2017 EconomistGMATTutor posted a reply to To travel to China and Japan have always been John's dream. in the Sentence Correction forum “Hello! Let''s take a look at each option, and what makes each one correct/incorrect: To travel to China and Japan have always been John''s dream. (a) To travel to China and Japan have always "To travel to" isn''t the best way to write about actions John is dreaming of. Instead, ...” November 16, 2017 EconomistGMATTutor posted a reply to it Vs their - confusion in the Sentence Correction forum “Hello! I will be the first to admit that this question is worded a bit vaguely, so I definitely see your point. I think the intention was for the word "their" to refer back to "economic trends," rather than the board itself, like arocks pointed out. This is why it''s ...” November 16, 2017 EconomistGMATTutor posted a reply to Varieties of influenza range in severity in the Sentence Correction forum “Hello! Thanks for your question. Option C isn''t the best answer because it breaks up the phrases that describe mild flus too much. It creates a "non-essential" phrase that really is essential to the meaning of the sentence. One way to make sure your commas are in the right place is ...” November 16, 2017 EconomistGMATTutor posted a reply to More and more companies have begun to consume in the Critical Reasoning forum “The conclusion: The federal government should encourage companies to consume less energy by providing the necessary incentives. The evidence: These efforts could place the United States at the forefront of an emerging global market for cleaner technologies and could help with the issues of global ...” November 15, 2017 EconomistGMATTutor posted a reply to The rhombus (AFCE) is inscribed in a rectangle (ABCD).... in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. Since AFCE is a rhombus, there it has all sides of equal length let''s say ''x''.$$CD=25AD=20$$Let''s suppose,$$DE\ =\ y$$Therefore, we can write:$$DE\ +EC=\ 25y+x=\ 25x=\ 25-y...\left(i\right)$$In the ...” November 15, 2017 EconomistGMATTutor posted a reply to In jar A there are 3 white balls and 2 green ones... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. There are two jars A and B. Jar A has 3 white balls and 2 green ones. Jar B has one white ball and three green ones P(Picking up a white ball out of jar A) = P(selecting Jar A) * P(Picking white ball from Jar A) ...” November 15, 2017 EconomistGMATTutor posted a reply to Given the three points below in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. Three points (0,3), (-3,-3), (3,-3) are making a triangle at the coordinate plane. (0, 3) will be the top vertex of the triangle and (-3, -3) and (3, -3) are the vertices at the base of the triangle. We know that, Area of triangle = ...” November 15, 2017 EconomistGMATTutor posted a reply to In order to increase revenues, a cell-phone company has deci in the Critical Reasoning forum “The conclusion: The new plan will increase revenue. The evidence: Instead of charging a flat rate of 20 per month and 0.50 for every minute over 200 minutes, the company will now charge 50 per month for unlimited usage. We are asked to weaken the conclusion -- to show that the new plan ...” November 15, 2017 EconomistGMATTutor posted a reply to If the circumference of circle P is 15.174 and the circumfer in the Problem Solving forum “Hi ardz24, Let''s take a look at your question. Let''s find the diameter of circle P using circumference formula:$$Circumference=2\pi r15.174=2\pi r2r=\frac{15.174}{\pi}\pi=3.14\approx32r=\frac{15.174}{3}2r\approx5Diameter\approx5$$...” November 15, 2017 EconomistGMATTutor posted a reply to In the year 2006 in the Critical Reasoning forum “The apparent discrepancy: Tuition and fees increased, but money collected from these sources held constant and then decreased. Your job is to explain how both of these things can be true. Or, since it''s an EXCEPT question, find four choices that explain away the discrepancy and one that ...” November 15, 2017 EconomistGMATTutor posted a reply to If b is greater than 1, which of the following must be... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. We will check each option one by one that if b is a number greater than 1, whether the result is negative or positive. Lets start from Option A. (2 - b)(b - 1) Let b = 2 (2-2)(2-1) = zero We will discard this, since zero is neither ...” November 14, 2017 EconomistGMATTutor posted a reply to Making the possession of guns illegal will never reduce the in the Critical Reasoning forum “The conclusion: No laws restricting the sale and ownership of guns will prevent those who want to purchase one from purchasing one. The evidence: People are aware of the uses for guns and will find new, and possibilly illegal, ways to get them. Choice C, the correct choice, simply makes a ...” November 14, 2017 EconomistGMATTutor posted a reply to Peter rolls two dice at the same time. What is . . . in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. Peter rolls two dice at a time, so let''s first find the total number of outcomes. (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6) (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6) (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6) (4, 1), (4, 2), (4, ...” November 14, 2017 EconomistGMATTutor posted a reply to If it takes 50 workers 8 hours to build . . . in the Problem Solving forum “Hi M7MBA, Let''s take a look at your question. The question states: "If it takes 50 workers 8 hours to build a log cabin, how long would it have taken 30 workers to build the same cabin? " 50 workers build a log cabin = 8 hours If we want to calculated how many hours will one ...” November 14, 2017 EconomistGMATTutor posted a reply to A recent survey conducted in one North American city reveale in the Critical Reasoning forum “The discrepancy: 1) 60 percent of surveyed adults in one city said they were willing to pay higher taxes to improve the city’s schools. BUT . . . 2) A proposition to increase funding for schools by raising taxes failed to win majority approval. Your job is to explain how both of these ...” November 14, 2017 EconomistGMATTutor posted a reply to According to the Department of Social Services, new taxes ne in the Critical Reasoning forum “The conclusion: The governor''s plan for securing the needed funds should NOT be rejected as unfair. The evidence: There is no evidence provided, but clearly we are meant to choose an answer that shows that the plan would actually benefit those taxpayers who, according to the author, would ...” November 14, 2017 EconomistGMATTutor posted a reply to If two trains ,travelling at a speed of 72mph and 48 mph. . in the Problem Solving forum “Hello M7MBA. It is easier and faster as regor60 said. But if you don''t know about the combine speed, you can solve it as follows. Train A travels at 48mph, which is equivalent to 48/60=4/5 miles per minute. Train B travels at 72mph, which is equivalent to 72/60=6/5 miles per minute. ...” November 14, 2017 EconomistGMATTutor posted a reply to Which of the following CANNOT be the median of the 3 . . . in the Problem Solving forum “Hello M7MBA. Let''s try with some examples. The median of y, x, z and z, x, y is x. So, option A is possible. The median of x, z, y and y, z, x is z. So, option B is possible. If x=1, y=2 and z=3, then the median is 2. By the other hand,$$median\ 2=\frac{1+3}{2}=\frac{x+z}{2}.$$So, ...” November 14, 2017 EconomistGMATTutor posted a reply to The average length of all the sides of a rectangle equals in the Problem Solving forum “Hello M7MBA. Let''s take a look at your question. We have the next rectangle: https://s8.postimg.org/3jsq0hvg1/rectangle.png The area of the rectangle is 18, that is to say,$$x\cdot y=18.$$. Also, "the average length of all the sides of a rectangle equals twice the width of the ...” November 14, 2017 EconomistGMATTutor posted a reply to If 4x^2 + 9y^2 = 100 and (2x + 3y)^2 = 150, then what is... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. We will be solving this question using the following polynomial identity.$$\left(a+b\right)^2=a^2+b^2+2ab$$We are given with:$$\left(2x+3y\right)^2=150$$Evaluate the LHS using the polynomial identity (a+b)^2 = a^2 + b^2 + 2ab, we ...” November 12, 2017 EconomistGMATTutor posted a reply to Probability in the Problem Solving forum “Hello Roland2rule. As the probability that event B occurs is 1/3, then the probability that event B doesn''t occur is 2/3. In the question " what is the probability that event A occurs but event B does not occur?", it is asked for both events at the same time. So, the probability of ...” November 12, 2017 EconomistGMATTutor posted a reply to If the product of 6 integers is positive... in the Problem Solving forum “Hello LUANDATO. First, I think there is a mistake in the OA, because if we consider the set$$A=\left\{-1,-2,-3,-4,-5,1\right\}$$then A has 5 integers and the product of these 6 integers is negative. The correct answer is E . At most, all the 6 integers can be negative, and their ...” November 12, 2017 EconomistGMATTutor posted a reply to If a positive integer n, divided by 5 has... in the Problem Solving forum “Hello LUANDATO. We only have to find an integer "n" that help us in each case. For example, let''s take n=12. When we divide 12 by 5 the remainder is 2, and: - 12 is NOT odd. So, option I is out. - n+1=12+1=13, and 13 is a prime number. So, option II is out too. - n+2 = ...” November 12, 2017 EconomistGMATTutor posted a reply to Probability in the Problem Solving forum “Hello Roland2rule. The question tell us that the probability that event M will NOT occur is 0.8, it implies that the probability that event M will OCCUR is 0.2. Also, as the probability that event R will NOT occur is 0.6, then the probability that event R will OCCUR is 0.4. Finally, it is ...” November 12, 2017 EconomistGMATTutor posted a reply to It takes 3 employees in the Problem Solving forum “Hello lheiannie07. Let''s take a look at this PS question. 3 employees complete 500 pages in 5 hours. So, they complete 100 pages per hour. So, 6 employees, who work all at the same rate as before, can complete: - 200 pages per hour. - 100 pages in 30 minutes (0.5 hours). - 50 pages ...” November 12, 2017 EconomistGMATTutor posted a reply to Percents in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. We will suppose that there are a total of 100 males in the town. 60% of them are married, which means that the total number of males married out of 100 is 60. If 60 males are married then we can say that 60 females are married as well to ...” November 11, 2017 EconomistGMATTutor posted a reply to How can I solve the equation? in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. We will use the substitution method to solve it. The first equation is :$$\frac{x}{y}=3$$Which implies:$$x=3y\ $$Plugin x = 3y in second equation.$$\frac{\left(x-y\right)}{x}=?=\frac{\left(3y-y\right)}{3y}$$...” November 10, 2017 EconomistGMATTutor posted a reply to The average wages of a worker during a fortnight... in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. The wages of a worker during a fortnight comprising 15 consecutive working days = 90 per day We know that,$$Average\ \ =\ \frac{Sum}{Days}Sum\ =\ Average\ \times\ DaysSum\ =\ 90\ \times15\ =\ 1350$$Therefore, Sum of wages ...” November 10, 2017 EconomistGMATTutor posted a reply to During the course of an hour, an employee at Ultimate... in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. We are asked to find the median weight of the packages weighing 48, 32, 63, 12, 40, 8. To find median of ungrouped data, we arrange the data in ascending or descending order. The weights in ascending order can be written as:$$8,\ 12,\ 32,\ ...”
November 10, 2017
EconomistGMATTutor posted a reply to The number of vertices formed by four lines could be any num in the Problem Solving forum
“Hello Vincen. Here is a graphic with both situations. The correct answer is A . https://s1.postimg.org/9u1mnupe0r/Nuevo_Presentaci_n_de_Microsoft_Power_Point.png Feel free to ask me again if you have a doubt. Regards.”
November 10, 2017
EconomistGMATTutor posted a reply to (2^(4-1)^2)/(2^(3-2)) in the Problem Solving forum
“Hello Vincen. Let''s do the calculus step by step. $$1-\,\, \left(4-1\right)^2=\left(3\right)^2=9.$$ So, $$2^{\left(4-2\right)^2}=2^9.$$ Now, $$2-\,\, \ 2^{\left(3-2\right)}=2^1.$$ Finally, $$3-\,\, \ ...” November 10, 2017 EconomistGMATTutor posted a reply to Gambling experts contend that with a sufficiently advanced c in the Critical Reasoning forum “The conclusion: The gambling experts'' contention -- with a sufficiently advanced computer technology, a skilled technician will soon be able to win almost every time -- cannot be evaluated The evidence: Losses would simply be blamed on immature technology or the technician''s lack of ...” November 10, 2017 EconomistGMATTutor posted a reply to Alan & Charlie in the Critical Reasoning forum “Alan''s conclusion: Industrialization must be promoted extensively for the welfare of a nation. Alan''s evidence: Industrialisation helps in achieving a variety of social objectives. Charlie''s conclusion: Nations should promote the positive impacts of industrial development while limiting or ...” November 10, 2017 EconomistGMATTutor posted a reply to In a visual perception experiment, a scientist asked individ in the Critical Reasoning forum “This is an inference question -- the correct choice will be the only one that must be true based on the given evidence. The correct choice, D, states that each subject could only recognize the original sequence. This is just a restatement of the given information: "The only time that the ...” November 10, 2017 EconomistGMATTutor posted a reply to strengthen in the Critical Reasoning forum “The conclusion: A developer who wishes to make a large profit would be wise to buy urban waterfront lots and erect residential buildings on them. The evidence: Waterfront properties are generally seen as prestigious, as evidenced by the large sums paid for homes along the beach front The ...” November 9, 2017 EconomistGMATTutor posted a reply to A machine manufactures notebooks in a series of... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The question states: A machine manufactures notebooks in a series of five colors: red, blue, black, white and yellow. If the machine starts its production from a red notebook and ends at a black note book, then the sequence must be like: ...” November 9, 2017 EconomistGMATTutor posted a reply to Inference in the Critical Reasoning forum “This is an inference question. Given all the evidence, what must be true about an eastward-traveling train that is approached by a westward-traveling train that is blowing its horn? The evidence: Whenever distance between the listener and the source of the sound decreases, the sound seems ...” November 8, 2017 EconomistGMATTutor posted a reply to q is the smallest positive integer for which 3q3q is a facto in the Problem Solving forum “Hello ardz24. I think there is something wrong here, because the prime factorization of 8124 is$$2^2\cdot3\cdot677.$$So, all the posible factors of 8124 are$$\left\{2,\ 3,\ 4,\ 6,\ 12,\ 677,\ 1354,\ 2031,\ 2708,\ 4062,\ 8124\right\}.$$No factor has the form 3q3q. I would like to ...” November 8, 2017 EconomistGMATTutor posted a reply to Kim purchased n items from a catalog for 8 each. in the Problem Solving forum “Hello Vjesus12, I hope you''re well. First, as Kim purchased "n" items, we have to notice that the total cost for these "n" items is  8n , because each item cost 8. Now, let''s calculate the postage and handling charges. For the first item 3. For the rest ...” November 8, 2017 EconomistGMATTutor posted a reply to If a, b, and c are integers and ab^2/c . . . in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. The question says,$$\frac{ab^2}{c}>0$$and$$\frac{ab^2}{c}=evenab^2=c\times even$$When any number is multiplied by an even number, it will result into an even number as well. Therefore,$$ab^2=even$$ab^2 can be even if ...” November 8, 2017 EconomistGMATTutor posted a reply to A machine at the golf ball in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. The machine produces 16 golf balls in 5 minutes. 1 golf ball can be produced in (5/16) minutes. 32 golf balls can be produced in:$$=\ \frac{5}{16}\times32=\ 5\times2\ =\ 10\ $$Therefore, one machine will produce 32 golf ...” November 8, 2017 EconomistGMATTutor posted a reply to Which of the following are/is prime? in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. We are asked to find the prime number from the options given. We know that a prime number has only two divisors 1 and the number itself. So to find if a number is a prime number or not we will check if it has any divisor other than 1 and the ...” November 8, 2017 EconomistGMATTutor posted a reply to 2,600 has how many positive divisors? in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. We are asked to find the number of positive divisors of 2600. In order to find number of positive divisors a number has, we find the prime factorization, and add one to all the exponents and multiply them. Let''s write 2600 as a product of ...” November 8, 2017 EconomistGMATTutor posted a reply to A set X={a_1, a_2, a_3, a_4, a_5} . . . in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. The mean of the set$$X=\left\{a_1,\ a_2,\ a_3,\ a_4,\ a_5\right\}$$is M. We know that mean is equal to the sum of the values divided by the number of the values, therefore,$$M\ =\ \frac{a_1+a_2+a_3+a_4+a_5}{5}$$Now , lets find the mean ...” November 8, 2017 EconomistGMATTutor posted a reply to Critical reasoning in the Critical Reasoning forum “To start with, this is of course an EXCEPT question, so we''re looking for something that Mary does NOT do. We therefore need to examine her two sentences (outside of "Don''t be silly") to see if they correctly describe her reasoning. I would suggest simply going through the choices one ...” November 8, 2017 EconomistGMATTutor posted a reply to Kim purchased n items from a catalog for 8 each. in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. Let''s first find the total purchase price. Kim purchased n items for 8 each, therefore, the total purchase price of n items is 8n. Now, let''s find the postage and handling charges of n items, which is 3 for the first item and 1 for each ...” November 8, 2017 EconomistGMATTutor posted a reply to In the figure above m1 is parallel to m2, and n1 is... in the Problem Solving forum “Hi Swerve, Let''s take a look at your question. In the image, m1 is parallel to m2, and n1 is parallel to n2. We need to find the degree measure of which of the angles given in the options is NOT necessarily equal to the degree measure of angle S. Let''s start with Option A. The degree ...” November 7, 2017 EconomistGMATTutor posted a reply to In the figure above, if m and n are parallel, then x=? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. Lines m and n are parallel. The angles x and (2x - 30) are called corresponding angles. When two parallel lines are cut by another line then the corresponding angles formed are always congruent. Therefore, x = 2x - 30 2x - x = 30 x = 30 ...” November 7, 2017 EconomistGMATTutor posted a reply to In the figure above, if m and n are parallel, then x=? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. Lines m and n are parallel. The angles x and (2x - 30) are called corresponding angles. When two parallel lines are cut by another line then the corresponding angles formed are always congruent. Therefore, x = 2x - 30 2x - x = 30 x = 30 ...” November 7, 2017 EconomistGMATTutor posted a reply to weaken in the Critical Reasoning forum “The conclusion: Teachers can encourage creativity by showing students different perspectives for viewing the significance of events in their daily lives. NOTE: This is not the best written question. You are asked to weaken the author''s claim, but there is more than one. The first sentence ...” November 7, 2017 EconomistGMATTutor posted a reply to The mean of twenty-five consecutive positive integers. . . in the Problem Solving forum “Hello M7MBA. The mean of 25 consecutive positive integers is:$$M=\frac{a_1+a_2+.\ .\ .\ +\ a_{25}}{25}.$$The total is:$$T=a_1+a_2+.\ .\ .\ +\ a_{25}.$$So, the mean can be write as follows:$$M=\frac{1}{25}\cdot T=\frac{4}{100}\cdot T=4\%\cdot T.$$So, the mean is the 4% of the ...” November 6, 2017 EconomistGMATTutor posted a reply to Number N is randomly selected from a set of all primes betwe in the Problem Solving forum “Hello ardz24. First, you have to notice that N is always an odd number. Then, if you want that N+K is odd, then K has to be even (because N is odd). (it doesn''t matter how we select N). Now, K has to be selected from {10, 15, 20, 25, 30, 35, 40}. (7 options). So, the favorable cases are ...” November 6, 2017 EconomistGMATTutor posted a reply to Inference in the Critical Reasoning forum “This is an inference question, so you must take the evidence given and see what can be absolutely concluded. The correct choice is D. Since box office receipts are greater this half-year -- with only 20 releases -- than box office receipts last year, with 50 releases, the average receipts must ...” November 6, 2017 EconomistGMATTutor posted a reply to Strengthen in the Critical Reasoning forum “The conclusion: It is not true that meditation causes people to perform better on the GMAT. The evidence: Students who meditate are more likely than other students to have adequate time to study. Assumption: Having adequate study time is the actual cause of superior scores. This is shown ...” November 6, 2017 EconomistGMATTutor posted a reply to What is the perimeter of Δ ABC ? in the Problem Solving forum “Hello. Using the Pythagora''s Theorem we can find CE.$$CE=\sqrt{2^2-1^2}=\sqrt{3}.$$Now, AE=AC+CE, this implies that:$$AC=AE-CE=6\sqrt{3}-\sqrt{3}=5\sqrt{3}.$$To calculate AB, we will use that triangles ABC and EDC are similar. So,$$\frac{AB}{ED}=\frac{AC}{CE},\ this\ implies\ that,\ ...”
November 4, 2017
EconomistGMATTutor posted a reply to Which of the following distribution of numbers has the great in the Problem Solving forum
“Hello. Let''s take a look at your question. We first need to calculate the mean value of each set of numbers: $$M_A=0;\ M_B=0;\ M_C=5;\ M_D=2;\ M_E=2.$$ Now, we have to calculate the standard deviation of each set of numbers: $$SD_A=\sqrt{7};\ SD_B=\sqrt{\frac{10}{3}};\ SD_C=2;\ ...” November 4, 2017 EconomistGMATTutor posted a reply to What is the product of integers a, b, and c if... in the Problem Solving forum “Hi LUANDATO, Lets take a look at your question.$$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,0002^a.3^b.5^c=27\times10,000,000$$...” November 4, 2017 EconomistGMATTutor posted a reply to If x must be divisible by both 4 and 10, then... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The number that is divisible by both 4 and 10 must the least common multiple of both. Let''s first find LCM of 4 and 10. Multiples of 4 = 4, 8, 12, 16, 20, ... Multiples of 10 = 10, 20, 30, 40, ... LCM = 20 Now 20 is divisible by both 4 ...” November 3, 2017 EconomistGMATTutor posted a reply to Statistics and set problems in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. The temperatures, in degree Celsius, listed in increasing order, are:$$21,\ 25,\ X,\ 40,\ 50$$We know that if we have odd number of values arranged in ascending or descending order, the middle value is known as median. Hence, for the ...” November 3, 2017 EconomistGMATTutor posted a reply to Which expression is equivalent to (5x − 3y)^2? in the Problem Solving forum “Hi AAPL, Let''s take a look at your question.$$\left(5x-3y\right)^2=\left(5x-3y\right)\left(5x-3y\right)=5x\left(5x-3y\right)-3y\left(5x-3y\right)=25x^2-15xy-\left(15xy-9y^2\right)=25x^2-15xy-15xy+9y^2=25x^2-30xy+9y^2$$Therefore, Option E is ...” November 3, 2017 EconomistGMATTutor posted a reply to A travel agent offers a vacation plan which costs z dollars in the Problem Solving forum “Hi AAPL, Let''s take a look at your question. The question states: "A travel agent offers a vacation plan which costs z dollars for the first day and z/6 dollars for each additional day. How much does a vacation of y days cost, in dollars, where y>1??" Total days of vacation = y ...” November 3, 2017 EconomistGMATTutor posted a reply to Assumption in the Critical Reasoning forum “The conclusion: Selling radicchio 5 for 4 is a good idea. The evidence: Selling marmalade at that discount was a good idea. The assumption: There are no significant differences between sales of the two items. This is what Choice B says. If this were not true, if people who were willing to ...” November 3, 2017 EconomistGMATTutor posted a reply to Weaken in the Critical Reasoning forum “The conclusion: The candidate who does not support the plan will win the election for mayor. The evidence: 60% of the city’s residents are opposed to the plan, while about 35% are in support of the plan. The assumption: The survey accurately reflects how the election will turn out. ...” November 3, 2017 EconomistGMATTutor posted a reply to strengthen in the Critical Reasoning forum “The conclusion: The decline in the US infant mortality rate does not indicate that US babies are now healthier at birth. The evidence: None is given explicitly. This means that there is unstated evidence, otherwise known as an assumption. The assumption: More infants are surviving birth, ...” November 3, 2017 EconomistGMATTutor posted a reply to A successful clothing department store in the Critical Reasoning forum “The conclusion: Relocating to the suburbs will save costs. The evidence: The cost per square foot in the suburb is half of the cost per square foot in the downtown region. The assumption: The store will not have to purchase a much greater lot in the suburb. Even though the cost per foot is ...” November 3, 2017 EconomistGMATTutor posted a reply to The lobbyist accused of offering a large cash bribe in the Critical Reasoning forum “The conclusion: I did not offer a bribe. The evidence: I left the house without money. I then spent all my money on lunch. You ask about finding the "best argument." I''m not sure what that means. Your task here is to find the flaw in the argument. Clearly, the lobbyist is ...” November 3, 2017 EconomistGMATTutor posted a reply to problem solving in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question.$$\left(x+2\right)^2=-4+10x$$Evaluate Left hand side,$$x^2+4x+4=-4+10xx^2+4x+4+4-10x=0x^2+4x-10x+4+4=0x^2-6x+8=0$$Let''s now factorize it by grouping method,$$x^2-4x-2x+8=0$$...” November 3, 2017 EconomistGMATTutor posted a reply to Word problems in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question and solve it algebraically. Jack attempted 20 questions in total. For each correct answer he got +4 points and for each incorrect answer he got -2 points. The question states that Jack would have scored 44 points if he had got two more ...” November 3, 2017 EconomistGMATTutor posted a reply to If m is a positive integer and m^2 is divisible by 48, then in the Problem Solving forum “Hi ardz24, Let''s take a look at your question. The question states: "If m is a positive integer and m^2 is divisible by 48, then the largest positive integer that must divide m is? " The largest positive integer that must divide m will be m itself. One way to solve this question ...” November 3, 2017 EconomistGMATTutor posted a reply to Work/Rate problem in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. The questions states that: "The first puncture by itself would make the tire flat in 9 minutes. The second puncture by itself would make the tire flat in 6 minutes." In one minute, the part of the tire made flat by the first ...” November 2, 2017 EconomistGMATTutor posted a reply to Exponential/power in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question.$$\left(4^x\right)\left(8^y\right)\left(16^{7x}\right)=\left(8^{4y}\right)\left(32^x\right)\left(64^y\right)$$...” November 2, 2017 EconomistGMATTutor posted a reply to Algebra in the Problem Solving forum “Hi Roland2rule, Lets take a look at your question, We can use this problem using the formula:$$\left(x+y\right)^2-\left(x-y\right)^2=4xy$$Plugin the given values,$$a^2-b^2=4xya^2-b^2=2\times2xy\frac{a^2-b^2}{2}=2xy2xy=\frac{a^2-b^2}{2}$$Therefore, option ...” November 2, 2017 EconomistGMATTutor posted a reply to For-profit colleges serve far fewer students than either pub in the Critical Reasoning forum “The conclusion: For-profit colleges enroll a greater proportion of financially disadvantaged students than do non-profit colleges. The evidence: Relative to non-profit colleges, for-profit colleges draw a disproportionate share of federal and state financial aid. The assumption: The people ...” November 2, 2017 EconomistGMATTutor posted a reply to Newspaper editors should not allow reporters to write the he in the Critical Reasoning forum “The conclusion: Newspaper editors should not allow reporters to write the headlines for their own stories. (Conclusions often use the word "should.") The evidence: The headlines that reporters write allude to little-known information that never appears explicitly in the story itself. ...” November 2, 2017 EconomistGMATTutor posted a reply to A company is considering changing its policy concerning dail in the Critical Reasoning forum “This question can be thought of as a "Strengthen" problem. The conclusion is then the following: The adoption of this policy would be likely to decrease employees’ productivity. The evidence is that the proposed policy would permit each employee to decide when to arrive-from as ...” November 1, 2017 EconomistGMATTutor posted a reply to If 0.0030<x−√30<0.0031, which of the following... in the Problem Solving forum “This is an interesting question. First thing you have to notice is 0.0030<x-√30<0.0031 implies that$$x\approx\sqrt{30}.$$By the other hand,$$\frac{1}{\sqrt{30}}-\frac{1}{x}=\frac{x-\sqrt{30}}{\sqrt{30}\cdot x}.$$Now, as$$x\approx\sqrt{30},\ then\ \sqrt{30}\cdot ...”
November 1, 2017
EconomistGMATTutor posted a reply to In a group of students, 5 participate in no after school... in the Problem Solving forum
“Hello AAPL. Let''s see your question. We have that the total of students in the group is 26. Also, we have that 5 students participate in NO after school activities. So, we have that 21 students PARTICIPATE in after school activities. From this 21 students, 16 participate in ...”
November 1, 2017
EconomistGMATTutor posted a reply to Let function # be defined as follows: in the Problem Solving forum
“Hello AAPL. It is simple. You just have to eval f on 6 and the simplify. I will show you: $$f\left(6\right)=\frac{6!+\left(6+1\right)!}{\left(6+2\right)!}=\frac{6!+7!}{8!}.$$ Now, we can write 7! and 8! as follows: $$7!=7\cdot6!\ \ \ \ \ \ and\ \ \ \ 8!=8\cdot7\cdot6!$$ Now, let''s ...”
November 1, 2017
EconomistGMATTutor posted a reply to The School of Architecture at Augury University had... in the Problem Solving forum
“Hello. Let''s see the hypothesis step by step. Total of applicants: 300. - two-thirds had previous experience working in an architectural office: this is equivalent to $$\frac{2}{3}\cdot300=200\ applicants.$$ - two-fifths had extensive artistic portfolios: this is equivalent to ...”
November 1, 2017
EconomistGMATTutor posted a reply to Studies by neuropsychologists show that in the Critical Reasoning forum
“The question asks for a conclusion, something that must be true based solely on the evidence. Here''s the evidence. 1) For a marketing campaign to result in a large number of sales, a high degree of brand recognition and generally positive associations with the brand''s logo must both be ...”
October 31, 2017
EconomistGMATTutor posted a reply to The supernova event of 1987 in the Critical Reasoning forum
“The conclusion: Supernovas of a certain size do not always produce neutron stars. The evidence: There is no evidence of the neutron star that current theory says should have remained after the supernova of 1987 even though many of the most sensitive instruments ever developed have searched for ...”
October 30, 2017
EconomistGMATTutor posted a reply to For most people, the left half of the brain controls linguis in the Critical Reasoning forum
“The conclusion: People who have suffered a serious stroke on the left side of the brain without suffering linguistic impairment must have their language centers in the right half. Evidence: 1) The left (usually) or right half of the brain controls linguistic capabilities. 2) When a language ...”
October 30, 2017
EconomistGMATTutor posted a reply to theory is either true in the Critical Reasoning forum
“The conclusion: Galileo''s observations of Jupiter''s satellites proved the truth of the Copernican theory. The evidence: 1) A theory is either true or false. 2) Galileo''s observations of Jupiter''s satellites showed that the Ptolemaic theory of the motion of celestial bodies is false. ...”
October 30, 2017
EconomistGMATTutor posted a reply to If n=1 and (m−n) / p=2, then which of the following . . . in the Problem Solving forum
“Hello M7MBA. Yes, of course. Let''s take a look at it. We have that n=1, so $$\frac{m-n}{p}=2\ <=>\frac{m-1}{2}=2.$$ If we replace m=1 on the equation above we will get $$\frac{1-1}{2}=0\ and\ 0\ne2.$$ That is why m can not be 1. The correct option is D. I hope this may help ...”
October 29, 2017
EconomistGMATTutor posted a reply to The various prices that a certain product were sold... in the Problem Solving forum
“Hello LUANDATO. Let''s take a look at your question. The median price of the set consist in sum the two numbers in the middle of the set (12 and 14) and then divide the result by 2. In our case, the median price is $$\frac{12+14}{2}=\frac{26}{2}=13.$$ By the other hand, the mean price is ...”
October 29, 2017
EconomistGMATTutor posted a reply to If a rectangle With Width 49.872 inches and length 30.64. . in the Problem Solving forum
“Hello M7MBA. The area of a rectangle is $$A_R=W\cdot L.$$ Let''s take the aproximations $$W\approx50\ and\ L\approx30.$$ So, we will get $$A_R\approx50\cdot30\approx1500.$$ Now, the area of a square is $$A_S=a^2$$ where a is the length of each side. Now, we can set the equation ...”
October 29, 2017
EconomistGMATTutor posted a reply to Which of the following could be t if |5t – 8| < 1? in the Problem Solving forum
“Hello M7MBA. You could try obtion by option but I will give you another way to solve it. $$|5t-8|<1<=>-1<5t-8<1\ <=>\ 7<5t<9\ <=>\frac{7}{5}<t<\frac{9}{5}\$$ $$<=>\ 1,4\ <\ t\ <\ 1,8$$ Now, let''s take a look at the options. a) ...”
October 29, 2017
EconomistGMATTutor posted a reply to Arithmetic in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. $$\frac{\sqrt{73}\sqrt{239}}{\sqrt{7.2}+\sqrt{15.7}}$$ We are asked to approximate its value, so let''s first approximate all the numbers used in the square roots with the closest possible number that is a perfect square. Using ...”
October 28, 2017
EconomistGMATTutor posted a reply to Divisibility/factors in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. It''s a bit tricky one. We are asked to find the number of multiples of 5 between 81 and 358. We know that first multiple of 5 between 81 and 358 will be 85 and the last one would be 355. So why not write an arithmetic sequence of multiples ...”
October 28, 2017
EconomistGMATTutor posted a reply to Prime factors/number properties in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. Since, {x} is the product of all even integers from 1 to x inclusive, therefore we can write {22} as, $$\left\{22\right\}=22\times20\times18\times16\times...\times2$$ Similarly {20} can be written in product form as: ...”
October 28, 2017
EconomistGMATTutor posted a reply to A salesman sold vacuum cleaners with a special 30-day... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. Total Vacuum clear sold = T Cost of each Vacuum cleaner = D Total Money made for selling T Vacuum cleaners = TD Number of Vacuum cleaners returned = Q Amount that salesman had to refund = (Number of Vacuum cleaners)(Cost of each Vacuum ...”
October 28, 2017
EconomistGMATTutor posted a reply to Word problems in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. According to the telecom company charges the first three minutes costs 50 cents then the next 15 minutes cost 20 cents for every 5 minutes and thereafter the company charges 2 cents per minute. Using this plan, we are asked to find the call ...”
October 28, 2017
EconomistGMATTutor posted a reply to set problem in the Problem Solving forum
“Hi Roland2rule, Let''s take a look at your question. The given set is: $$\left\{10,\ 14,\ 17,\ 24\right\}$$ The subsets that include odd number elements could have either one element or 3 elements. So let''s first write all possible subsets that have only one element. $$\left\{10\right\},\ ...” October 28, 2017 EconomistGMATTutor posted a reply to Algebra in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question. The formula for the height H, that a penny falls is given by:$$H=vt+5t^2$$The building is 60m high, It means$$H=60m$$Initial speed of penny is given by 20m/s, therefore,$$v=20\ \frac{m}{s}$$We are asked to find the time ...” October 28, 2017 EconomistGMATTutor posted a reply to Arithmetic- roots in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question.$$\sqrt{\left(4.9\right)\times10^9}$$Let''s write 10^9 as 10 * 10^8, we actually want to eliminate the decimal point from 4.9$$=\sqrt{4.9\times10\times10^8}=\sqrt{49\times10^8}=\sqrt{49}\times\sqrt{10^8}$$...” October 28, 2017 EconomistGMATTutor posted a reply to Algebra in the Problem Solving forum “Hello Roland. I hope I can clarify it to you. You can establish a function that represents the growth of bacteria as follows:$$f\left(t\right)=2^t$$where t is the number of days. If it takes 30 days to fill a laboratory dish it implies that the capacity of the laboratory dish is ...” October 28, 2017 EconomistGMATTutor posted a reply to Number properties in the Problem Solving forum “Hello Roland. To solve this PS question, you need to pick 5 numbers such that their product is negative, that is, you have to pick an odd number of negative integers. Also, you have to select the biggest and the smallest ones. So, let''s pick -5, 5, -4, 4 and -3. their product will be ...” October 28, 2017 EconomistGMATTutor posted a reply to Inequalities in the Problem Solving forum “Hello Roland. I hope you''re well. You can pick two numbers and try option by option. Let''s take a=1 and b=2. Now,$$Option\ E:\ b-a=2-1=1,$$this is not greater than a. INCORRECT.$$Option\ D:\ ab=1\cdot2=2,$$this is not less than b. INCORRECT.$$Option\ C:\ b^2-a^2=2^2-1^2=4-1=3,$$...” October 28, 2017 EconomistGMATTutor posted a reply to Each bead in an urn is marked with... in the Problem Solving forum “Hello LUANDATO. I hope you''re well. This is a tough question, but let''s take a look at it. We only have to take care about the remainders. * It has been removed 15 numbers whose remainder when divided by 5 is 1. The product of these 15 numbers could be write as ...” October 28, 2017 EconomistGMATTutor posted a reply to The number of diagonals of two different regular... in the Problem Solving forum “Dear LUANDATO. I understand you because this is a hard question. But I will try to give you a good explanation. First, the number of diagonals of a polygon is$$D=\frac{\left(n-3\right)\cdot n}{2}$$where n is the number of sides. Now, we have that the number of diagonals of each polygon ...” October 28, 2017 EconomistGMATTutor posted a reply to Two long time friends want to meet for lunch on... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The two cities Portland and seattle are 200 miles apart. Let Anne covered a distance of x miles and Bill covered a distance of 200 - x miles when they met at point C. The whole situation is represented in the image below. ...” October 27, 2017 EconomistGMATTutor posted a reply to Red is a color which has powerful effects in the Critical Reasoning forum “Conclusion: either the teams wearing red subconsciously felt themselves more powerful, or that the non-red teams were subconsciously intimidated by the red color. Evidence: The teams wearing red won in a disproportionate number of matches. Assumption: Wearing red caused the outcome. ...” October 27, 2017 EconomistGMATTutor posted a reply to If the area of a number is defined... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. It is stated in the question that area of the number is defined as the difference between the number''s greatest and least prime factors, hence, we will first find write 100 as a product of its prime factors to find out its prime factors. 100 ...” October 26, 2017 EconomistGMATTutor posted a reply to 5 and 15 are the first in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. First two terms of geometric sequence are 5 and 15.$$a_1=5a_2=15$$We can find the common ratio by dividing the second term by first term.$$r=\frac{a_2}{a_1}=\frac{15}{5}=3$$Now, we will find 11th term and 13th term of ...” October 26, 2017 EconomistGMATTutor posted a reply to The function f(x) represents the number of ways that... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. We are asked to find out the number of ways 12 can be written as sum of prime numbers. Let''s explore. 12 = 2 + 2 + 2 + 2 + 2 + 2 12 = 2 + 2 + 3 + 5 12 = 2 + 2 + 2 + 3 + 3 12 = 2 + 5 + 5 12 = 3 + 3 + 3 + 3 + 3 12 = 7 + 3 + 2 12 = 7 + 5 ...” October 26, 2017 EconomistGMATTutor posted a reply to The wages earned by Robin is 30% more than... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The question states: The wages earned by Robin is 30% more than that earned by Erica. Let Erica''s earning = x Then Robin''s earning = x + (30%)x = x + (30/100) x = x +0.3 x = 1.3 x Next the question states: The wages earned by Charles is ...” October 26, 2017 EconomistGMATTutor posted a reply to If the complement of a certain angle is three times... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. We know that when two angles add to 90°, they are said to be complement of each other. So, if a and b are complement of each other then,$$a+b=90$$The question states: If the complement of a certain angle is three times the measure of ...” October 26, 2017 EconomistGMATTutor posted a reply to Two dice are rolled. What is the probability... in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. When two dice are rolled, all possible outcomes will be:$$\left(1,\ 1\right),\ \left(1,\ 2\right),\ \left(1,\ 3\right),\ \left(1,\ 4\right),\ \left(1,\ 5\right),\ \left(1,\ 6\right)\left(2,\ 1\right),\ \left(2,\ 2\right),\ \left(2,\ ...”
October 26, 2017
EconomistGMATTutor posted a reply to What is the unit digit of the sum... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. We will first look at some of the exponents of 3, 5 and 2 to find out the pattern of units digit in each number. $$3^1,\ 3^2,\ 3^3,\ 3^4,\ 3^5,\ 3^6,\ ...$$ $$=3,\ 9,\ 27,\ 81,\ 243,\ 729,...$$ We can see that in the powers of 3, the ...”
October 25, 2017
EconomistGMATTutor posted a reply to One of the ironies of contemporary history in the Sentence Correction forum
“Hello! This is an example of using parallel format to list two different effects or reasons for an action: Action: democratic processes were exploited Why were they exploited?: FOR the creation of anti-democratic regimes and FOR the promulgation and enforcement of laws denying the right to ...”
October 25, 2017
EconomistGMATTutor posted a reply to Which of the following most closely approximates in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$\sqrt{\frac{\left(3.97\right)\left(50.02\right)}{1.84}}=?$$ Since we are asked to approximate the value of the radical expression given, so let''s round off the decimals to simplify. ...”
October 25, 2017
EconomistGMATTutor posted a reply to The end of the eighteenth century in the Sentence Correction forum
“Hello! This sentence correction question has to do with parallel structure. All of the action verbs need to match up in terms of format or tense. Let''s look at the original sentence, but I''ll put the action verbs in bold: The end of the eighteenth century saw the emergence of prize-stock ...”
October 25, 2017
EconomistGMATTutor posted a reply to Neuroscientists,having amassed a wealth in the Sentence Correction forum
“Hello! For this question, I would suggest reading each option out loud to yourself. I think you will find that each of the incorrect answers is adding or deleting a word or two, making them either run-on sentences or incomplete fragments. For each answer, here are the missing pieces: A: ...”
October 25, 2017
EconomistGMATTutor posted a reply to Posting two similar questions together to clarify a doubt in the Problem Solving forum
“Hi vinni.k, Let''s take a look at question 1. In the first question, we are given a wire of 24 ft long and we are asked to cut 5/4 foot pieces of wire. We just need to divide 24 by 5/4 to find the maximum number of 5/4 foot pieces. So it will be $$24\div\frac{5}{4}$$ ...”
October 25, 2017
EconomistGMATTutor posted a reply to Alice Robie Resnick was elected in 1988 as only the second w in the Sentence Correction forum
“Hello! To answer ardz24''s question, here is the problem with answer D: Using the words "...was elected in 1988 as only..." implies that Resnick is still only one of two women to serve on the state bench, which isn''t true. In answer B, they change the wording to say "...was ...”
October 25, 2017
EconomistGMATTutor posted a reply to A wheel of a car of radius 21 cms... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. We can see that the radius of the wheel is given in cm. We will first convert it to km because we need to find the speed of the car in km/h. Therefore, Radius = 21 cm = 21/100 m = 0.21m Now convert m to km by dividing 0.21 by 1000, Radius = ...”
October 25, 2017
EconomistGMATTutor posted a reply to Having studied the mystic art of shamanism in the Critical Reasoning forum
“Conclusion: It would be impossible to summon rain using the chant during the three weeks before the full moon. Evidence: When the Chant of Rain was recited by a group of shamans during the night of a full moon, the place mentioned in the chant would get rainfall within a week. The evidence ...”
October 25, 2017
EconomistGMATTutor posted a reply to is closest in value to in the Problem Solving forum
“Hi Vincen, Let''s take a look at your question. We are asked to find the the closest value of $$\sqrt{4.8\cdot10^9}$$. Let''s write 10^9 as 10 x 10^8. $$\sqrt{4.8\times10\times10^8}$$ $$=\sqrt{48\times10^8}$$ $$\approx\sqrt{49\times10^8}$$ $$\approx7\times10^4$$ ...”
October 24, 2017
EconomistGMATTutor posted a reply to How many different subsets of the set {10, 14, 17, 24} are t in the Problem Solving forum
“Hi ardz24, Let''s take a look at your question. We are asked to find the number of subsets of the set {10, 14, 17, 24} that contain an odd number of elements. The subsets that have odd number of elements have either 1 or 3 elements. Let''s find those subsets. Subsets with one element = ...”
October 24, 2017
EconomistGMATTutor posted a reply to Cooperative apartment houses in the Sentence Correction forum
“Hello! The reason why option D is incorrect has to do with something called "nonessential clauses." By putting the phrase "as dwellings" in between commas, we''re telling the reader that information is non-essential to the meaning of the sentence. It basically means you ...”
October 23, 2017
EconomistGMATTutor posted a reply to During the last interglacial period in the Sentence Correction forum
“Hello! Let''s start with the difference between raise and rise: Raise: We use the verb "to raise" when talking about a person performing an action onto another person or thing. We can raise the temperature in our room by lighting a fire, raise a book over our head, or raise money for ...”
October 23, 2017
EconomistGMATTutor posted a reply to In 1776 Adam Smith wrote that it is young people who have in the Sentence Correction forum
“Hello! Let''s break down what is wrong with each of the incorrect answers: In 1776 Adam Smith wrote that it is young people who have “the contempt of risk and the presumptuous hope of success” needed to found new businesses. A. who have This one is correct because it''s telling us ...”
October 23, 2017
EconomistGMATTutor posted a reply to Kaplan Premier--Q35--The Laysan Rail in the Critical Reasoning forum
“The conclusion: Increased competition for food was ultimately responsible for the Layson Rail''s inability to survive. Evidence: None given. Since no evidence is given for the new explanation, providing some will strengthen the conclusion. That''s what we''re asked to do here. Choice D ...”
October 23, 2017
EconomistGMATTutor posted a reply to Which of the following equations is NOT equivalent in the Problem Solving forum
“Hi Vincen, Let''s take a look at your question. To find out which of the given options is not equivalent to 10y^2=(x+2)(x-2), we will check each option one by one. The equation $$10y^2=\left(x+2\right)\left(x-2\right)$$ can also be written as, $$10y^2=x^2-4$$ So the equivalent expressions ...”
October 22, 2017
EconomistGMATTutor posted a reply to If x^2 + 12x + 20 < 0, how many integer values can x be? in the Problem Solving forum
“Hi VJesus12, Let''s take a look at your question. $$x^2+12x+20<0$$ $$x^2+2x+10x+20<0$$ $$x\left(x+2\right)+10\left(x+2\right)<0$$ $$\left(x+2\right)\left(x+10\right)<0$$ The product can only be negative if any one of the binomial is less than zero. There can be two ...”
October 22, 2017
EconomistGMATTutor posted a reply to If 6-9/x = x, then x has how many... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$6-\frac{9}{x}=x$$ $$6=x+\frac{9}{x}$$ Simplify right hand side by adding up like terms. $$6=\frac{x^2+9}{x}$$ $$6x=x^2+9$$ $$x^2-6x+9=0$$ Let''s factorize the left hand side by grouping, $$x^2-3x-3x+9=0$$ ...”
October 22, 2017
EconomistGMATTutor posted a reply to For what value(s) of k... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$2k-9-k=4k+6-3k$$ $$2k-k+9=4k-3k+6$$ $$k+9=k+6$$ $$k+9-k=6$$ $$k-k=6+9$$ $$0=15$$ Which means, k has no value. Therefore, option D is correct. Hope it helps. I am available if you''d like any follow up.”
October 22, 2017
EconomistGMATTutor posted a reply to The value of 12! is closest... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. We are asked to estimate the value of 12!. $$12!\ =\ 12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1$$ Let''s now make groups of products that are aproximately equal to 10 or 100, $$=\ ...” October 21, 2017 EconomistGMATTutor posted a reply to Thousands who suffer heart attacks in the Critical Reasoning forum “The conclusion: The new agent could save the lives of many people who would otherwise join this group of heart attack victims. The evidence: Thousands who suffer heart attacks each year die before reaching a hospital or clinic where they can benefit from the drugs that dissolve clots in ...” October 21, 2017 EconomistGMATTutor posted a reply to For which value of k does the following pair... in the Problem Solving forum “Hello Vincen. From the second equation we get: (3)$$y^2-k^2=-\left(x+2k\right)^2.$$Now, from the first equation we can get: (4)$$x^2-2kx+k^2-y^2=8\ <=>x^2-2kx-\left(y^2-k^2\right)=8.$$Substituiting equation (3) in (4) we will get: (5)$$x^2-2kx+\left(x+2k\right)^2=8\ <=>\ ...”
October 20, 2017
EconomistGMATTutor posted a reply to What is the number of three-digit multiples of 5 that are no in the Problem Solving forum
“Hello Anaira. You have to build the three-digit number. We have 3 places _ _ _. _ For the first place you can select any number form 1 to 9. (9 options) _ _ For the second place you can select any number from 0 to 9. (10 options). _ _ _ For the last option you can select only the number ...”
October 20, 2017
EconomistGMATTutor posted a reply to Each of the integers from 0 to 9. . . . in the Problem Solving forum
“Hello VJesus12. The worst scenario you can have is that the extracted splits of paper are: 0, 1, 2, 3 ,4 and 5 (or 5, 6, 7, 8 and 9). In each case, there are 6 splits extracted and no pair of them sum 10. So, you have to extract one more split to ensure that two of them sum 10. In ...”
October 20, 2017
EconomistGMATTutor posted a reply to 500 PS section2 #20 in the Problem Solving forum
“Hello dunkin77. At the begining each student should pay y/R dollars. When x students failed contributing their share, the rest of the students (R-x) had to pay their part, it is, x*(y/R) dollars. Now, each one of the remaining students had to pay ...”
October 20, 2017
EconomistGMATTutor posted a reply to Remainder in the Problem Solving forum
“Hello Roland2rule. The idea here is to find a number N such that $$16\cdot N+3\le1000\ and\ N\ge0.$$ Let''s try some test values: $$N=50=>16\cdot50+3=803\ \le\ 1000.$$ This tell us that all there are 51 integers that satisfy the condition above. Now, let''s try with a greater N. ...”
October 20, 2017
EconomistGMATTutor posted a reply to The high cost of productions is severely limiting which oper in the Critical Reasoning forum
“I''m available if you''d like any follow up.”
October 20, 2017
EconomistGMATTutor posted a reply to The high cost of productions is severely limiting which oper in the Critical Reasoning forum
“The conclusion: If we reduce production budgets so that operas can be supported exclusively by box-office receipts and donations from individuals, then the public will be able to see less famous operas. The evidence: The high cost of productions is severely limiting which operas are available ...”
October 20, 2017
EconomistGMATTutor posted a reply to The term 'robot' in the Critical Reasoning forum
“First off, this is a somewhat faulty question. Obviously, two choices are identical. Furthermore, the grammar is Choice E is not correct, which might lead to some confusion. The conclusion: Robots will become smarter than humans in a not so distant future, making even more complex the ...”
October 20, 2017
EconomistGMATTutor posted a reply to A foot race had 36 teams of a dozen runners each... in the Problem Solving forum
“Hi LUANDATO, Lets take a look at your question. Total teams = 36 The question states that "By noon, 4/9 of the teams had finished the race". Let''s find the number of teams that finished the race by noon. $$=36\times\frac{4}{9}=4\times4=16$$ 16 teams had finished the race by ...”
October 20, 2017
EconomistGMATTutor posted a reply to What is the greatest prime factor... in the Problem Solving forum
“Hi LUANDATO, Lets take a look at your question. $$49^{19}-7^{35}$$ $$=\left(7^2\right)^{19}-7^{35}$$ $$=7^{38}-7^{35}$$ $$=7^{35+3}-7^{35}$$ $$=7^{35}.7^3-7^{35}$$ $$=7^{35}\ \left(7^3-1\right)$$ $$=7^{35}\ \left(343-1\right)$$ $$=7^{35}\ \left(342\right)$$ Write 342 as ...”
October 20, 2017
EconomistGMATTutor posted a reply to People tend to estimate the likelihood of an . . . in the Critical Reasoning forum
“This question asks you for something that is most likely true -- a conclusion that can be drawn from the evidence. The evidence: 1) People estimate the likelihood of an event’s occurrence according to how strongly and how often it comes to their attention. 2) Newspapers emphasize stories ...”
October 20, 2017
EconomistGMATTutor posted a reply to 1/4 of all the juniors and 2/3 of all the seniors are... in the Problem Solving forum
“Hi LUANDATO, Let''s look at your question. If there are a total of ''x'' seniors, then the juniors will be (2/3)x. Total students = seniors + juniors Total students = $$=x+\frac{2}{3}x=\frac{5}{3}x$$ The students going on the trip are: 1/4 of all juniors = ...”
October 20, 2017
EconomistGMATTutor posted a reply to Lark Manufacturing Company initiated a voluntary Quality in the Critical Reasoning forum
“To start with, this is an EXCEPT question. Four choices will weaken the conclusion. One won''t. The conclusion: Obviously, any workers who participate in a Quality Circles program will, as a result, become less satisfied with their job. The evidence: Independent surveys of employee ...”
October 20, 2017
EconomistGMATTutor posted a reply to A telecom company charges in the following manner each call in the Problem Solving forum
“Hi ardz24, Let''s take a look at your question. The questions states the charges of Telecom company as, 50 cents for first 3 minutes; 20 cents each of 5 minutes for the next 15 minutes; and two cents per minutes thereafter. We need to find the charges for a 50 minutes call. Let break down ...”
October 19, 2017
EconomistGMATTutor posted a reply to Street crime can be averted in the Critical Reasoning forum
“The passage provides us with a bunch of evidence. The question asks us to draw a conclusion from that evidence. Inferences are unstated conclusions, statements that MUST be true from the evidence. To start with the correct choice, E says that daytime streetlight regulations would probably do ...”
October 19, 2017
EconomistGMATTutor posted a reply to Similar reasoning in the Critical Reasoning forum
“This is an IF-THEN argument. If Joan grows marijuana, THEN she would not allow the warrantless search. That''s the evidence. If Joan DOES the allow the warrantless search, THEN she does not grow marijuana plants in her home. That''s the conclusion. That''s right. Given an IF A, THEN B ...”
October 18, 2017
EconomistGMATTutor posted a reply to If the majority of the residents of the apartment in the Critical Reasoning forum
“The conclusion: Therefore, the management of the complex will not have to engage the services of an exterminator. The evidence: 1) If the majority of the residents complain that their apartments are infested with ants, then the management will engage the services of an exterminator. 2) The ...”
October 18, 2017
EconomistGMATTutor posted a reply to Critical reasoning in the Critical Reasoning forum
“The conclusion of this argument is the "explanation" we''ve been asked to support: The seasonal variation in group size can probably be explained by seasonal variation in mortality among young voles. The evidence is that "Voles commonly live in large groups from late autumn ...”
October 18, 2017
EconomistGMATTutor posted a reply to The number of n satisfying in the Problem Solving forum
“Hi LUANDATO , Let''s take a look at your question. $$-n+2\ge0$$ $$-n\ge-2$$ the inequality is reversed when it is multiplied by a negative number. Therefore, $$n\le2$$ The next inequality given in the question is, $$2n\le5$$ $$n\le\frac{5}{2}$$ $$n\le2.5$$ Therefore, n ...”
October 18, 2017
EconomistGMATTutor posted a reply to Critical and tactical reasoning in the Critical Reasoning forum
“The conclusion is "Thus, as researchers claim, psychic phenomena will soon be explainable." The first sentence is nearly identical to this -- it tells us that yes, this is what they believe. The last sentence concludes "they''re right." The evidence is that psychic phenomena ...”
October 18, 2017
EconomistGMATTutor posted a reply to Simplify $$(4^y+4^y+4^y+4^y)\cdot(3^y+3^y+3^y)$$ in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$(4^y+4^y+4^y+4^y)\cdot(3^y+3^y+3^y)$$ Factor out 4^y and 3^y $$=\ 4^y\left(1+1+1+1\right).3^y\left(1+1+1\right)$$ $$=\ 4^y\left(4\right).3^y\left(3\right)$$ $$=\ 4^{y+1}.3^{y+1}$$ $$=\ \left(4\times3\right)^{y+1}$$ $$=\ ...” October 18, 2017 EconomistGMATTutor posted a reply to Critical reasoning in the Critical Reasoning forum “No need for a complicated explanation here. You ask why the answer is D, but it''s not -- it''s C. A higher percentage of the older cars were discarded, and that''s why a smaller percent were repaired. Make sense? If not, let me know.” October 18, 2017 EconomistGMATTutor posted a reply to If N is a positive integer... in the Problem Solving forum “Hello. If you see carefully the options on the list you can determine which is the correct answer. Let''s see option by option. - Option A: 30 30=2*3*5, so 30 has 3 different prime factors. OUT - Option B: 60 60=2*2*3*5, so 60 has 3 different prime factors. OUT. - Option C: 180 ...” October 18, 2017 EconomistGMATTutor posted a reply to Let f(x) denotes the sum of... in the Problem Solving forum “Hello LUANDATO. It is a really interesting question. The idea is that we must find the numbers of two digits such that the sum of their digits is: - 3, that is to say, f(x)=3, so that f(f(x))=f(3)=3. - 12, that is to say, f(x)=12, so that f(f(x))=f(12)=3. The numbers that satisfy this ...” October 18, 2017 EconomistGMATTutor posted a reply to Of the countries that were the world's twenty in the Critical Reasoning forum “The conclusion: These countries can serve as models for those countries that wish to keep their share of the global export trade stable over the years. The evidence: These countries had the same share of total world exports in 1984 as in 1953. This question asks you to weaken the ...” October 18, 2017 EconomistGMATTutor posted a reply to What is the perimeter... in the Problem Solving forum “Hello LUANDATO. Let''s take a look at your question. The area of a square is equal to L² where L is the lenght of the side of the square. So, we have$$L^2=\frac{9P^2}{16},$$this implies that$$L=\frac{3P}{4}.$$Now, the perimeter of a square is 4L. It is, ...” October 18, 2017 EconomistGMATTutor posted a reply to If the length and width of a rectangular garden plot in the Problem Solving forum “Hello lheiannie07. I will show you with an example how to determine the correct answer. Let''s take a rectangular garden whose length is 20 and its width is 10. So, its area is equal to 200. Now, if we increase each dimension by 20%, we will obtain that the new dimensions are 24 and 12 ...” October 18, 2017 EconomistGMATTutor posted a reply to Science, because people engage in it, is a socially embedded in the Critical Reasoning forum “This question presents you with many related pieces of evidence. The correct choice is the one that is supported by evidence -- in other words, a conclusion. The question itself gives you the beginning of the conclusion: Those who rely on scientific results should . . . ? The correct choice ...” October 18, 2017 EconomistGMATTutor posted a reply to Bird species around London in the Critical Reasoning forum “I''m available if you''d like any follow up.” October 17, 2017 EconomistGMATTutor posted a reply to Bird species around London in the Critical Reasoning forum “At the risk of being obvious, this is a NOT question. You want the choice that is NOT an assumption. Now . . . The conclusion: Similar air-pollution rules should be imposed in other major cities. (The word "should" is usually found in conclusions.) The evidence: In the years ...” October 17, 2017 EconomistGMATTutor posted a reply to Sentence balancing in the Critical Reasoning forum “Regarding Choice C -- as soon as you see that word "other," alarms should go off. Who gives a hoot about other infections? This argument is about strep reinfections.” October 17, 2017 EconomistGMATTutor posted a reply to Sentence balancing in the Critical Reasoning forum “A tricky one. The conclusion: Reinfection will probably be less common in cases where the new antibiotic is prescribed than in cases where either penicillin or erythromycin is prescribed. The evidence: A new antibiotic requires only a three-day course of treatment. The old one antibiotics ...” October 17, 2017 EconomistGMATTutor posted a reply to Set X consists of all two-digit primes and set Y in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. Set X consists of all two-digit primes.$$X=\left\{11,\ 13,\ 17,\ ...,\ 97\right\}$$Set Y consists of all positive odd multiples of 5 less than 100.$$Y=\left\{5,\ 15,\ 25,\ ...,\ 95\right\}$$Combine both the sets:$$XUY=\left\{5,\ ...”
October 17, 2017
EconomistGMATTutor posted a reply to A particular printer can print 96 pages in the Problem Solving forum
“Hi VJesus12, Let''s take a look at your question. The question states, A particular printer can print 96 pages in 25 minutes. Since, 48 pages are half the 96 pages, therefore, the printer will take half the time to print half the pages. It means, the printer will take 25/2 = 12.5 minutes to ...”
October 17, 2017
EconomistGMATTutor posted a reply to A straight picket fence is composed of x pickets each of whi in the Problem Solving forum
“Hi ardz24, Let''s take a look at your question. Since there are x pickets in the fence and each picket is 1/2 inch wide, so width of all x pickets will be (1/2)x Now, lets find the total gap between x pickets. If there are only 2 pickets, the gap between them is (2-1)(6) = (1)(6) = 6 inches ...”
October 17, 2017
EconomistGMATTutor posted a reply to If each of the following fractions... in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. To find the number of digits to the right of the decimal point, we need to convert the fractions to decimals. $$\frac{1}{8}=0.125$$ $$\frac{1}{5\ }=0.2$$ $$\frac{1}{3}=0.3333...$$ $$\frac{2}{3}=0.6666...$$ $$\frac{3}{4}=0.75$$ ...”
October 17, 2017
EconomistGMATTutor posted a reply to Which of the following numbers in the Problem Solving forum
“Hi lheiannie07, Let''s take a look at your question. To find the greatest distinct prime factors we need to factorize all the numbers in the options. Prime factors of 165 = 3 * 5 * 11 Distinct Prime factors of 165 = 3, 5, 11 165 has 3 distinct prime factors. Prime factors of 192 = 2 * 2 * ...”
October 16, 2017
EconomistGMATTutor posted a reply to In dividing a number by 585 in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. The question states that when the number is divided by 5 the remainder is 4. Let the number be x and q be the quotient, then $$x=5p+4 --- (i)$$ The successive division by 9 result into the remainder 8. $$p=9q+8 --- (ii)$$ ...”
October 16, 2017
EconomistGMATTutor posted a reply to In a sequence a1,a2,a3,… in the Problem Solving forum
“Hi LUANDATO, Let''s take a look at your question. $$a_1=2$$ $$a_2=-2+1=-1$$ $$a_3=-\left(-1\right)+1=1+1=2$$ $$a_4=-2+1=-1$$ $$a_5=-\left(-1\right)+1=1+1=2$$ Since, all odd terms are 2 and all even terms are -1, therefore, $$a_{99}=2$$ The sequence will be like, $$2,\ ...” October 16, 2017 EconomistGMATTutor posted a reply to The function f is defined for all in the Problem Solving forum “Hi LUANDATO, Let''s take a look at your question. The question statement should be like: The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p ...” October 16, 2017 EconomistGMATTutor posted a reply to 500 PS #5 in the Problem Solving forum “Hi dunkin77, The correct answer is 1.62. Answer choices seems incorrect.” October 15, 2017 EconomistGMATTutor posted a reply to If the sum of two prime numbers x and y is odd, in the Problem Solving forum “Hi VJesus12, Let''s take a look at your question. The question states that the sum of two prime numbers x and y is odd. Sum of two numbers is odd only when one number is even and the other is odd. SUM (ODD) = EVEN NUMBER + ODD NUMBER Now, we will see if the product of an even number and ...” October 15, 2017 EconomistGMATTutor posted a reply to Arithmetic- roots in the Problem Solving forum “Hi Roland2rule, Let''s take a look at your question.$$\sqrt{98}+\sqrt{72}=?$$Simplify the square roots,$$=\sqrt{2\times7\times7}+\sqrt{2\times6\times6}=7\sqrt{2}+6\sqrt{2}=\sqrt{2}\left(7+6\right)=13\sqrt{2}=\sqrt{2\times13\times13}=\sqrt{338}$$...” October 15, 2017 EconomistGMATTutor posted a reply to Algebra in the Problem Solving forum “Hi Roland2rule, Lets take a look at your question.$$\left(3+a\right)\left(\frac{a}{10}-0.4\right)=-1$$In the first step, we will simplify the equation,$$\left(3+a\right)\left(\frac{a-4}{10}\right)=-1$$Multiply both sides of the equation by 10, ...” October 15, 2017 EconomistGMATTutor posted a reply to When Leo imported a certain item, he paid a 7 in the Problem Solving forum “Hi Vjesus12. You have to be careful here. The statement says that Leo paid a 7% import tax on the portion of the total value of the item in excess of 1000. Let''s suppose that X is the total value of the item. According to the statement above,$$X>1000$$and we have to calculate 7% of the ...” October 14, 2017 EconomistGMATTutor posted a reply to If the sum of two prime numbers x and y is odd, in the Problem Solving forum “Hello Vjesus12. First of all, not all the prime numbers are odd numbers. The number 2 is the only prime number which is an even number. Now, if we add two odd numbers the result will be an even number. This is not our situation. We have the result of the sum is an odd number. The only way ...” October 14, 2017 EconomistGMATTutor posted a reply to The “primeness” in the Problem Solving forum “Hi lheiannie07, Let''s take a look at your question. The question states that the “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. To find the greatest primeness, we will find the primeness of each number given one by ...” October 13, 2017 EconomistGMATTutor posted a reply to The total remittance transfers in the Sentence Correction forum “Hello! The main problem with both D and E is the incorrect use of punctuation to create non-essential clauses. By putting the phrases "almost 100 billion annually" and "an amount that is almost 100 billion annually" between commas or hyphens, they now become non-essential ...” October 13, 2017 EconomistGMATTutor posted a reply to OG Between 14,000 and 8,000 b.c. in the Sentence Correction forum “Hello! Let''s break down each answer for its individual problems. A: Correct answer; no question of what -ing phrase is referring to B: By saying "to uncover," it suggests that the ice cap somehow chose to melt because it wanted to uncover land. I know it sounds nutty to think about ...” October 13, 2017 EconomistGMATTutor posted a reply to SC|after the drought in the Sentence Correction forum “Hello! Answer A suggests that the drought caused the cattle loss, though I can totally see why it''s confusing for some readers. Other than that, I don''t see anything wrong with how it''s worded. If I had to pick a more clearly worded answer, I would go with answer C. It splits up the drought ...” October 13, 2017 EconomistGMATTutor posted a reply to What is the sum of the multiples of 7 from 84 to 140? in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. First of all we need to find the number of terms between 84 to 140 inclusive. Since we are talking about multiples of 7, lets find out the term numbers of 84 and 140 in the sequene of multiples of 7.$$\frac{84}{7}=12$$84 is 12th term. ...” October 13, 2017 EconomistGMATTutor posted a reply to Designed to attract maximum attention in the Sentence Correction forum “Hello! When you''re dealing with modifiers, it''s best to start by finding the modifier. In this case, it''s the phrase "designed to attract maximum attention." Next, figure out what that phrase is referring to - what is designed to attract maximum attention? In this case, it''s ...” October 13, 2017 EconomistGMATTutor posted a reply to percentage and interest in the Problem Solving forum “Hi Roland2rule, Lets take a look at your question. Let the property X has original value of x, then, it sale price i.e. 30,000 at 20% profit can be represented as:$$x\ +\ \left(20\%\right)x=30,000x\ +\ \left(\frac{20}{100}\right)x=30,000x\ +\ \left(0.2\right)x=30,000$$...” October 13, 2017 EconomistGMATTutor posted a reply to Lines y=√3x−2 and y=2√3x−5 in the Problem Solving forum “Hi Vincen, Let''s take a look at your question. It seems that you have typed the question incorrectly. I assume that the question you typed in the subject line is correct.$$y=\sqrt{3}x-2 --- (i)$$and$$\ y=2\sqrt{3}x-5---(ii)$$From Equation (i) we can write,$$\sqrt{3}x=y+2 --- (iii) ...”
October 13, 2017
EconomistGMATTutor posted a reply to The tiny nation of Navatanya won seven... in the Critical Reasoning forum
“Hi. Since you''ve figured out what''s wrong with A, let''s look at Choice C. The question presents you with evidence and then asks you for a conclusion -- something that must be true. Choice C is sly. It says that some of the athletes from Navatanya who competed at the last Olympics will not ...”
October 13, 2017
EconomistGMATTutor posted a reply to Senator Janice White is quietly lobbying in the Critical Reasoning forum
“The passage provides a good deal of evidence, some in the form of if-then statements. The question asks you for the choice that is false. In other words, the correct answer choice is a conclusion: Based on the evidence above, it is conclusively false that . . . You''ve asked about Choice C. ...”
October 13, 2017