iwillsurvive101

iwillsurvive101

Brent@GMATPrepNow posted a reply to Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} in the Problem Solving forum
“The test-makers like to test the following concept: If we take a set of numbers with a Standard Deviation of X and add k to each value in the set, the resulting set will still have a Standard Deviation of X. This should make sense, since Standard Deviation is a measurement of dispersion (i.e., how ...”
Today
Brent@GMATPrepNow posted a reply to If \(\sqrt{3-2x} = \sqrt{2x} +1\), then \(4x^2\) in the Problem Solving forum
“GIVEN: √(3-2x) = √(2x) +1 Square both sides to get: [√(3-2x)]² = [√(2x) +1]² Expand and simplify to get: 3 - 2x = 2x + 2√(2x) + 1 Subtract 1 from both sides to get: 1 - 2x = 2x + 2√(2x) Subtract 2x from both sides to get:2 - 4x = 2√(2x) Divide both sides by 2 to ...”
Today
Brent@GMATPrepNow posted a reply to Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to in the Problem Solving forum
“GIVEN: oil: vinegar : water = 3 : 2 : 1 Let''s first try to use ALL 8 cups of oil Take 3 : 2 : 1 and multiply all 3 parts by 8/3 to get the EQUIVALENT ratio 8 : 16/3 : 8/3 Simplify to get: 8 : 5 1/3 : 2 2/3 So, in this case, the dressing is comprised of 8 cups of oil, 5 1/3 cups of vinegar, ...”
Today
GMATGuruNY posted a reply to Tom travels the same distance in 4 steps as Alice travels in in the Problem Solving forum
“Since each of Alice''s steps = 36 cm, the distance traveled by Alice in 5 steps = 5*36 = 180 cm. Since Tom requires only 4 steps to travel this 180-cm distance, each of Tom''s steps = 180/4 = 45 cm. Thus, the distance traveled by Tom in 18 steps = 18*45 = 810 cm. The correct answer is E.”
Today
GMATGuruNY posted a reply to Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to in the Problem Solving forum
“Since oil:vinegar:water = 3:2:1, we get: part attributed to oil = 3 cups part attributed to vinegar = 2 cups part attributed to water = 1 cup sum of the parts = 3+2+1 = 6 cups Since Larry has 8 cups of oil, we get: (available oil)/(part attributed to oil) = 8/3. The fraction in blue implies ...”
Today
Ian Stewart posted a reply to Is x > y ? in the Data Sufficiency forum
“It''s possible to answer a question like this by adding inequalities, but I think it''s a difficult way to solve this type of problem. Neither Statement is sufficient alone (though you need to consider a negative value for x to see that Statement 2 is not sufficient). Using both Statements, we ...”
Yesterday
Brent@GMATPrepNow posted a new topic called Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} in the Problem Solving forum
“Set A = {22, 27, 11, 12, 2}, and set B: {14, 19, 3, 4, x} If x < 0, and the standard deviation of set A = the standard deviation of set B, what is the value of x? A) -2 B) -3 C) -4 D) -5 E) -6 Difficulty level: 600-650 Answer: E Source: www.gmatprepnow.com”
Yesterday
Brent@GMATPrepNow posted a reply to x, y and p are integers, and xyp ≠ 0. in the Problem Solving forum
“Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = POSITIVE and (POSITIVE)^(EVEN integer) ...”
Yesterday
GMATGuruNY posted a reply to Working together at their respective constant rates, Machine in the Problem Solving forum
“The prompt should read as follows: Since A+B take 8 hours to produce 1200 units, the combined rate for A+B = w/t = 1200/8 = 150 units per hour. Since B take 50% more time than the 8 hours required when A+B work together, B''s time = 8 + (50% of 8) = 8 + 4 = 12 hours. Since B takes 12 ...”
Yesterday
Brent@GMATPrepNow posted a new topic called x, y and p are integers, and xyp ≠ 0. in the Problem Solving forum
“x, y and p are integers, and xyp ≠ 0. If p^x < p^y, which of the following MUST be true? i) x − y < 0 ii) x < 2y iii) x^p < y^p A) i only B) ii only C) iii only D) i and ii only E) none of the above Difficulty level: 650-700 Answer: E Source: ...”
July 15, 2019
Brent@GMATPrepNow posted a reply to Five friends play blackjack in Las Vegas and lose an average in the Problem Solving forum
“Let A, B, C, D and E represent the LOSSES (in dollars) of the 5 friends Five friends play blackjack in Las Vegas and lose an average of $100 each. So, we can write: (A+B+C+D+E)/5 = 100 Multiply both sides by 5 to get: A+B+C+D+E = 500 If the losses of two of the friends total $380, what is ...”
July 15, 2019
Ian Stewart posted a reply to A library bought b books for its collection. What was the in the Data Sufficiency forum
“All you know using both Statements is that the books cost at least (40)(12.50) dollars, but we have no way to work out the exact cost, so the answer is E.”
July 15, 2019
Ian Stewart posted a reply to A certain shop only sells items for a whole number of dollar in the Data Sufficiency forum
“For every additional item she buys, the total price will be one additional cent less than a round number of dollars. So if she buys one item, the total price will end in .99, if she buys two items it will end in .98, and so on. So if the price ended in .72, she must have bought 28 items (she can''t ...”
July 15, 2019
Ian Stewart posted a reply to It takes Amy between 6 and 7 minutes to grill a steak, and in the Data Sufficiency forum
“Statement 1 is not sufficient because we don''t know how much time she has, and Statement 2 is not sufficient because we don''t know how many steaks she needs. Using both, it will take her at most 4*7 = 28 minutes to grill four steaks, so if she has 30 minutes, she has enough time, and the two ...”
July 15, 2019
GMATGuruNY posted a reply to Tom painted 1/3 of a wall red, 1/5 of the wall blue and the in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the total area. When the correct answer is plugged in, the area painted black = 238. Since 1/3 of the wall is painted red, it is almost certain that correct answer is a multiple of 3. For an integer to be a multiple of 3, its digit sum must be a ...”
July 15, 2019
Ian Stewart posted a reply to If \(x, y\), and \(z\) are positive integers such that in the Data Sufficiency forum
“The factors of 57 are all odd. If x and y are two different primes, and x+y equals one of those odd factors, one of x or y must be even. But the only even prime is 2, and 2 is the smallest prime, so if x < y, then x = 2 must be true. So x is certainly a factor of the even number z, and Statement ...”
July 14, 2019
GMATGuruNY posted a reply to There are three varieties of sugar in a store. Sugar S1 in the Data Sufficiency forum
“Statement 1: Case 1: A=10 kg and B=10 kg, for a total of 20 kg In this case, A=B, so the answer to the question stem is NO. Case 2: A=11 kg and B=9 kg, for a total of 20 kg In this case, A>B, so the answer to the question stem is YES. Since the answer is NO in Case 1 but YES in Case 2, ...”
July 14, 2019
Brent@GMATPrepNow posted a reply to If k is an integer and 2 < k < 7, for how many differe in the Problem Solving forum
“IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . . DIFFERENCE between A and B < length of third side < SUM of A and B We''re told that the two KNOWN sides have lengths 2 and 7 So, we can write: (7 - 2) < k < (7 + 2) Simplify: 5 < k < 9 Since k is an ...”
July 14, 2019
GMATGuruNY posted a reply to In the figure shown, what is the value of x? in the Data Sufficiency forum
“Neither statement alone is sufficient to determine the value of x. When we combine the two statements, here''s an efficient way to determine whether we have sufficient information. 1. Plug in values for all of the angle measurements, satisfying the constraints in the problem and the rules of ...”
July 14, 2019
Brent@GMATPrepNow posted a reply to For the 5 days shown in the graph, how many kilowatt-hours in the Problem Solving forum
“Where''s the graph? Cheers, Brent”
July 13, 2019
Ian Stewart posted a reply to A marketer bought \(N\) crates of empty cardboard gift boxes in the Problem Solving forum
“The person bought NQ boxes in total, then packaged sets of J boxes together, so sold a total of NQ/J sets. If those sold for P dollars each, the revenue was PNQ/J dollars. The profit was the revenue minus the expense, W, so the profit Z is given by: Z = PNQ/J - W We need to solve for P: Z+W ...”
July 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are both integers greater than 1, is x a multiple in the Data Sufficiency forum
“Target question: Is x a multiple of y? Asking whether x is a multiple of y is the same as asking whether x = (y)(some integer) For example, 12 is a multiple of 3 because 12 = (3)(4) So, let''s rephrase the question as... REPHRASED target question: Does x = (y)(some integer)? Statement 1: ...”
July 12, 2019
Brent@GMATPrepNow posted a reply to In how many different ways can 3 identical green shirts and in the Problem Solving forum
“We can take this question and ask an easier question: In how many ways can we choose 3 of the 6 children to receive a green shirt? Notice that, once we have given a green shirt to each of those 3 chosen children, the remaining children must get red shirts. In other words, once we have given ...”
July 12, 2019
Brent@GMATPrepNow posted a reply to Bill took 4 math tests, and each test received a score out in the Data Sufficiency forum
“Target question: What was Bill''s average (arithmetic mean) score for all 4 tests? Statement 1: Bill''s first 3 tests received an average score of 50. Since we don''t have any information about the 4th test, statement 1 is NOT SUFFICIENT Statement 2: Bill''s last 2 tests received an ...”
July 12, 2019
Brent@GMATPrepNow posted a reply to Did Insurance Company \(K\) have more than $300 million in in the Data Sufficiency forum
“Target question: Did Insurance Company \(K\) have more than $300 million in total net profits last year? Jump straight to... . . . Statements 1 and 2 combined Statement 2 tells us about profits from ONE PART of Company K''s business. Statement 1 tells us a tiny bit about Company K''s ...”
July 12, 2019
GMATGuruNY posted a reply to Between the first day of May and last day in June, the price in the Problem Solving forum
“We can PLUG IN THE ANSWERS. When the correct answer is plugged in, Blue''s resulting price and Melange''s resulting price will be EQUAL. D: 100 Here, Blue''s initial price is 100% of Melange''s initial price, implying that the two initial prices are equal. Let Blue = May = $100. From May to ...”
July 12, 2019
Ian Stewart posted a reply to n points are equally spaced on a circle, where n is an even in the Problem Solving forum
“I did this the same way Scott did - with those answer choices, it''s a very fast question. I doubt they meant to make the question so easy to answer. If we had better-chosen answer choices, and needed to actually solve: if you connect three points on a circle, you only get a right triangle if ...”
July 11, 2019
GMATGuruNY posted a reply to What is the remainder when a is divided by 4? in the Data Sufficiency forum
“Statement 1: An odd integer can be written as follows: 2x+1, where x is an integer. Since a is the square of an odd integer, we get: a = (2x+1)² = (2x)² + 2(2x)(1) + 1² = 4x² + 4x + 1 = 4(x²+x) + 1 = (multiple of 4) + 1 Since a is equal to 1 more than a multiple of 4, dividing a by 4 will ...”
July 11, 2019
Brent@GMATPrepNow posted a reply to a, b, c, d satisfy a-1=b+2=c-3=d+4. Which of a, b, c, d is t in the Problem Solving forum
“Rewrite each value in terms of the same variable. Given: a - 1 = b + 3 Subtract 3 from both sides to get: b = a - 4 Given: a - 1 = c - 3 Add 3 to both sides to get: c = a + 2 Given: a - 1 = d + 4 Subtract 4 from both sides to get: d = a - 5 So, a, b, c and d are equal to a, a-4, a+2 ...”
July 10, 2019
Ian Stewart posted a reply to At the close of the market on Monday, the price of a certain in the Problem Solving forum
“The stock first increases from $100 to $120. This increases a further 10%, so by $12, to $132. This then decreases by 30%, so we''re multiplying it by 0.7, and we get (7/10)(132) = $92.4.”
July 10, 2019
Ian Stewart posted a reply to While making a non-stop trip, a bus averaged m mph for the in the Data Sufficiency forum
“The total distance traveled was 5m + 4n, and the total time was 9 hours, so the average speed we want to find is (5m + 4n)/9. In Statement 1, if we divide by 1.5 on both sides, we get 5m + 4n = 310, so the average speed for the trip was 310/9. From Statement 2 we can''t find 5m + 4n, so we ...”
July 10, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #8: - Choosing Good Numbers Video: https://www.youtube.com/watch?v=bu-WhqM0j1Q Cheers, Brent”
July 9, 2019
Ian Stewart posted a reply to If Anil can finish a job in 4 hours and Gustavo can finish in the Problem Solving forum
“Anil would do 3 jobs in 12 hours, Gustavo 2 jobs in 12 hours, so together 5 jobs in 12 hours, and thus 1 job in 12/5 hours = 2.4 hours = 2 hours and 24 minutes.”
July 9, 2019
Ian Stewart posted a reply to What is the length of line segment \(AB\) in the figure in the Problem Solving forum
“If we draw a vertical height from A down to BC, that divides the triangle into a 45-45-90 triangle on the left, and a 30-60-90 triangle on the right. The hypotenuse of the 45-45-90 is AC, so is of length 1, and the height we''ve drawn is thus of length 1/√2 = √2/2 (since the sides of a 45-45-90 ...”
July 9, 2019
Ian Stewart posted a reply to If \(A\) and \(B\) are consecutive positive integers less in the Data Sufficiency forum
“Clearly neither Statement is sufficient alone. Using both, the only positive cubes less than 100 are 1, 8, 27 and 64, and the only cube that is one away from a positive perfect square is 8 (since it''s one less than 9), so B = 9, and the answer is C.”
July 9, 2019
Ian Stewart posted a reply to For a set \(X\) containing \(n\) integers, is the mean even? in the Data Sufficiency forum
“If the set is {2, 4}, the mean is 3, so is odd, and if the set is {2, 6}, the mean is 4, so is even. So using both Statements we cannot answer the question and the answer is E.”
July 9, 2019
GMATGuruNY posted a reply to If m and n are positive integers and r is the remained when in the Data Sufficiency forum
“5(10^n) = 5 followed by n zeros. If n=1, then 5(10^n) = 5*10¹ = 5 followed by 1 zero = 50 If n=2, then 5(10^n) = 5*10² = 5 followed by 2 zeros = 500 If n=3, then 5(10^n) = 5*10³ = 5 followed by 3 zeros = 5000 Rule: An integer whose digits sum to a multiple of 3 is itself a multiple of 3. ...”
July 9, 2019
GMATGuruNY posted a reply to What is 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56? in the Problem Solving forum
“1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 = 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + (1/5 - 1/6) + (1/6 - 1/7) + (1/7 - 1/8) = 1/2 + 1/2 - 1/8 = 1 - 1/8 = 7/8 The correct answer is C.”
July 9, 2019
Brent@GMATPrepNow posted a reply to A certain candy manufacturer reduced the weight of Candy Bar in the Problem Solving forum
“Let''s assign nice values to the ORIGINAL weight and price of the candy bar. Let''s say it ORIGINALLY weight 100 ounces and cost $100 $1 per ounce If we decrease the weight be 20%, the NEW weight is 80 ounces. The price remains at $100 per bar So, the NEW price per ounce =$100/80 ounces = ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to While driving on the expressway, did Robin ever exceed the in the Data Sufficiency forum
“NOTE: There''s nothing here to suggest that Robin''s speed was constant. Sure, she MIGHT have traveled at a constant speed, or her speed may have varied throughout the trip. Target question: Did Robin''s speed ever exceed 55 miles per hour? Statement 1: Robin drove 100 miles No information ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when positive integer x is divided by in the Data Sufficiency forum
“Target question: What is the remainder when positive integer x is divided by 5? Statement 1: x divided by 10 has a remainder of 7. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to If x and y are greater than 0, is x = 1 ? in the Data Sufficiency forum
“Target question: Is x = 1 ? Given: x and y are POSITIVE Statement 1: x/y = 1 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, x DOES equal 1 Case b: ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to The function f(a) is defined for all positive integers a as in the Problem Solving forum
“Since 77 = (11)(7), any positive multiple of 7 or 11 will have a common factor with 77 where that common factor is greater than 1. For example, 77 and 14 share a common factor of 7. And 77 and 35 share a common factor of 7. Likewise, 77 and 55 share a common factor of 11. And 77 and 33 share ...”
July 8, 2019
Brent@GMATPrepNow posted a reply to The table above shows the number of students in a certain in the Data Sufficiency forum
“ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I''ll treat it as such. Target question: What is the total number of students in the class? Statement 1: Of the boys in the class, 15 are studying biology. Add this information to our diagram to get: ...”
July 8, 2019
Ian Stewart posted a reply to A certain list of 300 test scores has an arithmetic mean of in the Problem Solving forum
“It''s a near-verbatim copy of this GMATPrep question, they just changed a couple of numbers: https://www.beatthegmat.com/standard-deviation-t45521.html”
July 8, 2019
Brent@GMATPrepNow posted a reply to The table above shows the number of students in a certain in the Data Sufficiency forum
“ASIDE: Since the diagram closely resembles a Double Matrix Method diagram, I''ll treat it as such. Target question: What is the total number of students in the class? Statement 1: Of the boys in the class, 15 are studying biology. Add this information to our diagram to get: ...”
July 7, 2019
Brent@GMATPrepNow posted a reply to If x is a positive integer such that x^2 + 5x − 14 = 0, wh in the Problem Solving forum
“GIVEN: x² + 5x − 14 = 0 Factor: (x + 7)(x - 2) = 0 So, EITHER x = -7 OR x = 2 Since we''re told x is POSITIVE, the correct answer is D Cheers, Brent”
July 7, 2019
GMATGuruNY posted a reply to Inequalities :If x is an integer, what is the value of x? in the Data Sufficiency forum
“In statement 1, |x²| is redundant: since x² cannot be negative, |x²| = x². Statement 1: |x-x²|=2 x - x² = ±2 x(1-x) = ±2. The resulting equation implies that x is a factor of ±2, yielding the following options: x=±1 or x=±2. Check which of these values are valid solutions for ...”
July 7, 2019
Ian Stewart posted a reply to If \(m\) and \(n\) are positive integers and \(r\) is the in the Data Sufficiency forum
“If you want a number''s remainder when you divide it by 3, you can sum the digits of the number and take the remainder by 3 of that sum. The sum of the digits of (5)(10^n) is always going to be 5 no matter what n equals, so we only need the value of m. If m = 1, then the digits of (5)(10^n) + m will ...”
July 7, 2019
Ian Stewart posted a reply to A bigger circle (with center A) and a smaller circle (with in the Data Sufficiency forum
“Using Statement 1, there''s only one way to draw the diagram, and we know a length, so from Statement 1 alone it must be possible to find every length - there''s no need to solve anything. If we wanted to actually solve, you could draw the lines AS and BT and notice that the two right triangles ...”
July 7, 2019
Ian Stewart posted a reply to Ann and Bob planted trees on Friday. What is the ratio of in the Data Sufficiency forum
“For Statement 1, if Bob planted 1 tree, then Ann planted 21, and the ratio is 1 to 21. But if Bob planted 1 billion trees, the ratio is very close to 1 to 1, so Statement 1 is not sufficient. For Statement 2, for every 10 trees Bob planted, Ann planted 11, so the ratio is 10 to 11 and Statement 2 ...”
July 7, 2019
GMATGuruNY posted a reply to What is the value of n in the equation: - 25 + 19 + n = s ? in the Data Sufficiency forum
“What do we want? The value of n. Before we look at the statements, what do we have? A linear equation with two variables (n and s). To answer the question stem, what do we need? Another linear equation with one or both of the variables. Each statement gives us what we need and thus is ...”
July 6, 2019
Brent@GMATPrepNow posted a reply to What is the value of n in the equation: - 25 + 19 + n = s ? in the Data Sufficiency forum
“ Given: -25 + 19 + n = s Simplify: -6 + n = s Add 6 to both sides to get: n = s + 6 Target question: What is the value of n? Statement 1: s = 2 We already know that n = s + 6 Replace s with 2 to get: n = 2 + 6 = 8 The answer to the target question is n = 8 Since we can answer the ...”
July 6, 2019
Ian Stewart posted a reply to The average American spends y dollars on food per month, in the Problem Solving forum
“Whose food purchases? As the question is written, it''s impossible to tell what they''re asking for. Assuming they mean to ask about the spending of an average American: with no discount, they''d spend $9y in nine months. They save x% in one month, so save (x/100)y = xy/100 dollars in one month. So ...”
July 6, 2019
Ian Stewart posted a reply to George bought a large electronic item with a 15% off coupon, in the Problem Solving forum
“That''s a lot of words for such a straightforward setup. When he pays back half of the additional 15% discount, he is paying back 7.5% of the original price of the item. So $40.50 is 7.5% of the original price, and doubling everything, $81 is 15% of the original price. Of course we could do algebra ...”
July 6, 2019
Ian Stewart posted a reply to Point \(P\) lies on the equation \(y=x^2−1\) and Point \(Q in the Problem Solving forum
“If y = x^2 - 1, then since x^2 is at least zero, the smallest possible value of y is -1. If y = -x^2 + 1, then since -x^2 is at most zero, the largest possible value of y is 1. So the answer is -1 - 1 = -2.”
July 6, 2019
Ian Stewart posted a reply to Line \(k\) is in the rectangular coordinate system. If line in the Problem Solving forum
“If (a, b) is on the x-axis, then b is zero. So the line intersects the x-axis at (a, 0), and if (a, 0) is on the line, that point must ''work'' in the line''s equation. Plugging in x=a and y=0 we get 3(0) = 2(a) + 6 2a = -6 a = -3”
July 6, 2019
Ian Stewart posted a reply to What is the probability that the sum of two dice will yield in the Problem Solving forum
“If you roll one die, you can always make a sum of 7 if you get the perfect roll on the second die. There''s a 1/6 chance you roll the perfect number, so that''s the probability of getting a sum of 7. The probability we do that twice in a row is (1/6)(1/6) = 1/36. You could get down to A or B ...”
July 6, 2019
Ian Stewart posted a reply to Three friends, A, B and C have houses along a straight road, in the Data Sufficiency forum
“They''ll travel the minimum combined distance if they meet in the middle house, B. Then person B won''t travel at all, and persons A and C will travel, combined, the total distance between house A and house C (if instead they meet at house A or C, one person travels the total distance from A to C, ...”
July 6, 2019
GMATGuruNY posted a reply to If a coin has an equal probability of landing heads up or in the Problem Solving forum
“P(HHT) = 1/2 * 1/2 * 1/2 = 1/8. Since T can occur on the 1st, 2nd or 3rd flip, we multiply by 3: 3(1/8) = 3/8 = 0.375 The correct answer is C.”
July 6, 2019
Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum
“BTW, you posted the same question in January: https://www.beatthegmat.com/the-price-of-a-phone-call-consists-of-a-standard-connection-t305974.html Cheers, Brent”
July 5, 2019
Brent@GMATPrepNow posted a reply to The price of a phone call consists of a standard connection in the Problem Solving forum
“Let C = price of connection fee Let M = the price PER MINUTE A 10-minute call costs $2.90 We can write: C + 10M = 2.90 A 16-minute call costs $4.40. We can write: C + 16M = 4.40 How much does a 13-minute call cost? So far, we have: C + 10M = 2.90 C + 16M = 4.40 ONE (slower) ...”
July 5, 2019
Ian Stewart posted a reply to A bag contains ping pong balls, each with a number written in the Data Sufficiency forum
“It''s a weighted average -- if 1/3 of the pingpong balls average to 20, and all of them average to 50, the other 2/3 will need to average to 65 (since there are twice as many of them as in the 1/3 group, their average will need to be "twice as close" to the overall average). Statement 2 ...”
July 5, 2019
Ian Stewart posted a reply to Q. Is ABC an equilateral triangle? in the Data Sufficiency forum
“Statement 1 alone only ensures the triangle is isosceles. From Statement 2, two sides are equal, so two angles must be equal. We also know one angle is 60 degrees. If that''s one of the two equal angles, we have two 60 degree angles, and the third angle then must also be 60 degrees (because a ...”
July 5, 2019
Brent@GMATPrepNow posted a reply to A certain family has 3 sons: Richard is 6 years older than in the Problem Solving forum
“We can also solve this with 1 variable David is 8 years older than Scott Let x = Scott''s age NOW So, x + 8 = David''s age NOW Richard is 6 years older than David If x + 8 = David''s age NOW, then... (x + 8) + 6 = Richard''s age NOW In other words, x + 14 = Richard''s age NOW In in 8 ...”
July 4, 2019
GMATGuruNY posted a reply to The British Admiralty and the War Office in the Sentence Correction forum
“Neuroscientists are now drawing solid conclusions about the disease. Here, the disease serves as the object of the preposition about. A clause includes both a subject and a verb. A clause may function as a noun. SC720 in the OG18: Neuroscientists are now drawing solid conclusions about how ...”
July 4, 2019
Ian Stewart posted a reply to What is the range of a set consisting of the first 100 multi in the Problem Solving forum
“The range of one hundred consecutive multiples of 7 will always be the same no matter what the smallest value in your list is, so we can just find the range of 7, 14, 21..., 693, 700, which is 700-7 =693.”
July 4, 2019
Ian Stewart posted a reply to Patrick is cleaning his house in anticipation of the arrival in the Data Sufficiency forum
“Statement 1 tells us he can do two of the tasks well before the guests arrive, but we don''t know how long putting the dishes away will take, so Statement 1 is not sufficient. Statement 2 tells us that he''ll need 55+7 = 62 minutes to wash and put away the dishes, so he can''t finish that in less ...”
July 4, 2019
GMATGuruNY posted a reply to What is the number of solutions of x = |x-|30-2x||? in the Problem Solving forum
“|x-|30-2x|| = x if the blue portion is equal to x or -x. Case 1: x-|30-2x| = x 0 = |30-2x| The equation above is valid if 30-2x=0: 30-2x = 0 30 = 2x 15 = x Case 2: x-|30-2x| = -x 2x = |30-2x| Case 2a: 2x = 30-2x 4x = 30 x = 30/4 = 7.5 Case 2b: -2x = 30-2x 0 = 30 Not valid. ...”
July 4, 2019
Brent@GMATPrepNow posted a reply to When the positive integer x is divided by 11, the quotient in the Problem Solving forum
“A fast approach is to find a value of x that meets the given conditions. When the positive integer x is divided by 11, the quotient is y and the remainder 3. When x is divided by 19, the remainder is also 3.... Notice that x = 3 meets the above conditions. 3 divided by 11 = 0 with remainder ...”
July 3, 2019
Brent@GMATPrepNow posted a reply to A palindrome, such as 12321, is a number that remains the sa in the Problem Solving forum
“If a number is divisible by 4, then the number created by the last 2 digits is divisible by 4. For example, we know that 76512, 311,244 and 2128 are divisible by 4 because 12, 44, and 28 are divisible by 4 So, the last 2 digits of the 4-digit palindromes must be 00, 04, 08, 12, . . . , 92 or ...”
July 3, 2019
Ian Stewart posted a reply to When the positive integer x is divided by 11, the quotient in the Problem Solving forum
“There''s an old GMATPrep question that is almost identical to this one. Since the value of x can be 3, the quotient can be 0 (when we divide 3 by 11, the quotient is zero and the remainder is 3), so if one of the five answers is right, it has to be E. Or, if one wants a proper ''proof'', then the ...”
July 3, 2019
Ian Stewart posted a reply to In 2008, a certain factory produced 25% more widgets than it in the Problem Solving forum
“If we start with 100 widgets in 2007, we have 125 in 2008, and then (1.2)(125) = 150 in 2009. For this to decrease to 100, it needs to fall by 50, or by 50/150 = 33 1/3 %.”
July 3, 2019
GMATGuruNY posted a reply to The LCM of three numbers is four times their GCF. Which of in the Problem Solving forum
“Try to prove that I, II and III DON''T have to be true. To disprove I -- which states that at least one number must be odd -- let the GCF = 2. Since the LCM = 4(GCF), the LCM = 8. In this case: The greatest factor common of all three numbers must be 2. The least value divisible by all 3 ...”
July 3, 2019
Brent@GMATPrepNow posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum
“Thanks Ian. Not sure how I missed "unique." Thanks for clarifying. Cheers, Brent”
July 2, 2019
Ian Stewart posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum
“To answer Brent''s question, when they say x, y and z are "unique numbers", I''m guessing they''re trying to say that the selection is being done without replacement. But it''s mathematically wrong to present a probability question this way (and I missed their ''unique'' comment the first ...”
July 2, 2019
Brent@GMATPrepNow posted a reply to x, y and z are all unique numbers. If x is chosen randomly in the Problem Solving forum
“Are the numbers chosen with or without replacement? For example, can y and z both be 23?”
July 2, 2019
Ian Stewart posted a reply to In a group of 100 adults, 75 percent of the women are left- in the Problem Solving forum
“The question is unanswerable if some people could be ambidextrous. Assuming everyone is either left or right-handed, we know that among women, the ratio of left to right-handed people is 3 to 1. So if 12 women are right-handed, 36 are left-handed, and there are 48 women in total. There are thus ...”
July 2, 2019
Ian Stewart posted a reply to What is the value of y? in the Data Sufficiency forum
“Using Statement 1, y can be 29, 31 or 33. Using Statement 2, y can be 32.7 or 33 or 35.419 among other possibilities. Using both Statements, y can only be 33, so the answer is C.”
July 2, 2019
GMATGuruNY posted a reply to In addition to her work on the miocene homicide fossil in the Sentence Correction forum
“A possessive such her may serve to refer to a preceding possessive. More importantly, her is a personal pronoun. Only a PERSON or PEOPLE may serve as referent for a personal pronoun (he, she, him, his, her). Since only a person or people may serve as referent for a personal pronoun -- and a ...”
July 1, 2019
Ian Stewart posted a reply to The LCM of three numbers is four times their GCF. Which of in the Problem Solving forum
“The numbers could be 2, 4, and 8, so I and II need not be true. That leaves only answer B.”
July 1, 2019
Ian Stewart posted a reply to The numbers in which of the following pairs do NOT have a in the Problem Solving forum
“32 = 2^5 has only one prime divisor, so it could never have a "pair" of distinct prime divisors in common with any other number. So the answer is C.”
July 1, 2019
Ian Stewart posted a reply to Suppose x is a positive even number, all of whose digits in the Problem Solving forum
“If the number is even, and its digits are all 3s and 4s, it must end in 4. If the number is divisible by 4, its last two digits must form a multiple of 4, so must be "44" (and not "34"). If the number is divisible by 3, the sum of its digits is a multiple of 3, and we can see ...”
July 1, 2019
Ian Stewart posted a reply to a and b are integers such that a/b=3.45. If R is the remaind in the Problem Solving forum
“When you divide a by b, the quotient/remainder formula tells us a = Qb + R where Q is the quotient, R the remainder. Divide this by b on both sides and we have a/b = Q + (R/b) Since R < b by the definition of a remainder, on the right side above Q is the integer part of the result of ...”
July 1, 2019
Brent@GMATPrepNow posted a reply to How many two-digit whole numbers yield a remainder of 1 when in the Problem Solving forum
“...two-digit whole numbers yield a remainder of 1... Possible values are: 11, 21, 31, 41, 51, 61, 71, 81, and 91 ...and also yield a remainder of 1 when divided by 6 Take each value from 11, 21, 31, 41, 51, 61, 71, 81, and 91, and see which ones leave a remainder of 1 when divided by 6 11, 21, ...”
July 1, 2019
Ian Stewart posted a reply to Sets R and S each contain three distinct positive integers. in the Data Sufficiency forum
“Since r is positive (so since it cannot be zero), we can divide by r in the question "What is the probability that rs = r?" to get the simpler question "What is the probability that s = 1?" So it doesn''t matter what is in set R, since we only care if we pick a "1" ...”
July 1, 2019
Ian Stewart posted a reply to Coach Jackson will choose at least two players for his team in the Data Sufficiency forum
“I have no idea what this question is even asking. From the stem, the coach is choosing "two players *for* his team", and then Statement 1 talks about the total number of teams he can choose. Is he choosing his complete team on Saturday? Or just part of it? If just part of it, when he ...”
July 1, 2019
Ian Stewart posted a reply to A triangle is formed by the x-axis, the y-axis, and Line M. in the Data Sufficiency forum
“There''s a reason you never see percentages combined with coordinate geometry in any actual GMAT question: intercepts and slopes can be negative, and the GMAT will never ask you to work out what number is "25% less than" some negative number. It''s also not even clear what Statement 2 is ...”
July 1, 2019
Ian Stewart posted a reply to In a group of 80 college students, how many own a car? in the Data Sufficiency forum
“From Statement 2, 21 out of 50 car-owners are women. That''s a reduced ratio, so the number of car owners must be a multiple of 50, and the only multiple of 50 less than or equal to 80 is 50 itself, so there must be 50 car owners, and Statement 2 is sufficient. Since Statement 1 only tells us we ...”
July 1, 2019
Ian Stewart posted a reply to If \(z\) is an odd integer, is \(300z > 1500?\) in the Data Sufficiency forum
“It''s also possible that z is negative, so z can also be equal to -3 or -5. That doesn''t change the answer to the question though. I''d find it useful to rephrase the question by dividing by 300 on both sides: we want to know "is z > 5?"”
July 1, 2019
GMATGuruNY posted a reply to A palindrome, such as 12321, is a number that remains the sa in the Problem Solving forum
“The difference between the two palindromes = 32. Since subtracting 32 from the 4-digit palindrome must yield a 3-digit palindrome. the 4-digit palindrome must be just a bit more than 1000. Test 1001: 1001 - 32 = 969 Success! Subtracting 32 from 1001 (a 4-digit palindrome) yields 969 (a 3-digit ...”
July 1, 2019
Brent@GMATPrepNow posted a reply to Is it true that a > b? in the Data Sufficiency forum
“Target question: Is a > b? Statement 1: 2a > 2b Divide both sides by 2 to get: a > b The answer to the target question is YES, a IS greater than b Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: a + c > b + c Subtract b from ...”
June 30, 2019
Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum
“Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...”
June 30, 2019
GMATGuruNY posted a reply to Ellipsis in comparison in the Sentence Correction forum
“Since the red portion refers to the FUTURE -- the expected level in 2010 -- the verb should be in the future tense: a level that WILL BE more than one-third higher than was the level in 1990 From context, we know that a level refers to the expected level of carbon emissions in 2010. Since ...”
June 30, 2019
GMATGuruNY posted a reply to The ratio of flour to water to sugar in a recipe is 7:4:1. T in the Problem Solving forum
“Original ratio: F:W:S = 7:4:1 A new recipe calls for a doubling of the ratio of flour to water. Doubling F/W = 7/4, we get: 2 * 7/4 = 7/2 Resulting ratio: F:W:S = 7:2:1 A halving of the ratio of flour to sugar. Halving F/S = 7/1, we get: (1/2)(7/1) = 7/2 Resulting ratio: F:W:S = ...”
June 30, 2019
GMATGuruNY posted a reply to Amy's grade was 90th percentile of the 80 grades for her in the Problem Solving forum
“Alternate approach: In Amy''s 80-student class, her percentile = 90. In the 100-student class, 19 scores are higher than Amy''s, implying that 81 scores are lower. Thus: Amy''s percentile in the 100-student class = 81. Amy''s AVERAGE percentile for all 180 students = (80*90 + 100*81)/180 = ...”
June 30, 2019
Brent@GMATPrepNow posted a reply to If a certain wheel turns at a constant rate of \(x\) in the Problem Solving forum
“We can solve the question using equivalent ratios Wheel turns at a constant rate of x revolutions per minute We can also say the wheel turns at a constant rate of x revolutions per 60 seconds In other words, # of revolutions/seconds elapsed = x/60 How many revolutions will the wheel make in ...”
June 29, 2019
Ian Stewart posted a reply to Sequence A is defined by the equation An = 3n + 7 in the Data Sufficiency forum
“I wouldn''t solve this problem by generating a formula -- we know exactly what our sequence is. The sequence is 10, 13, 16, 19, etc. Every term is positive, so as you add more and more terms, the sum gets larger and larger. If we know the sum of the first n terms is 275, there can thus only be one ...”
June 29, 2019
Ian Stewart posted a reply to What is the X intercept of non horizontal line m? in the Data Sufficiency forum
“Our line has an equation y = mx + b, where m is the slope, b the y-intercept. To find the x-intercept of a line, we find the value of x when y=0. If we plug in y=0 here, we find 0 = mx + b x = -b/m Statement 1 tells us m = 4b, and if we substitute that for m above, we learn that x = ...”
June 29, 2019
Ian Stewart posted a reply to Data sufficiency in the GMAT Math forum
“If x > 1, then 1/x is between 0 and 1. So 1 + (1/x) will be between 1 and 2, and answers C and E are both possible (for C, x = 7/2, and for E, x = 7). If there''s a typo in D, and instead it''s meant to read "15/11", then D is also possible (x = 11/4). It''s only if the question tells ...”
June 28, 2019
Ian Stewart posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum
“This is not a "series". It is a "sequence". A series is a sum of a sequence, and this question has nothing to do with summing a sequence. It would be understandable for a test taker to be confused by the wording here (I was at first), because test takers aren''t expected to know ...”
June 28, 2019
Brent@GMATPrepNow posted a reply to Leona bought a 1-year, $10,000 certificate of deposit that in the Problem Solving forum
“If the interest is at an ANNUAL rate of 8 percent compounded semiannually, then EVERY SIX MONTHS, we add 4% interest to the certificate. No need to apply the compound interest formula. It''s just as fast to make the 2 calculations. After 6 months, the value of the certificate = $10,000 + (4% of ...”
June 28, 2019
Ian Stewart posted a reply to Is \(x \geq 0?\) in the Data Sufficiency forum
“Rewriting Statement 1 with zero on one side, x^2 - 9x = 0, so x(x-9) = 0, and x = 0 or x = 9. Either way, x is greater than or equal to zero, so Statement 1 is sufficient. Statement 2 tells us |x| = -x, which only happens when x is less than or equal to zero (when x is positive, the absolute ...”
June 27, 2019
Ian Stewart posted a reply to Is the slope of line z positive? in the Data Sufficiency forum
“It''s hard to guess which line has the slope of -1/4 in Statement 1. If they''re talking about line z, then the Statement is clearly sufficient. If they''re talking about line m, then since perpendicular lines have slopes that are negative reciprocals of each other, line z would have a slope of 4. ...”
June 27, 2019
Ian Stewart posted a reply to S is a set of n consecutive positive integers. Is the mean in the Data Sufficiency forum
“A set of consecutive integers is equally spaced, so its mean and median are always equal. So Statement 2 is instantly sufficient. The median will also be halfway between the smallest and largest values in the set, so if S is the smallest value, and R is the range, the median will be S + (R/2). If ...”
June 27, 2019
Ian Stewart posted a reply to What is the LCM of the numbers 3, a, and 7, if ‘a’ is an in the Data Sufficiency forum
“Statement 1 is not sufficient, because the LCM will be different if a=5 or if a=97. For Statement 2, the GCD of 3 and anything must be a divisor of 3, so it could only be 1 or 3, and will always be a divisor of 30. So Statement 1 only tells us "the LCM of 3 and a is a divisor of 30". ...”
June 27, 2019
Ian Stewart posted a reply to A new cell phone plan is offering pricing based on average m in the Data Sufficiency forum
“If Brandon averaged q minutes per month, his total usage for the year was 12q minutes. From Statement 1, we know for 8 months Jodie averaged 1.5q minutes per month, so during those 8 months, she used (8)(1.5q) = 12q minutes in total. She might have used zero minutes the rest of the year, in ...”
June 27, 2019
Brent@GMATPrepNow posted a reply to A computer routine was developed to generate two numbers, in the Problem Solving forum
“Check each answer choice... (A) (99, 10) √100 = 10 So, √99 is LESS THAN 10 In other words, 10 is GREATER THAN √99 So, answer choice A breaks the rule that says the second number must be less than or equal to the square root of the first" Answer: A Cheers, Brent”
June 27, 2019
Brent@GMATPrepNow posted a reply to If Lucy walks to work at a rate of 4 miles per hour, but she in the Problem Solving forum
“Let d = distance from home to work Average speed = (total distance traveled)/(total travel time) total distance traveled = d + d = 2d total travel time = travel time TO work + travel time FROM work time = distance/speed We get: total travel time = d/4 + d/6 = 3d/12 + 2d/12 = ...”
June 26, 2019
Brent@GMATPrepNow posted a reply to Right triangle PQR is to be constructed in the xy-plane so in the Problem Solving forum
“Take the task of building triangles and break it into stages. Stage 1: Select any point where the right angle will be (point P). The point can be selected from a 10x11 grid. So, there 110 points to choose from. This means that stage 1 can be completed in 110 ways. Stage 2: Select a point ...”
June 26, 2019
GMATGuruNY posted a reply to -2 ≤ x ≤ -1 and 1 ≤ y ≤ 2. What is the greatest poss in the Problem Solving forum
“(x+y)/x = 1 only if y=0. Since the range for y does not include 0, eliminate E. If x=-2 and y=1, then (x+y)/y = (-2+1)/-2 = 1/2. Since 1/2 is the greatest of the remaining answer choices, the correct answer is D.”
June 26, 2019
Brent@GMATPrepNow posted a reply to If y= 4 + (x - 3)^2, then y is lowest when in the Problem Solving forum
“KEY CONCEPT: In order to minimize the value of y, we must minimize the value of (x -3)² We know that (some number)² ≥ 0 So, the SMALLEST possible value of (some number)² is 0 Likewise, the SMALLEST possible value of (x -3)² is 0 (x -3)² = 0 when x = 3 Answer: D Cheers, Brent”
June 25, 2019
Brent@GMATPrepNow posted a reply to In the figure shown, what is the value of x? in the Data Sufficiency forum
“The diagram (aka figure) is missing.”
June 25, 2019
Brent@GMATPrepNow posted a reply to For integers x and y, which of the following MUST be an in the Problem Solving forum
“One approach: The question is asking us to determine which expression MUST be an integer for ALL integer values of x and y. So, let''s TEST a pair of values. Let''s plug in x = 1 and y = 1 If an expression evaluates to be a non-integer, we can ELIMINATE that answer choice. We get... ...”
June 25, 2019
Brent@GMATPrepNow posted a reply to A certain basketball team that has played 2/3 of its games in the Problem Solving forum
“Given: The team has played 2/3 of its games. The team has played 20 games. If 2/3 of the total number of games = 20, then the total number of games = 30. This means that there are 10 games remaining. We want the team to win at least 3/4 of its games. 3/4 of 30 = 22.5 So, in order to ...”
June 25, 2019
GMATGuruNY posted a reply to A certain basketball team that has played 2/3 of its games in the Problem Solving forum
“Games played thus far = 17 wins + 3 losses = 20. Since these 20 games constitute 2/3 of the total number of games, we get: 20 = (2/3)T 60 = 2T 30 = T Since the team must win at least 3/4 of these 30 games, it may lose at most 1/4 of these 30 games: (1/4)30 = 7.5 Implication: The total ...”
June 25, 2019
GMATGuruNY posted a reply to What is the average (arithmetic mean) of all 5-digit numbers in the Problem Solving forum
“For any set that is SYMMETRICAL ABOUT THE MEDIAN: average = median Number of integers that can be composed from the 5 given digits = 5! = 120. Since the number of integers is EVEN, the median will be equal to the average of the two middle values: ...53791, 53917, 53971, 57139, 57193, ...”
June 25, 2019
GMATGuruNY posted a reply to Ashok and Brian are both walking east along the same path; in the Data Sufficiency forum
“Let A = A''s rate and B = Brian''s rate. Ashok has to CATCH-UP by 30 miles. The CATCH-UP rate is equal to the DIFFERENCE between the two rates. If A = 3mph, while B = 2mph, then every hour A walks 1 more mile than B, with the result that every hour A catches up by 1 mile -- the DIFFERENCE ...”
June 23, 2019
GMATGuruNY posted a reply to GMAT Official Guide 2019 The city of Workney in the Critical Reasoning forum
“When the correct answer is negated, the conclusion will be invalidated. Conclusion: Selling 9 tokens for $10 will alleviate the burden on POOR PEOPLE. E, negated: More riders would regularly purchase 18 tokens at once than would purchase only 9 tokens at once. Since this negation tells us ...”
June 23, 2019
Brent@GMATPrepNow posted a reply to If 2xy + z = 9, what is the value of the positive integer z? in the Data Sufficiency forum
“ Given: 2xy + z = 9 Target question: What is the value of the positive integer z? Statement 1: xyz - z² = 0 Factor to get: z(xy - z) = 0 This means that EITHER z = 0 OR xy - z = 0 HOWEVER, we''re told that z is a POSITIVE integer, which means z ≠0 So, it must be the case that xy - ...”
June 22, 2019
Brent@GMATPrepNow posted a reply to What is the perimeter of isosceles triangle MNP? in the Data Sufficiency forum
“Target question: What is the perimeter of isosceles triangle MNP? Statement 1: MN = 16 No idea about the other 2 sides Statement 1 is NOT SUFFICIENT Statement 2: NP = 20 No idea about the other 2 sides Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Since we have an ...”
June 22, 2019
Brent@GMATPrepNow posted a reply to f x and y are positive, what is the value of y ? in the Data Sufficiency forum
“Target question: What is the value of y? Given: x and y are positive Statement 1: xy is the square of an integer. There are several values of x and y that satisfy this condition. Here are two: Case a: x = 1 and y = 1. Here xy = (1)(1) = 1, which is the square of an integer. In this ...”
June 21, 2019
Brent@GMATPrepNow posted a reply to Which of the following is an integer? I. 12! / 6! II. 12! / in the Problem Solving forum
“I. 12!/6! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)/(6)(5)(4)(3)(2)(1) = (12)(11)(10)(9)(8)(7) = some integer II. 12!/8! = (12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)/(8)(7)(6)(5)(4)(3)(2)(1) = (12)(11)(10)(9) = some integer III. 12!/7!5! = ...”
June 21, 2019
Brent@GMATPrepNow posted a reply to The average salary of 15 people in the shipping department in the Problem Solving forum
“]The average salary of 15 people in the shipping department at a certain firm is $20,000 So, (sum of all 15 salaries)/15 = $20,000 Multiply both sides by 15 to get: sum of all 15 salaries = $300,000 The salary of 5 of the employees is $25,000 each and the salary of 4 of the employees is $16,000 ...”
June 20, 2019
Brent@GMATPrepNow posted a reply to In how many different ways can 3 fiction books and 3 in the Problem Solving forum
“Take the task of arranging the 6 books and break it into stages. Stage 1: Arrange the 3 fiction books in a row We can arrange n unique objects in n! ways So, we can arrange the 3 books in 3! ways (= 6 ways) So, we can complete stage 1 in 6 ways Stage 2: Arrange the 3 non-fiction books in ...”
June 20, 2019
GMATGuruNY posted a reply to What is the value of 1 / (√2+√1) + 1 / (√3+√2) + 1/( in the Problem Solving forum
“1/(√2+√1) = √2-√1) + (√3-√2) + (√4-√3) +...+ (√24-√23) + (√25-√24) The red values all cancel out, yielding the following: -√1 + √25 = -1 + 5 = 4 The correct answer is D.”
June 20, 2019
Brent@GMATPrepNow posted a reply to Data sufficiency in the GMAT Math forum
“Take: y = 1 + 1/x Rewrite as: y = x/x + 1/x Simplify: y = (x + 1)/x So, we''re looking for an answer choice that can be expressed as a fraction in which the numerator is 1 greater than the denominator. Answer: E Cheers, Brent”
June 19, 2019
GMATGuruNY posted a reply to OG 2018 CR Q Political theorist: Even with in the Critical Reasoning forum
“Since the correct answer must SUPPORT the conclusion that a national leader with such , the argument above seems best classified as a STRENGTHEN CR.”
June 19, 2019
Brent@GMATPrepNow posted a reply to If is n is multiple of 5, and n=p^2*q where p and q are prim in the Problem Solving forum
“Let''s test some values that satisfy the given conditions (n is multiple of 5, and n = p²q, where p and q are prime numbers) How about: p = 2 and q = 5. In this case, n = (2²)(5) = 20, and 20 is a multiple of 5, which satisfies the given condition. Now plug p = 2 and q = 5 into the ...”
June 19, 2019
GMATGuruNY posted a reply to If is n is multiple of 5, and n=p^2*q where p and q are prim in the Problem Solving forum
“Try to prove that four of the answer choices DO NOT have to be a multiple of 25. The correct answer will be the remaining answer choice. In order for n to be a multiple of 5, either p and/or q must be a multiple of 5. Since the goal is to prove that four of the answer choices do NOT have to ...”
June 19, 2019
Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the set { in the Problem Solving forum
“If 3 different integers are randomly selected from the set {1, 2, 3, 4, 5, 6}, what is the probability that a triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers? A) 0.25 B) 0.3 C) 0.35 D) 0.40 E) 0.45 Source: www.gmatprepnow.com Difficulty level: ...”
June 19, 2019
Brent@GMATPrepNow posted a reply to A certain zoo has mammal and reptiles and birds, and no in the Data Sufficiency forum
“Target question: How many birds are in the zoo? Given: The ratio of mammals to reptiles to birds is 11: 8:5. Given this ratio, we could say that there are: 11x mammals 8x reptiles 5x birds for some value of x. Statement 1: there are twelve more mammals in the zoo than there are ...”
June 19, 2019
GMATGuruNY posted a reply to What is the value of the following sum? 1/(1*2) + 1/(2*3) + in the Problem Solving forum
“x = 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + 1/(5*6) 60x = 60D.”
June 19, 2019
Brent@GMATPrepNow posted a reply to If x, y and z are three different non-negative integers, whi in the Problem Solving forum
“Nice work, Mitch! I created this question to illustrate the importance of checking the answer choices each time you analyze one of the statements. Here’s why: Once we know that statement i COULD be true (it''s true when x = 0, y = 1 and z = 2), we should check the answer choices…. ...”
June 18, 2019
GMATGuruNY posted a reply to If x, y and z are three different non-negative integers, whi in the Problem Solving forum
“i: |x−y| = |x+y| = |y−z| This statement is true if x=0, y=1 and z=2: |0-1| = |0+1| = |1-2| 1 = 1 = 1 Since the correct answer must include i, eliminate B and C. ii) x^y = y^z This statement is true if x=1, y=2 and z=0: 1^2 = 2^0 1 = 1 Since the correct answer must include ii, ...”
June 18, 2019
GMATGuruNY posted a reply to Over the first x games of his basketball season, Martin in the Problem Solving forum
“Since the seasonal average = 30 points per game, the total number of points must be a MULTIPLE OF 30. Over the first x games of his basketball season, Martin averaged 32 points per game. In his last game, he scored 14 points. Implication: 32x + 14 = MULTIPLE OF 30 32x = (MULTIPLE OF 30) - 14 ...”
June 18, 2019
Brent@GMATPrepNow posted a reply to A certain machine produces 1,000 units of product P per hour in the Problem Solving forum
“A certain machine produces 1,000 units in 1 hour So, the machine produces 24,000 units in 24 hours In other words, the machine produces 24,000 units in 1 DAY So, the machine produces (24,000)(7) units in 7 DAYS (20,000)(7) = 140,000 So, (24,000)(7) = some number greater than 140,000 ...”
June 18, 2019
Brent@GMATPrepNow posted a new topic called If x, y and z are three different non-negative integers, whi in the Problem Solving forum
“If x, y and z are three different non-negative integers, which of the following COULD be true? i) |x−y| = |x+y| = |y−z| ii) x^y = y^z iii) x³ + y³ = z³ A) i only B) ii only C) iii only D) i and ii E) i and iii Source; www.gmatprepnow.com Difficulty level: 700+ Answer: D”
June 18, 2019
GMATGuruNY posted a reply to If |2x|>|3y|, is x >y? 1) x>0 2) y>0 in the Data Sufficiency forum
“Statement 1: Test x=3. Plugging x=3 into |2x|>|3y|, we get: |2*3|>|3y| 6 > 3|y| |y| < 2 -2 < y < 2 Since x=3 and -2 < y < 2, we get: x > y. Test x=1/2. Plugging x=1/2 into |2x|>|3y|, we get: |2 * 1/2|>|3y| 1 > 3|y| |y| < 1/3 -1/3 < y < ...”
June 18, 2019
GMATGuruNY posted a reply to How many arrangements of the letters A, C, C, E, N, T includ in the Problem Solving forum
“Good arrangements = total arrangements - bad arrangements. Total arrangements: Number of ways to arrange 6 elements = 6!. But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of identical elements can be ARRANGED. The reason: When the identical ...”
June 18, 2019
GMATGuruNY posted a reply to If \(\frac{(ab)^2+3ab-18}{(a-1)(a-2)}=0\) where \(a\) and in the Problem Solving forum
“The equation is valid only if (ab)²+3ab-18 = 0. I: b=1 Plugging b=1 into (ab)²+3ab-18 = 0, we get: a²+3a-18 = 0 (a+6)(a-3) = 0 a=-6 or a=3 This works. Since the correct answer must include I, eliminate B. II: b=2 Plugging b=2 into (ab)²+3ab-18 = 0, we get: 4a²+6a-18 = 0 2a²+3a-9 ...”
June 18, 2019
Brent@GMATPrepNow posted a reply to If p is an integer greater than 1, is p a prime number? in the Data Sufficiency forum
“ Given: p is an integer greater than 1 Target question: Is p a prime number? Statement 1: p is a factor of 13 13 has exactly two factors: 1 and 13 Since p > 1, we KNOW that p = 13 (which is prime) The answer to the target question is YES, p IS prime Since we can answer the target ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to How many ways are there to arrange the letters in the word in the Problem Solving forum
“------------ASIDE----------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this: If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to If |2x + 5| = |3x − 2|, which of the following is a possib in the Problem Solving forum
“If |x| = |y|, then either x = y OR x = -y GIVEN: |2x + 5| = |3x − 2| So, EITHER 2x + 5 = 3x − 2 OR 2x + 5 = -(3x − 2) Let''s solve each equation... Take: 2x + 5 = 3x − 2 We get: 5 = x - 2 Solve: x = 7 Check answer choices.....x = 7 is not there. Try the other equation: Take: ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to Is h^2 = h? in the Data Sufficiency forum
“Target question: Is h² = h? Statement 1: h + h = h Subtract h from both sides to get: h = 0 If h = 0, then h² = h becomes 0² = 0 (WORKS!) The answer to the target question is YES, h² = h Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to Is z > 0.5? in the Data Sufficiency forum
“Target question: Is z > 0.5 ? SCAN the statements to see we can jump straight to.... Statements 1 and 2 combined There are infinitely-many values of z that satisfy BOTH statements. . Here are two: Case a: z = 0.6. In this case, the answer to the target question is YES, z IS greater ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum
“Target question: What is the value of x? Statement 1: 5x + 3y = 15 Since this is a linear equation with infinitely many solutions. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x = 3 Case b: x = 0 and y = 5. In this case, the answer to the target ...”
June 17, 2019
Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of seven consecutive in the Problem Solving forum
“Another approach: For any set of consecutive integers, mean = median. So, in this case, mean = median = k + 2 So, the three values that come AFTER k + 2 are k+3, k+4, and k+5 And the three values that come BEFORE k + 2 are k-1, k, k+1, k+2, k+3, k+4, k+5 The product of the greatest and ...”
June 17, 2019
GMATGuruNY posted a reply to If the average (arithmetic mean) of seven consecutive in the Problem Solving forum
“For any set of consecutive integers, average = median. Let the 7 integers be 1, 2, 3, 4, 5, 6, 7. Since k+2 = average = median = 4, k=2. Product of the greatest and least = 7*1 = 7. The correct answer must yield 7 when k=2. Only C works: k² + 4k - 5 = 2² + (4*2) - 5 = 7 The correct ...”
June 17, 2019
GMATGuruNY posted a reply to In how many different ways can 3 fiction books and 3 in the Problem Solving forum
“Case 1: The 3 fiction books appear to the left of the 3 nonfiction books Number of ways to arrange the 3 fiction books = 3! = 6 Number of ways to arrange the 3 nonfiction books = 3! = 6 To combine these options, we multiply: 6*6 = 36 Case 2: The 3 nonfiction books appear to the left of the 3 ...”
June 17, 2019
GMATGuruNY posted a reply to Is x<0? 1) x^3+1<0 2) x^3+2x^2+x+2=0 in the Data Sufficiency forum
“Statement 1: x³ + 1 < 0 x³ < -1 The resulting inequality will hold true only if x < 0. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: x³ + 2x² + x + 2 = 0 x²(x+2) + (x+2) = 0 (x+2)(x²+1) = 0 The blue factor is equal to 0 if x=-2. It is not possible ...”
June 17, 2019
GMATGuruNY posted a reply to How many rectangles can be formed by connecting the grid poi in the Problem Solving forum
“https://i.postimg.cc/k681TSrJ/lattice-six-by-five.png To form a rectangle, we must combine a HORIZONTAL LENGTH with a VERTICAL LENGTH: Horizontal length: Number of ways to choose a horizontal length of 1: AB, BC, CD, DE, EF, FG = 6 Number of ways to choose a horizontal length of 2: AC, BD, ...”
June 17, 2019
GMATGuruNY posted a reply to If a fair 6-sided die is rolled three times, what is the in the Problem Solving forum
“P(exactly n times) = P(one way) * all possible ways. Let T = 3 and N = not 3. P(one way): One way to get exactly one 3: TNN. P(T on the 1st roll) = 1/6. (Of the 6 possible rolls, one is 3.) P(N on the 2nd roll) = 5/6. (Of the 6 possible rolls, five are not 3.) P(N on the 3nd roll) ...”
June 16, 2019
GMATGuruNY posted a reply to 10^25 – 560 is divisible by all of the following EXCEPT: in the Problem Solving forum
“RULE: MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X For an integer to be divisible by 3, its digit sum must be a multiple of 3. 10²⁵ - 560 = (100000...) - (560) = 99999...440 Sum of the digits = (9+9+9+9+9...) + (4+4+0) = (multiple ...”
June 16, 2019
Brent@GMATPrepNow posted a reply to Of the first three dozen cookies baked at a bake shop on a in the Data Sufficiency forum
“ Given: Of the first three dozen (36) cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, 1/3 of 36 = 12. So, 12 chocolate cookies were baked in the first round of baking. Let x = ...”
June 15, 2019
Brent@GMATPrepNow posted a reply to List \(K\) consists of seven numbers. Is the average in the Data Sufficiency forum
“Target question: Is the average (arithmetic mean) of the seven numbers negative? Statement 1: Four of the seven numbers in list K are negative. There are several scenarios that satisfy statement 1. Here are two: Case a: List K = {-10, -10, -10, -10, 1, 1, 1}. Average = sum/7 = -37/7. The ...”
June 15, 2019
Brent@GMATPrepNow posted a reply to A set of 15 different integers has median of 25 and a range in the Problem Solving forum
“Let''s tackle this one step at a time. First, we have 15 different integers. We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _ Notice that 7 ...”
June 15, 2019
GMATGuruNY posted a reply to At a certain picnic, each of the guests was served either a in the Data Sufficiency forum
“Let D = the double-scoop guests and S = the single-scoop guests. What is value of D? Statement 1: Since 60% received a double-scoop, the remaining 40% received a single scoop. Thus: D/S = 60%/40% = 3/2 No way to solve for D. INSUFFICIENT. Statement 2: Since the D double-scoop guests ...”
June 15, 2019
GMATGuruNY posted a reply to A set of 15 different integers has median of 25 and a range in the Problem Solving forum
“Range = biggest - smallest. Thus: 25 = biggest - smallest. Smallest = biggest - 25. We can plug the answer choices into the equation above. Since we need the greatest possible integer that could be in the set, we should start with the greatest answer choice. Answer choice E: 50 Smallest ...”
June 15, 2019
GMATGuruNY posted a reply to Mixture problem in the Problem Solving forum
“2 liters of 25% solution are combined with 6 liters of 40% solution. Average percentage for the entire 8 liters = (2*25 + 6*40)/8 = 290/8 = 36.25. The closest answer is C. Alligation approach: Let V1 and V2 = the two vessels and M = the mixture. Step 1: Plot the three percents on a ...”
June 15, 2019
Ian Stewart posted a reply to If x and y are integers, and x + y < 0, is x — y > 0 in the Data Sufficiency forum
“We can rephrase the question "is x > y?" Subtracting |x| on both sides, Statement 1 only tells us that |y| > 0. But that''s always true unless y = 0, so Statement 1 only tells us y is nonzero. Assuming x is nonzero (something the question needs to tell us, so that the left side ...”
June 14, 2019
Ian Stewart posted a reply to In a network of car dealerships, a group of \(d\) sales in the Data Sufficiency forum
“If we have d directors, and each director has a associates, we have ad associates. If the directors each sell 10 cars, they all sell 10d cars in total, and if the associates each sell 20 cars, they sell 20ad cars in total. So 10d + 20ad = 10d(1 + 2a) is the total number of cars sold. Statement 1 ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to 8, 5, x, 6 The median of the list of positive integers in the Problem Solving forum
“Since there is an even number of values in the list, the median will be the AVERAGE of the two middlemost values (when all values are listed in ASCENDING order) Let''s the answer choices... A) If x = 3, then the values are {3, 5, 6, 8}, which means the median = (5 + 6)/2 = 5.5 NO GOOD. We ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to Will the first 10 volumes of a 20-volume encyclopedia fit in the Data Sufficiency forum
“Target question: Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above? Statement 1: x = 50 centimeters. We have no idea how THICK the first 10 volumes are. They COULD each be 1 mm thick, in which case the 10 volumes will easily fit in the 50 cm ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to For every integer \(k\) from 1 to 10, inclusive the "k& in the Problem Solving forum
“T = 1/2 - 1/4 + 1/8 - 1/16 + . . . Notice that we can rewrite this as T = (1/2 - 1/4) + (1/8 - 1/16) + . . . When you start simplifying each part in brackets, you''ll see a pattern emerge. We get... T = 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 Now examine the last 4 terms: 1/16 + 1/64 + 1/256 + ...”
June 14, 2019
Brent@GMATPrepNow posted a reply to Jim is twice as old as Fred ... in the Problem Solving forum
“I''ve added the answer choices.... TODAY''S AGES Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Let x = Fred''s age TODAY So, 2x = Jim''s age TODAY And x - 2 = Sam''s age TODAY AGES FOUR YEARS AGO Let''s first determine Jim''s age and Sam''s age FOUR YEARS ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to in terms of k and m in the Problem Solving forum
“One approach is to plug in values. Let $100 be the original price per share of Stock X Choose a "nice" value for k. How about k = 200 So, after a 200% increase, the new price per share = $300 Let $100 be the original earnings per share of Stock X Choose a "nice" ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to cd? in the Data Sufficiency forum
“Target question: Is the product cd positive? Statement 1: 3c = -8d³ Divide both sides by d to get: 3c/d = -8d² Divide both sides by 3 to get: c/d = -8d²/3 Rewrite as: c/d = (-8/3)(d²) Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to If f(x) = x^3 + 9, is f(x) positive? in the Data Sufficiency forum
“ Given: f(x) = x³ + 9 Target question: Is f(x) positive? Statement 1: x < −1 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -2. In this case, f(-2) = (-2)³ + 9 = (-8) + 9 = 1. So, the answer to the target question is ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to In May Mrs Lee's earnings were 60 percent of the Lee family' in the Problem Solving forum
“Since we''re asked to find a PERCENT (and not an actual value), we can assign a nice value to the Lee family''s total income. In May Mrs Lee''s earnings were 60 percent of the Lee family''s total income Let''s say $100 = Lee family''s total income IN MAY This means $60 = Mrs Lee''s earnings ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to Which of the following could be the median for a set of in the Problem Solving forum
“Since 20 < x < 80, we can see that, if we arrange the 5 numbers in ASCENDING order, we get two possible cases: case a: {x, 56, 86, 97, 98} case b: {56, x, 86, 97, 98} In both cases, the median is 86 Answer: B Cheers, Brent”
June 13, 2019
Ian Stewart posted a reply to Mixture problem in the Problem Solving forum
“The answer needs to be between 25% and 40%, and because we''re using more of the 40% solution, the answer must be closer to 40%, so only one answer makes sense, 37.5%. That''s assuming both vessels are full, something the question needs to mention (but doesn''t). If you want to use alligation, ...”
June 12, 2019
Ian Stewart posted a reply to Three gnomes and three elves sit down in a row of six chairs in the Problem Solving forum
“If there''s a gnome in the first chair, the arrangement must alternate: GEGEGE. We''ll have 3 choices for the first gnome, 2 for the second, and 1 for the third, and the same for the elves, for 3! * 3! = 36 arrangements in total. But we can also have an elf in the first chair, and the arrangement ...”
June 12, 2019
Ian Stewart posted a reply to A state legislator drafts an income tax proposal that in the Data Sufficiency forum
“Statement 1 is insufficient, because maybe everyone earns $65,000, and the answer to the question is ''no'', or maybe someone earns $1 trillion, and the percent of income collected is close to 40%. If someone earns $350,000, they pay: 20% on their first $100k 25% on their next $50k 30% on ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to a, b and c are three distinct integers, greater than 1, such in the Problem Solving forum
“150 = (2)(3)(5)(5) There are three sets of 3 values (each greater than 1) that have a product of 150: {2, 3, 25} {3, 5, 50} {2, 5, 15} GIVEN: The greatest common divisor of any two numbers, among the three integers, is 1 The only set that meets this condition is {2, 3, 25} SUM = 2 + 3 + ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to David drove to work at an average (arithmetic mean) speed of in the Problem Solving forum
“Let''s start with a "word equation" We can write: (David''s travel time TO work) + (David''s travel time FROM work) = 2 hours time = distance/speed Let d = the distance each way We can write: d/45 + d/60 = 2 To eliminate the fractions, multiply both sides by 180, the LCM of 45 ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers, are x and y consecutive? in the Data Sufficiency forum
“ Given: x and y are positive integers Target question: Are x and y consecutive? Statement 1: x+y=3 Since x+y=3 are x positive integers, we know that one number must be 1 and the other number must be 2. The answer to the target question is YES, x and y ARE consecutive Since we can ...”
June 12, 2019
GMATGuruNY posted a reply to It is known that (1.1)^{17} is approximately equal to 5.05. in the Problem Solving forum
“1,1¹⁷ ≈ 5 (1.1¹⁷)³ ≈ 5³ 1.1⁵¹ ≈ 125 Thus: 1.1⁵⁰ = a bit less than 125 The correct answer is D.”
June 12, 2019
Ian Stewart posted a reply to If l1 and l2 are distinct lines in the xy coordinate system in the Data Sufficiency forum
“I''m not sure why they ask "is a^2 = ac", which will be true when a=0 or when a=c, when we can prove the narrower fact that a=c using one of the Statements. Here, a and c are the slopes of the two lines, so if we can be sure the lines have the same slope, we''ll have sufficient ...”
June 11, 2019
GMATGuruNY posted a reply to sum of these 24 integers? in the Problem Solving forum
“For any set that is SYMMETRICAL ABOUT THE MEDIAN: sum = (count)(median) The set is composed of integers in the following ranges: 1234...1432 2134...2431 3124...3421 4123...4321. Each range contains the same number of integers. Thus, the median of the set is equal to the average of ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to How many integers between in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to sum of these 24 integers? in the Problem Solving forum
“Since we''re adding 24 numbers, we know that: Six numbers will be in the form 1--- Six numbers will be in the form 2--- Six numbers will be in the form 3--- Six numbers will be in the form 4--- Let''s first see what the sum is when we say all 24 numbers are 1000, 2000, 3000 or 4000 The sum = ...”
June 11, 2019
June 11, 2019
GMATGuruNY posted a reply to In a certain deck of cards in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the least and greatest integers on the cards. D: least = 4, greatest = 14 (14)(next larger integer) = 14*15 = 210. Too big, since each possible product must be less than 200. Implication: The greatest integer must be LESS THAN 14. Eliminate ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to A certain library in the Problem Solving forum
“1st day - $0.10 2nd day - $0.20 or $0.40 (double or add $0.30) $0.20 is the lesser amount 3rd day - $0.40 or $0.50 (double or add $0.30) $0.40 is the lesser amount 4th day - $0.80 or $0.70 (double or add $0.30) $0.70 is the lesser amount The correct answer is B Cheers, Brent”
June 11, 2019
GMATGuruNY posted a reply to Is x^3-x^2+x-1 > 0? in the Data Sufficiency forum
“A critical point occurs when the two sides of an equality are EQUAL. To determine the ranges where the left side is GREATER than the right side, test one value to the left and right of each critical point. x³ - x² + x - 1 > 0? x²(x-1) + (x-1) > 0 (x-1)(x²+1) > 0 The two sides are ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to rates in the Problem Solving forum
“Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to DS in the Data Sufficiency forum
“Target question: Is b (the y-coordinate of the point on the line) positive? Given: Line k passes through the origin and through the point (a,b) Statement 1: The slope of line k is negative There are several lines and points that satisfy statement 1. Here are two: Case a: ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to In a certain pond in the Problem Solving forum
“We can use equivalent ratios here. We''re told that the proportion of tagged fish in the 50-fish SAMPLE is equal to the the proportion of tagged fish in the ENTIRE pond. So, (# tagged fish in SAMPLE)/50 = (total # tagged fish)/(total # of fish in POND) Let x = # of fish in the entire ...”
June 11, 2019
GMATGuruNY posted a reply to To celebrate a colleague's retirement, the T coworkers in an in the Problem Solving forum
“The T coworkers in an office agreed to share equally the cost of a catered lunch. The lunch costs a total of X dollars. Let X=5 and T=5, implying that the original cost per worker = 5/5 = $1. S of the coworkers fail to pay their share. Which of the following represents the additional amount, ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to In the multiplication above, # represents a single digit. in the Problem Solving forum
“We''re told that # times 512 equals two thousand and something. Well, 4 times 512 = two thousand and something. And 5 times 512 = two thousand and something. No other digits, when multiplied by 512 will give us two thousand and something So, let''s test 4 and 5 (answer choices C and D) If ...”
June 10, 2019
Brent@GMATPrepNow posted a reply to In the xy-plane shown, is the slope of the line L negative ? in the Data Sufficiency forum
“Target question: Is the slope of the line L negative ? After scanning the two statement, I see that we can jump straight to . . . Statements 1 and 2 combined The COMBINED statements tell us that line l passes through quadrants III and IV. There are several lines that satisfy BOTH ...”
June 10, 2019
Ian Stewart posted a reply to With # and & each representing different digits in the in the Problem Solving forum
“We''re subtracting something between 10 and 99, and arriving at 667. So we must be subtracting from a number between 677 and 766, and the digit # could only be 6 or 7. But it can''t be 6, because 6&& - 66 will never be equal to 667 (it could be at most 633), so # must be 7. So we have this ...”
June 10, 2019
Ian Stewart posted a reply to In the figure above, equilateral hexagon ABCDEF is in the Problem Solving forum
“"Equilateral" means "equal sides". It is not a synonym for "regular", which means "equal sides *and* equal angles". Now, it''s true that an equilateral hexagon that you can inscribe in a circle must be regular, but the GMAT certainly would never expect a test ...”
June 10, 2019
Ian Stewart posted a reply to In the figure above, square ABCD has an area of 25. in the Problem Solving forum
“The diameter of the circle is the diagonal of the square, and the diagonal of the square is the hypotenuse of a 45-45-90 triangle with legs of length 5. Since sides in a 45-45-90 triangle are in a 1 to 1 to √2 ratio, the diameter of the circle is 5√2, so the radius is (5√2)/2, and the area is ...”
June 10, 2019
Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum
“Approach #2: We''re asked to evaluate (find the value of) the given expression. Since all of the answer choices are constants (just numbers), we know that the given expression must evaluate to be ONE of the answer choices FOR ALL VALUES OF X. So, let''s test a value of x Try x = 1 We get: ...”
June 10, 2019
Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum
“(5x+10)/(x+2) = (5(x+2))/(x+2) = 5 Answer: D Cheers, Brent”
June 10, 2019
Ian Stewart posted a reply to Is Hector taller than Charley? (1) Hector is 5 feet in the Data Sufficiency forum
“Statement 1 is useless. Statement 2 tells us Charley is 2 inches taller than Hector, so is sufficient.”
June 10, 2019
Ian Stewart posted a reply to What will the ratio of birds to fish in a certain pet store in the Data Sufficiency forum
“Statement 1 is clearly insufficient. For Statement 2, imagine we take out 4 fish. Then we know that adding back 4 fish and 7 birds doesn''t change our ratio. That can only happen if the ratio is exactly 4 to 7 (if it weren''t exactly 4 to 7, then adding 4 fish and 7 birds would move the ratio ...”
June 10, 2019
Brent@GMATPrepNow posted a reply to For any integers a and b, min(a, b) and max(a, b) denote in the Data Sufficiency forum
“Notice that min(3, 4) = 3 Notice that min(2, 2) = 2 Notice that min(1, 11) = 1 KEY PROPERTY: In general, we can say that, if min(a,b) = c, then we know that c ≤ a and c ≤ b Target question: What is max(y, 8)? Statement 1: min(9, x) = y This tells us that y ≤ 9 Let''s test ...”
June 10, 2019
Ian Stewart posted a reply to Roger can chop down 4 trees in an hour. How long does it in the Data Sufficiency forum
“Statement 1 tells us nothing about how quickly Vincent chops down trees. From Statement 2, it takes Vincent twice as long as Roger to chop down trees, so if Roger chops down four in 1 hour, Vincent chops down four in 2 hours. The answer is B. The wording here is too imprecise for the GMAT, ...”
June 10, 2019
Ian Stewart posted a reply to x is a nonzero number. Is xy < 0? in the Data Sufficiency forum
“Each Statement is clearly insufficient alone, since if y is nonzero, we''ll get different answers to the question by making x positive or negative. Using both statements, y must be zero, so xy = 0, and the answer to the question "is xy < 0?" is ''no'', so the answer is C.”
June 10, 2019
Brent@GMATPrepNow posted a reply to From a group of 10 students, 7 girls and 3 boys, a teacher in the Problem Solving forum
“Take the task of arranging students and break it into stages. Stage 1: Select two girls Since the order in which we select the women does not matter, we can use combinations. We can select 2 girls from 7 girls in 11C2 ways (21 ways) So, we can complete stage 1 in 21 ways If anyone is ...”
June 10, 2019
GMATGuruNY posted a reply to When the integer n is divided by 6, the remainder is 3, Whic in the Problem Solving forum
“When the integer n is divided by 6, the remainder is 3. When we are given this wording, the smallest option for n is THE REMAINDER ITSELF. Test n=3 in the answer choices: (A) n – 3 = 3-3 = 0 (B) n + 3 = 3+3 = 6 (C) 2n = 2*3 = 6 (D) 3n = 3*3 = 9 (E) 4n = 4*3 = 12 Only D is not a ...”
June 10, 2019
Ian Stewart posted a reply to The ratio of red balls to green balls is 4:3. Three green in the Problem Solving forum
“Adding 3 balls corresponds to changing one value in the ratio by 1, so our ''multiplier'' must be 3, and we must have 12 and 9 balls of each colour, so the answer is 12.”
June 9, 2019
Ian Stewart posted a reply to In how many ways can 10 different paintings be distributed in the Problem Solving forum
“Half the time, the first collector gets less than 5 paintings, so 0, 2 or 4 paintings. We can choose those paintings in 10C0 + 10C2 + 10C4 ways, or 1 + (10)(9)/2! + (10)(9)(8)(7)/4! = 1 + 45 + 210 = 256 ways. The other half of the time, or another 256 times, the first collector gets more than ...”
June 9, 2019
GMATGuruNY posted a reply to A real estate investment firm began the year with 80% of its in the Problem Solving forum
“Let the total investment = $1000, implying that commercial holdings = 80% of 1000 = $800 and that residential holdings = 1000-800 = $200. Since the total $1000 investment grows by 3.5%, the total growth = 3.5% of 1000 = $35. Since the $800 in commercial holdings grows by 7%, the growth in ...”
June 9, 2019
GMATGuruNY posted a reply to In order to conserve the energy and heat in the Sentence Correction forum
“A: reducing the rate at which they burn energy so that it is 25 percent lower Since the penguins are REDUCING THE RATE, we know from context that it refers to the rate, conveying that THE RATE is lower. Regardless, an answer choice may be eliminated for pronoun ambiguity only if an alternate ...”
June 9, 2019
GMATGuruNY posted a reply to Ann deposited money into two new accounts, A and B. Account in the Data Sufficiency forum
“What is the value of 0.08B - 0.05A? Statement 1: B-A = 200 B = A+200 Case 1: A = $100 and B=$300, with the result that 0.08B - 0.05A = 0.08(300) - 0.05(100) = 24-5 = 19 Case 2: A = $200 and B=$400, with the result that 0.08B - 0.05A = 0.08(400) - 0.05(200) = 32-10 = 22 Since 0.08B-0.05A ...”
June 9, 2019
Ian Stewart posted a reply to Is the product of 3p and 4 greater than 20? in the Data Sufficiency forum
“We want to know if 12p > 20, or if p > 5/3, so if p > 1.6666.... Dividing by 5 on both sides in Statement 1, we learn p > 7/5, so p > 1.4, That doesn''t guarantee that p > 1.666..., so Statement 1 is not sufficient. Adding 5 to both sides of Statement 2, we find 3p > 6, ...”
June 8, 2019
Ian Stewart posted a reply to A combined of 55 light bulbs are stored in two boxes; of the in the Data Sufficiency forum
“We have 2 broken bulbs in the first box, so the rest of the 7 broken bulbs must be in the second box, and we have 5 broken bulbs in the second box. From Statement 1, we have 30 unbroken bulbs in the first box, and thus 32 bulbs in total in that box. The rest of the bulbs are in the other box, so ...”
June 7, 2019
Brent@GMATPrepNow posted a reply to If 3 different integers are randomly selected from the integ in the Problem Solving forum
“I specifically created this question to illustrate the importance of calculating the denominator first (when using counting techniques to solve a probability question) There are two reasons why you should calculate the denominator first: 1) The denominator is almost always easier to calculate ...”
June 7, 2019
Brent@GMATPrepNow posted a reply to Puzzling probability question in the Problem Solving forum
“P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student''s sibling) = P(select a business student with a sibling) x P(select a law student who is that business student''s sibling) = 30/500 x 1/800 = 30/400,000 = 3/40,000 = ...”
June 6, 2019
Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the integ in the Problem Solving forum
“If 3 different integers are randomly selected from the integers from 1 to 12 inclusive, what is the probability that a triangle can be constructed so that its 3 sides are the lengths of the 3 selected numbers? A) 3/8 B) 7/18 C) 19/44 D) 39/88 E) 11/24 Answer: C Source: ...”
June 6, 2019
Ian Stewart posted a reply to Find the area of the rectangle ABCD, if the length and bread in the Data Sufficiency forum
“From Statement 1, 2L + 2W = 28, so L + W = 14. There are a few pairs of positive odd integers that add to 14, say 9 and 5 or 3 and 11, and these will give us different areas, so this is not sufficient. From Statement 2, the area of an L by L square is 80% bigger than the area of our L by W ...”
June 6, 2019
Ian Stewart posted a reply to Hotel California in the Problem Solving forum
“We have two groups of lights: lights that should be on, and lights that should be off. Overall, 80% of lights are on. Of lights that should be on, 90% are on (since 10% are off), and of lights that should be off, 40% are on. So we have a standard mixtures situation, which is always a weighted ...”
June 5, 2019
Ian Stewart posted a reply to There are 1600 jelly beans divided between two jards, X and in the Problem Solving forum
“The wording is awkward, but if we have x beans in jar X, and y beans in jar Y, the question tells us x = 3y - 100. Since x+y = 1600, substituting for ''x'' we get 3y - 100 + y = 1600 4y = 1700 y = 425 and the rest of beans, 1600-425 = 1175 beans, are in jar X.”
June 5, 2019
Brent@GMATPrepNow posted a reply to GMAT Prep in the Problem Solving forum
“In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x) On March 1, x/2 rakes are SHIPPED, leaving 3.5x rakes for which the company must pay storage fees. On April 1, x/2 rakes are SHIPPED, leaving 3x rakes for which the company must pay storage fees. ...”
June 5, 2019
Brent@GMATPrepNow posted a reply to VIC question -- picking numbers in the Problem Solving forum
“Originally, T people were to pay total cost of x dollars. So, each person pays x/T each. After S people drop out, there are T-S people to pay total cost of x dollars. So, each person pays x/(T-S) each. The additional amount that each must pay = New cost per person - original cost per ...”
June 5, 2019
Brent@GMATPrepNow posted a reply to Hotel California in the Problem Solving forum
“One option is to use the Double Matrix method. Here, we have a population of lightbulbs, and the two characteristics of each bulb are: - incandescent or fluorescent - on or off Since the questions asks us to find a certain PERCENT, let''s say that there are 100 bulbs altogether. So, we ...”
June 5, 2019
Brent@GMATPrepNow posted a reply to Of the 12 temporary employees in a certain company, 4 will in the Problem Solving forum
“Take the task of selecting the employees and break it into stages. Stage 1: Select the 3 women The order in which we select the women does not matter, so we can use combinations. We can select 3 women from 5 women in 5C3 ways (= 10 ways) Aside: If anyone is interested, here''s video on ...”
June 5, 2019
Brent@GMATPrepNow posted a reply to If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum
“k is 96% greater than its reciprocal The reciprocal of k is 1/k So, we can write: k = (1/k) + (96% of 1/k) In other words: k = (1/k) + 0.96(1/k) Simplify: k = 1.96(1/k) Simplify: k = 1.96/k Multiply both sides by k to get: k² = 1.96 Solve: k = 1.4 of k = -1.4 Rewrite as follows: k = 7/5 of ...”
June 5, 2019
Brent@GMATPrepNow posted a new topic called If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum
“If k is 96% greater than its reciprocal, which of the following is an integer? A) 3k/7 B) 3k/5 C) 5k/7 D) 5k/3 E) 7k/5 Source: www.gmatprepnow.com Difficulty level: 600-650 Answer: C”
June 4, 2019
Ian Stewart posted a reply to Pat has a pocket full of quarters, dimes, and nickels. He in the Problem Solving forum
“He has 6 coins, and he has two types of coins, including nickels. If he has only nickels and dimes, he could have at most 60 cents. But he has 70 cents, so he must have nickels and quarters. Since he must have at least 1 quarter, and can''t have 3 or more (then he''d have more than 70 cents), ...”
June 4, 2019
Ian Stewart posted a reply to The length of one of the sides of an acute angled triangle in the Problem Solving forum
“Take the side of length 15 as the base. If we draw a height from that base, then since the area is 90, that height must be 12. When we draw that height, we divide the triangle into two smaller right triangles, each of which has, as its hypotenuse, one of the other two sides of the big triangle. ...”
June 4, 2019
GMATGuruNY posted a reply to The number line shown contains three points R, S, and T, in the Problem Solving forum
“Let R=-3, S=3 and T=6, implying that r=|-3|=3, s=|3|=3, and t=|6|=6. Average of R, S, and T = (-3+3+6)/3 = 2. The correct answer must yield 2 when r=3, s=3 and t=6. Only E works: (s + t - r)/3 = (3+6-3)/3 = 6/3 = 2 The correct answer is E.”
June 4, 2019
GMATGuruNY posted a reply to The principal feature of the redesigned checks is a series o in the Sentence Correction forum
“In the OA, the list of instructions includes THREE TYPES OF REMINDERS: a reminder TO WATCH a reminder TO COMPARE a reminder TO VIEW In option 2, the list of instructions seems to include the following three nouns: REMINDERS COMPARING VIEWING Thus, the intended meaning is not conveyed in ...”
June 3, 2019
GMATGuruNY posted a reply to Two pieces of fruit are selected out of a group of 8 pieces in the Data Sufficiency forum
“What is the value of P(BB)? Statement 1: From 8 pieces of fruit, the probability of picking an apple = A/8. After 1 of the A apples has been picked, the number of remaining apples = A-1. From the 7 remaining pieces of fruit, the probability of picking one of the A-1 remaining apples = ...”
June 3, 2019
Brent@GMATPrepNow posted a reply to Which of the following sets contains only factors of 45? in the Problem Solving forum
“Scan the answer choices....(C and D)..... 13 is NOT a factor of 45. ELIMINATE C By the process of elimination, the correct answer is D Cheers, Brent Scan the two remaining answer choices.... 7 is NOT a factor of 45. ELIMINATE A, B and E”
June 3, 2019
Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum
“Here''s another approach . . . When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour). Machine R can complete 1/36 of the job in 1 hour. Machine S can complete 1/18 of the job in 1 ...”
June 3, 2019
Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum
“One approach is to assign a "nice" value to the job. Say, the job is to make 36 widgets. R does a certain job in 36 hours This means that machine R''s rate is 1 widget/hour S does the job in 18 hours This means that machine S''s rate is 2 widgets/hour So, their combined rate ...”
June 3, 2019
Ian Stewart posted a reply to Last year Isabella took 7 math tests and received 7 differen in the GMAT Math forum
“Notice a few things here: - If her average after n tests is always an integer, then after n tests, the sum of her scores will always be divisible by n. - So after six tests, the sum of her score is a multiple of 6. Let''s call that sum, after six tests, "S" - If her scores are between ...”
June 3, 2019
Ian Stewart posted a reply to GMAC Official Practice Test #5 in the GMAT Math forum
“You should never assume that a sequence has any particular ''structure'' unless the question explicitly tells you it does. A sequence is just a list of numbers in order, and can have any structure at all. We can''t assume we have, say, consecutive integers here. We want to know what n is, or in ...”
June 3, 2019
Ian Stewart posted a reply to Help with a problem about transformations in the GMAT Math forum
“This is definitely not a GMAT question (so if you have future questions, direct them to a more relevant forum), but in general, geometric transformations cannot always be done in any order, so you should perform them in the order in which they''re listed: D then T.”
June 3, 2019
Ian Stewart posted a reply to Practice Quant problem in the GMAT Math forum
“2^a / 2^b is equal to 2^(a-b). So 2^(x+y)^2 / 2^(x-y)^2 is equal to 2^[ (x+y)^2 - (x-y)^2 ] We could expand both (x+y)^2 and (x-y)^2 and subtract, but it''s faster just to use the difference of squares factorization immediately, since we''re subtracting one square from another in the exponent. ...”
June 3, 2019
Brent@GMATPrepNow posted a reply to If k^2 = m^2, which of the following must be true? in the Problem Solving forum
“The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice. So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1 Now let''s check the answer choices. A. k = m. Test: 1 = 1. Works. Keep A. B. ...”
June 3, 2019
Brent@GMATPrepNow posted a reply to A company that ships boxes to a total of 12 distribution in the Problem Solving forum
“We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...”
June 2, 2019
Ian Stewart posted a reply to Rectangle \(ABCD\) is inscribed in circle \(P\). What is the in the Data Sufficiency forum
“That''s a very confusing diagram, because the letter ''P'', which the stem suggests is the name of the circle, appears to be used in the diagram to label the center of the circle. The same letter cannot be used for both of those things, and if I read the question alone before reading the first half ...”
June 2, 2019
Ian Stewart posted a reply to What is the positive integer n? in the Data Sufficiency forum
“Numbers that satisfy Statement 1 are known as "perfect numbers" in math. You certainly don''t need to know anything about "perfect numbers" for the GMAT, but I''d imagine if you weren''t familiar with them, this question could be time consuming, since using both Statements, there ...”
June 2, 2019
Ian Stewart posted a reply to If j and k are positive integers, is 6 a factor of j? in the Data Sufficiency forum
“Using both Statements, 6 clearly could be a factor of j, but it might be true that j = 2 and k = 3, say, or j = 3 and k =2, and that 6 is not a factor of j. So the answer is E.”
June 2, 2019
Ian Stewart posted a reply to If \(a, b\), and \(c\) are integers, what is the value of in the Data Sufficiency forum
“Just because this is so important in so many questions: if ac = 5, and a and c are integers, there are four possibilities, not two: a and c can be 5 and 1, in either order, or they can be -5 and -1, in either order. Of course, when we combine the two statements, we can discard the negative ...”
June 1, 2019
Ian Stewart posted a reply to In the finite sequence of positive integers \(k_1, k_2,\) in the Data Sufficiency forum
“Since we add two consecutive terms to find the next term, once we know two consecutive terms, it is easy to work out every subsequent term in the sequence (and every earlier term, though we don''t need to do that here). Using Statement 1, we know the 4th and 5th terms are 11 and 18, so the next is ...”
June 1, 2019
Ian Stewart posted a reply to Is the slope of Line 1 positive? in the Data Sufficiency forum
“Each Statement is clearly insufficient alone. Using both, if line two has a slope of 1, then line two would form a 45 degree angle where it meets any horizontal line. If lines one and two meet at a 40 degree angle, then line one either creates a 5 degree or an 85 degree angle with any horizontal ...”
June 1, 2019
Ian Stewart posted a reply to Of all houses on Kermit Lane, 20 have front porches, 20 have in the Data Sufficiency forum
“If every house has a back yard, and, as Statement 1 tells us, 40 houses have a back yard, there are 40 houses in total, so Statement 1 is sufficient. From Statement 2, if a house has a front porch, it does not have a front yard. So if a house has a front yard, it cannot have a front porch. So we ...”
June 1, 2019
Ian Stewart posted a reply to Robin drove from Townville to Villageton. Upon arriving in in the Data Sufficiency forum
“The distance each way is the same. If we call it ''d'', then since time = distance/speed, Robin''s time for the first part of the trip was d/40 and for the return trip was d/60. So her total time was d/40 + d/60 = 5d/120 = d/24. Her total distance was 2d, so her average speed was (total ...”
June 1, 2019
Brent@GMATPrepNow posted a reply to What is the total cost to make 7 long distance telephone in the Data Sufficiency forum
“When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: Case a: Each call was 2 minutes long, for a total of 14 minutes. At $0.32 per ...”
June 1, 2019
GMATGuruNY posted a reply to The vertices of a rectangle in the standard (x,y) coordinate in the Problem Solving forum
“To partition the rectangle into equal areas, the line must pass through the CENTER of the rectangle. To determine the x-coordinate of the center, take the average of the x-coordinates that form the base: (0+7)/2 = 3.5. To determine the y-coordinate of the center, take the average of the ...”
June 1, 2019
GMATGuruNY posted a reply to 10 factories, working for h hours per day, can produce P in the Problem Solving forum
“When the factories work for h hours per day, P cars are produced every 5 days, with the result that 2P cars are produced every 10 days. If the daily work-hours are CUT IN HALF -- to h/2 hours per day -- the number of days required for 2P cars will DOUBLE to 20. Since the time for 2P cars increases ...”
June 1, 2019
GMATGuruNY posted a reply to Being a United States citizen since 1988 and born in Calcutt in the Sentence Correction forum
“One purpose of the present perfect -- has/have + VERBed -- is to express a past action that affects the present. OA: Bharati Mukherjee...has lived in England and Canada. Conveyed meaning: At some time in the past, Bharati Mukherjet lived in England and Canada, and this past action somehow ...”
May 31, 2019
Ian Stewart posted a reply to Peter went to the store to buy paint. Small cans cost $30 in the Data Sufficiency forum
“Using Statement 1 alone, he can''t have bought zero large cans, because 220 is not divisible by 30. He can''t have bought one large can, because 140 is not divisible by 30. And he can''t have bought 3+ large cans, because then he would have spent more than $220. So he must have bought two large ...”
May 31, 2019
Ian Stewart posted a reply to A list contains twenty integers, not necessarily distinct. in the Data Sufficiency forum
“Using Statement 1 alone, we might have some scattered list of 20 distinct integers, say 10, 20, 30, 40, ...., 200. If we add one to any individual value in this list, we still have 20 distinct integers. So we can have a list with no consecutive integers. But our list could also be: 2, 2, 2, 2, ...”
May 31, 2019
Ian Stewart posted a reply to Rose grows two kinds of orchid plants, Phalaenopsises and in the Data Sufficiency forum
“Statement 1 only guarantees we have at least 14 of the P flowers, and Statement 2 only guarantees we have an even number of the G flowers (since we must be able to multiply that number by 1.5 = 3/2 and get a whole number answer). But there remain many possible numbers of P flowers using either ...”
May 31, 2019
Ian Stewart posted a reply to If N different positive integers are added and the sum is in the Data Sufficiency forum
“In the notation used in the question, S/N = sum/number of terms = the average of the list. So the question is just asking "is the average of the N numbers an integer?" Statement 1 tells us we have an odd number of integers, which is not sufficient, since we could have the list 1, 2, 3, ...”
May 31, 2019
Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, \(\frac{2}{3}\) are in the Data Sufficiency forum
“Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...”
May 31, 2019
Ian Stewart posted a reply to A certain diet program calls for eating daily calories from in the Data Sufficiency forum
“It''s a potentially confusing question, because the 40:30:30 ratio in the stem is the ratio of the "daily calories" from each source, while the numbers in Statement 1 are measured in grams, not in calories. So at first glance, looking at Statement 1, it might seem Bill followed the diet ...”
May 30, 2019
Ian Stewart posted a reply to If n is a positive integer and r is the remainder when 4 + 7 in the Data Sufficiency forum
“If, from Statement 1, n+1 is divisible by 3, then for some integer q, we know n+1 = 3q, and n = 3q - 1. Substituting "3q-1" for "n" in the expression 4 + 7n, we have 4 + 7n = 4 + 7(3q - 1) = 4 + 21q - 7 = 21q - 3 = 3(7q - 1) and since we can factor out a 3, this ...”
May 30, 2019
Ian Stewart posted a reply to A certain packing box contains books between 50 to 60. How in the Data Sufficiency forum
“There are at least three grammatical errors in the stem itself, so this might be a good SC question. I assume the question is saying we have between 50 and 60 books. Statement 1 says when we divide that number by 3, the remainder is 1. So we could have 52, 55 or 58 books (any number between 50 and ...”
May 30, 2019
GMATGuruNY posted a reply to If xy≠0, and 60% of x equals 87.5% of y, what is the value in the Problem Solving forum
“60x = 87.5y 120x = 175y 120(x/y) = 175 12(x/y) = 17.5 The correct answer is D.”
May 30, 2019
GMATGuruNY posted a reply to Last year, the price of a jar of peanut butter at a certain in the Problem Solving forum
“The price of a jar of peanut butter at a certain store was P dollars and the price of a jar of jelly at the same store was J dollars, where J=2P. Let P = 10 and J = 20 This year, the price of peanut butter increased by 20% and the price of jelly decreased by 20% New P = 10 + (20% of 10) = 10 + ...”
May 29, 2019
GMATGuruNY posted a reply to In the figure above, \(AB\) is perpendicular to \(BC\) and in the Problem Solving forum
“Let ∆ABD and ∆CBD each be a 45-45-90 triangle with sides 1, 1 and √2: https://i.postimg.cc/JGVTHJg1/two-45-45-90-triangles.png For the figure above, only option B is true: 1/BD² = 1/BC² + 1/AB² 1/1² = 1/√2² + 1/√2² 1 = 1/2 + 1/2 1 = 1 The correct answer is B.”
May 29, 2019
GMATGuruNY posted a reply to GMAT prep question-Confusing one ! in the Sentence Correction forum
“To refer to a noun that takes a SINGULAR verb, we use amount. To refer to a noun that takes a PLURAL verb, we use number. A and C: in terms of flights, an equal amount Here, amount cannot serve to refer to flights (a noun that takes a plural verb). Eliminate A and C. E: an equal number as ...”
May 29, 2019
Brent@GMATPrepNow posted a reply to A computer programmer needs to print 148 documents. The in the Problem Solving forum
“We can also answer this question using a step-by-step approach based on number sense. IMPORTANT: The word approximately typically suggests that we can be somewhat aggressive with our estimation There are 148 documents and the documents have an average length of 10 pages So, the TOTAL number ...”
May 29, 2019
Ian Stewart posted a reply to How many of the 60 balls in the basket are green? in the Data Sufficiency forum
“From Statement 1, 1/12 of the 60 balls are green, so 5 balls are green. So Statement 1 is sufficient. Statement 2 only tells us about 12 of the balls, so is not sufficient.”
May 28, 2019
Brent@GMATPrepNow posted a reply to x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x in the Problem Solving forum
“GIVEN: x + 2y + 3z = 4 5x + 4y + 3z = 8 ADD the two equations to get: 6x + 6y + 6z = 12 Factor: 6(x + y + z) = 12 Divide both sides by 6 to get: x + y + z = 2 Answer: B Cheers, Brent”
May 28, 2019
Brent@GMATPrepNow posted a reply to Two different primes may be said to"rhyme" around in the Problem Solving forum
“If two numbers are rhyming primes, then the integer the rhyme around will be the AVERAGE of the two primes. For example, 3 and 7 rhyme around 5. Notice that the AVERAGE of 3 and 7 is 5. Likewise, 5 and 23 rhyme around 14, and the AVERAGE of 5 and 23 is 14. Now onto the solution... List ...”
May 28, 2019
Brent@GMATPrepNow posted a reply to A certain fruit stand sold apples for $0.70 each and bananas in the Problem Solving forum
“Here''s an approach where we test the POSSIBLE SCENARIOS. FACT #1: (total cost of apples) + (total cost of bananas) = 630 CENTS FACT #2: total cost of bananas is DIVISIBLE by 50, since each banana costs 50 cents. Now let''s start testing POSSIBLE scenarios. Customer buys 1 apple. 1 ...”
May 28, 2019
Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joo, Kendra, Lee, Marnie, and in the Problem Solving forum
“Our goal is to find P(M and N both selected) There are two ways to approach this. Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them ...”
May 28, 2019
GMATGuruNY posted a reply to if x and y are positive , is 4x>3y? in the Data Sufficiency forum
“Since y is POSITIVE, the inequalities can safely be divided by y. 4x > 3y x > (3/4)y x/y > 3/4 Question stem, rephrased: Is x/y > 3/4? Statement 1: x > y-x 2x > y 2(x/y) > 1 x/y > 1/2 Case 1: x/y = 2/3 In this case, x/y < 3/4, so the answer to the ...”
May 28, 2019
GMATGuruNY posted a reply to A certain fruit stand sold apples for $0.70 each and bananas in the Problem Solving forum
“Consider the following equation: 2x + 3y = 30. If x and y are nonnegative integers, the following solutions are possible: x=15, y=0 x=12, y=2 x=9, y=4 x=6, y=6 x=3, y=8 x=0, y=10 Notice the following: The value of x changes in increments of 3 (the coefficient for y). The value ...”
May 28, 2019
Ian Stewart posted a reply to In an endurance race, a car drove the whole race at a in the Data Sufficiency forum
“The car is driving 180 miles per hour. If it drove more than 2 hours, all we know is that it drove more than 360 miles, so Statement 1 is not sufficient. If it drove less than 2.75 = 11/4 hours, then it drove less than (11/4)(180) = (11/2)(90) = 11*45 = 495 miles, so the total distance was certainly ...”
May 27, 2019
Brent@GMATPrepNow posted a reply to Car X is 40 miles west of Car Y. Both cars are traveling in the Problem Solving forum
“Let''s let Car X''s original position be the initial starting point. So, when Car X is at the initial starting point, Car Y has already traveled 40 miles. My word equation involves the conditions when Car X catches up to Car Y. At that point, we can say: Car X''s TOTAL distance traveled = ...”
May 27, 2019
GMATGuruNY posted a reply to probability in the Problem Solving forum
“3 wins and 2 losses = WWWLL. One way to determine the number of ways to get 3 wins is to count the number of ways to arrange the 5 letters WWWLL. The number of ways to arrange 5 elements = 5!. But when an arrangement includes IDENTICAL elements, we must divide by the number of ways each set of ...”
May 27, 2019
GMATGuruNY posted a reply to in old problem.. in other point.. in the Sentence Correction forum
“An ABSOLUTE PHRASE refers to the preceding subject. COMMA + APPOSITIVE serves to explain or define the nearest preceding noun or noun phrase. B and C: The computer company...will purchase the color-printing division of a rival company for $950 million, a part of a deal... Here, the modifier in ...”
May 27, 2019
Brent@GMATPrepNow posted a reply to Gita is 12 years older than Harvey. In 4 years, Gita will be in the Problem Solving forum
“Gita is 12 years older than Harvey. Let x = Harvey''s PRESENT age Let x + 12 = Gita''s PRESENT age In 4 years, . . . . x + 4 = Harvey''s age IN FOUR YEARS (x + 12) + 4 = Gita''s age IN FOUR YEARS . . . Gita will be twice as old as Harvey. So: (Gita''s age IN 4 YEARS) = 2(Harvey''s ...”
May 26, 2019
GMATGuruNY posted a reply to A bowl contains equal numbers of red, orange, green, blue, in the Problem Solving forum
“10 Let R=O=G=B=Y=20, for a total of 100 marbles. Kaz eats all of the green candies and half of the orange ones. R=20, O=10, G=0, B=20, Y=20 He eats half of the remaining pieces of each color. R=10, O=5, G=0, B=10, Y=10 He eats red and yellow candies in equal proportions until the total ...”
May 26, 2019
GMATGuruNY posted a reply to If a/b<c/d & bd < 0, which of the following inequa in the Problem Solving forum
“In I, II and III, test the following case: a=c=d=1 and b=-1, with the result that a/b < c/d and bd < 0. I: ad-bc < 0 Since ad=1*1=1 and bc=-1*1=-1, we get: 1 - (-1) < 0 2 < 0 Not true. Eliminate A and D, each of which include I. II: bc-ad > 0 Since bc=-1*1=-1 abd ...”
May 26, 2019
Ian Stewart posted a reply to What is the units digit of positive integer \(p\)? in the Data Sufficiency forum
“When we divide an integer by 10, its units digit is the remainder. So Statement 1 is immediately sufficient - the units digit is 8. The units digit of a number has nothing to do with the remainder you get when you divide by 11, so Statement 2 is useless (e.g. our number can be 19 or 30, which ...”
May 25, 2019
Ian Stewart posted a reply to A school has \(a\) students and \(b\) teachers. if \(a<15 in the Data Sufficiency forum
“From Statement 1, the number of students, a, is divisible by every number in that list, so it is divisible by the LCM of those numbers. If we just identify the prime divisors in that list, and their relevant exponents, we have a 2, a 5, and 3^2, so the LCM is 90. So the number of students is a ...”
May 25, 2019
GMATGuruNY posted a reply to A husband and wife can complete a certain task in 1 and 2 in the Data Sufficiency forum
“Let the job = 12 units. Dividing the four given times into the 12-unit job, we get the following hourly rates: Husband:Wife:Rae:Herman = (12 per hour): (6 per hour) : (3 per hour) : (2 per hour) (Husband + Wife) : (Rae + Herman) = (12+6 per hour) : (3+2 per hour) Couple : Children = 18:5 ...”
May 24, 2019
Ian Stewart posted a reply to In a certain alphabet, 12 letters contain a dot and a in the Problem Solving forum
“Strange question - the question tells us about 36 of the letters, and there are 40 letters in total. So there are 4 letters left, and they must be in the "dot and no line" category.”
May 24, 2019
Ian Stewart posted a reply to Gordon buys 5 dolls for his 5 nieces. The gifts include two in the Problem Solving forum
“Any 5-letter word we make using the letters S, S, E, G, T corresponds to one way to distribute the dolls. So the word SEGTS for example corresponds to giving the S doll to the oldest child, the E to the next oldest, and so on. If the letters were different, there would be 5! words we could make ...”
May 24, 2019
Ian Stewart posted a reply to A husband and wife can complete a certain task in 1 and 2 in the Data Sufficiency forum
“Using whatever rates method one prefers, you can just find how long the husband and wife take, how long the children take, and take the ratio of those two times. I''d get the same time for the husband and wife: h does 2 tasks in 2 hours w does 1 task in 2 hours h+w do 3 tasks in 2 hours so 1 ...”
May 24, 2019
Ian Stewart posted a reply to When the positive integer \(n\) is divided by \(25\), the in the Data Sufficiency forum
“Using Statement 1, n can be 13, 38, 63, and 88. Using Statement 2 alone, we''ll have an infinite number of values of n, separated by 100, the LCM of 25 and 20. Using both Statements, n must be 63, and the answer is C.”
May 24, 2019
Brent@GMATPrepNow posted a reply to Al and Ben are drivers for SD Trucking Company. One snowy da in the Problem Solving forum
“Let''s start with a "word equation" (Ben''s travel distance) + (Al''s travel distance) = 240 miles Let t = Al''s travel time (in hours) So, t + 3= Ben''s travel time (since Ben spent 3 more hours driving) Distance = (rate)(time) So, our word equation becomes... (20)(t + 3) = ...”
May 24, 2019
Brent@GMATPrepNow posted a reply to What is x in the diagram below? in the Problem Solving forum
“The important thing to recognize here is that there are two SIMILAR TRIANGLES hiding in this diagram. http://s24.postimg.cc/50bvp89dt/sim_tri.jpg Notice that these two triangles share both a 90-degree angle AND the angle I''ve denoted with a purple dot. Since the 3 angles in each triangle must ...”
May 24, 2019
Brent@GMATPrepNow posted a reply to j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum
“Useful remainder property: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0 When j is divided by k, the remainder is m The above property ...”
May 23, 2019
Ian Stewart posted a reply to What is the remainder when \(a\) is divided by 4? in the Data Sufficiency forum
“You could just see what happens with 1 and 3 here (the only two different odd remainders when you divide by 4), to see that Statement 1 is sufficient. Or you could prove it algebraically: we can write an odd number as 2m + 1, so if a is the square of an odd integer, a = (2m + 1)^2 = 4m^2 + 4m + 1, ...”
May 23, 2019
Ian Stewart posted a reply to Nancy, a car dealer, put 4 cars on sale. All cars on sale in the Data Sufficiency forum
“Is there a typo in the question? If Nancy only put 4 cars on sale, then it''s impossible for "30% of the cars with automatic gear are hybrids" to be true, because then there''s no way for the number of automatic hybrids to be an integer (unless there are zero of them, but then it makes no ...”
May 23, 2019
GMATGuruNY posted a reply to A jar contains 8 red marbles and \(y\) white marbles. in the Data Sufficiency forum
“Test the THRESHOLDS and try EXTREMES. Here, the THRESHOLDS are y=8 and y=4. Statement 1: y≤8 Case 1: 8 white marbles, 8 red marbles P(RR) = 8/16 * 7/15 = 7/30. P(one of each color): P(RW) = 8/16 * 8/15 = 8/30. Since RW can be reversed to WR, we multiply by 2: 2(8/30) = 16/30. In ...”
May 23, 2019
GMATGuruNY posted a reply to Robots X, Y, and Z each assembled components at their in the Data Sufficiency forum
“Let X = X''s rate, Y = Y''s rate, and Z = Z''s rate. r(x) = the ratio of X''s rate to Z''s rate = X/Z. r(y) = the ratio of Y''s rate to Z''s rate = Y/Z. Note: X, Y and Z all represent rates and thus must be POSITIVE. Statement 1: r(x) < r(y) In other words: X/Z < Y/Z. Since ...”
May 23, 2019
GMATGuruNY posted a reply to In the diagram above, line BC touches the circle at point C in the Data Sufficiency forum
“To determine the area of the circle, we need to know its radius. Question stem, rephrased: What is the value of r? A radius drawn to a tangent line forms a RIGHT ANGLE. Thus, angle OCB is a right angle, with the result that triangle OCB is a right triangle. In right triangle OCB, OB=r, BC=35, ...”
May 23, 2019
GMATGuruNY posted a reply to NNN in the Critical Reasoning forum
“Consider the following case: The networks airs over one hundred programs focused largely on the opinions of its viewers. The NUMBER of programs tells us nothing about the NATURE of the opinions (whether they are liberal or conservative) or about the network''s REACTION to these opinions (whether ...”
May 23, 2019
Brent@GMATPrepNow posted a reply to Challenge question: Is positive integer p even? in the Data Sufficiency forum
“------ASIDE--------------------- Here''s a useful rule: If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors. Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors ...”
May 22, 2019
Brent@GMATPrepNow posted a new topic called j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum
“j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz? i) 49 ii) 50 iii) 56 A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii ...”
May 22, 2019
Ian Stewart posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum
“Among any three consecutive integers, you always have exactly one multiple of 3. So if one of our answers here was something like (n-1)(n)(n+1), the product of three consecutive integers, it would certainly be divisible by 3. We don''t have something quite that easy, but if you look at answer A: ...”
May 22, 2019
Ian Stewart posted a reply to A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in the Problem Solving forum
“The diagrams are confusing, because they aren''t to scale -- in the second diagram, AF is suddenly much longer than in the first, even though the length AF hasn''t changed. Regardless, after folding the paper, the angle at E remains a 90 degree angle, the length of DE is still 12, and the lengths ...”
May 22, 2019
Ian Stewart posted a reply to Mr. Smith purchases books from the bargain bin. He buys only in the Data Sufficiency forum
“Using both Statements, he might have bought one $7 book, eight $2 books, and one $1 book, or he might have bought two $7 books, two $2 books and six $1 books, so the answer is E.”
May 22, 2019
Brent@GMATPrepNow posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum
“One approach is to test values If n = 7, we get: (A) 7(7 + 1)(7 – 4) = (7)(8)(3). Definitely divisible by 3. KEEP (B) 7(7 + 2)(7 – 1) = (7)(9)(6). Definitely divisible by 3. KEEP (C) 7(7 + 3)(7 – 5) = (7)(10)(4). NOT divisible by 3. ELIMINATE. (D) 7(7 + 4)(7 – 2) = (7)(11)(5). NOT ...”
May 22, 2019
GMATGuruNY posted a reply to NNN in the Critical Reasoning forum
“The two statements together serve to form the conclusion of the programming director. A premise is a FACT not in dispute. A conclusion is an OPINION that CAN be disputed. Only one FACT is presented in the passage: When a liberal news personality was recently added to the Network, an additional ...”
May 22, 2019
GMATGuruNY posted a reply to A conveyor belt moves bottles at a constant speed of 120 in the Data Sufficiency forum
“Given rate: 120 centimeters per second. Since the statements are in terms of MINUTES, calculate the number of minutes required to move the bottle 90 meters: 90 meters * (100 centimeters)/(1 meter) * (1 second)/(120 centimeters) * (1 minute)/(60 seconds) = (90)/(12*6) = 15/12 = 5/4 = 1.25 minutes ...”
May 22, 2019
Ian Stewart posted a reply to Each of three students is given fifteen tokens to spend at a in the Data Sufficiency forum
“This is not a good question, because what you would naturally and correctly assume in any other GMAT question turns out not to be true here. If you saw a question like this, for example: Amir goes to a store with $11 and buys at least one chair. How many chairs did he buy? 1. Chairs cost $10 ...”
May 21, 2019
GMATGuruNY posted a reply to ps 500 test27 #16 in the Problem Solving forum
“John and Mary were each paid x dollars in advance to do a certain job together. John worked on the job for 10 hours. Mary worked 2 hours less than John. Since a total of 18 hours are worked -- 10 hours by John, 8 hours by Mary -- let x=18. Since John and Mary are each given $18 in advance, the ...”
May 21, 2019
Ian Stewart posted a reply to In the morning, Chris drives from Toronto to Oakville and in in the Data Sufficiency forum
“Statement 1 is obviously not sufficient. For Statement 2, it takes just as long to drive d miles at 50 miles per hour as it does to drive 2d miles at 100 miles per hour. So if he drove half the distance at exactly 50 mph, he''d need to travel the other half instantaneously, in 0 seconds, to have ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Question from mba.com mock test in the Problem Solving forum
“The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. So, 120 = 120 * 2^10)] + 60 Divide both sides by 60: 2 = 2 * 2^ f = 120 * 2^ The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit? f = 120 * 2^30)] + ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to OG #132 in the Problem Solving forum
“We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to ps 500 test27 #16 in the Problem Solving forum
“One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to problem to solve in the Problem Solving forum
“What we really have here is an algebra question requiring us to combine like terms. First, notice that K + K = 2K Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6 Similarly, notice that M + M + M = 3M Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6 So, 2^5 + ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to test 39 #13 in the Problem Solving forum
“Here''s a related question to practice with: https://www.beatthegmat.com/intensity-scale-readings-t273997.html Cheers, Brent”
May 21, 2019
Brent@GMATPrepNow posted a reply to test 38 #15 in the Problem Solving forum
“red = 7 yellow = 5 green = 3 blue = 2 147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7) So, there are 3 blue beads, 1 green bead, 3 yellow beads and 2 red beads. Cheers, Brent”
May 21, 2019
Brent@GMATPrepNow posted a reply to test35 # 15 in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Help on PS problem- GMATprep in the Problem Solving forum
“Let''s test the values using x = 0 So, we can reword the question as, For which of the following functions is f(0)=f(1-0) In other words, we''re looking for a function such that f(0) = f(1) A) f(x)=1-x f(0)=1-0 = 1 f(1)=1-1 = 0 Since f(0) doesn''t equal f(1), eliminate A B) f(x) = 1 - ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Probability in the Problem Solving forum
“We want: a) # of teams that include both John and Peter b) total # of 5-person teams possible a) # of teams that include both John and Peter Put John and Peter on the team (this can be accomplished in 1 way) Select the remaining 3 team-members from the remaining 7 players (this can be ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to Mr. Jones spends $ 25 on movie tickets for a party of adults in the Data Sufficiency forum
“ Given: Mr. Jones spends $25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost $3 each and children''s tickets cost $2 each. There are several scenarios that satisfy statement 1. Here are ...”
May 21, 2019
Brent@GMATPrepNow posted a reply to A collection of 16 coins, each with a face value of either in the Problem Solving forum
“Let D = the NUMBER of 10-cent coins Let Q = the NUMBER of 25-cent coins Notice that the VALUE of Q 25-cent coins = ($0.25)Q For example, the VALUE of six 25-cent coins = ($0.25)6 = $1.50 And the VALUE of ten 25-cent coins = ($0.25)10 = $2.50 etc Likewise, the VALUE of D 10-cent coins = ...”
May 21, 2019
Brent@GMATPrepNow posted a new topic called Challenge question: Is positive integer p even? in the Data Sufficiency forum
“Is positive integer p even? (1) 4p has twice as many positive divisors as p has (2) 8p has 3 positive divisors more than p has Answer: A Source: www.gmatprepnow.com Difficulty level: 700+”
May 20, 2019
Ian Stewart posted a reply to Store S sold a total of 90 copies of a certain book during in the Data Sufficiency forum
“Using Statement 1 alone, Friday''s sales might have been greater than 11 (from Sunday through Saturday the sales might have been 1,2,3,4,8,22,50, say) or might not have been (the sales might have been 1,2,3,4,8,10,62, say). Using Statement 2 alone, we know that in the six days besides Saturday, ...”
May 20, 2019
GMATGuruNY posted a reply to Is x > 0? in the Data Sufficiency forum
“Note: |a|² = a² |a+b|² = (a+b)² Statement 1: Since an absolute value cannot be negative, both sides of the inequality must be nonnegative, allowing us to safely square it: (|x| + |y|)² > |x + y|² |x|² + |y|² + 2|x||y| > (x+y)² x² + y² + 2|x||y| > x² + y² + 2xy |x||y| ...”
May 20, 2019
GMATGuruNY posted a reply to If f(x)=x^4+4x^2+7, f(x)=g(x)^2+3 and g(x) > 0, then g(x) in the Problem Solving forum
“Let x=0, with the result that f(x) = 0+0+7 = 7. Remembering that g(x)>0 and plugging f(x)=7 into f(x)=g(x)²+3, we get: 7 = g(x)²+3 4 = g(x)² g(x) = 2 Since the question stem asks for the value of g(x), the correct answer must yield 2 when x=0. Only B works: x²+2 = 0²+2 = 2 The ...”
May 20, 2019
Ian Stewart posted a reply to n is a positive integer, and k is the product of all integer in the Problem Solving forum
“This is essentially a direct copy of an official question, with one number changed: https://gmatclub.com/forum/if-n-is-a-positive-integer-and-the-product-of-all-integers-90855.html though you might notice how much more elegant the wording of the official problem is (there''s no need to ...”
May 19, 2019
Ian Stewart posted a reply to The value of the variable E is determined by adding the reci in the Problem Solving forum
“This question makes no sense - as defined, E represents a single numerical value, so E is not a "variable". And if E has a single numerical value, so does its reciprocal, so it makes no sense to ask what "can be a possible value of the reciprocal of E". An answer is either equal ...”
May 19, 2019
Ian Stewart posted a reply to In the figure above, equilateral triangle ABC is inscribed in the Problem Solving forum
“By symmetry, since the triangle is equilateral, the length of each circular arc between two adjacent corners of the triangle must make up 1/3 of the entire circumference of the circle. Since the arc ABC is two of those arcs put together, 24 is 2/3 of the circumference, and 36 is the entire ...”
May 19, 2019
Ian Stewart posted a reply to A number of individuals volunteer to walk dogs at a certain in the Data Sufficiency forum
“If we have d dogs, and v volunteers, we just want to know if d is divisible by v. Statement 1 is not sufficient, because we could have 45 dogs, and 7 volunteers, and the answer is ''no'', or 45 dogs and 9 volunteers, and the answer is ''yes''. Statement 2 is not sufficient because we could ...”
May 19, 2019
Ian Stewart posted a reply to Do at least 60 percent of the students in Pat’s class walk in the Data Sufficiency forum
“Statement 1 is not sufficient - we''d need to know something about male students. Statement 2 tells us the ratio of walkers to not-walkers is 2 to 1, so 2/3 of students walk, and since we now know exactly what percentage walk to school, we can answer the question and the answer is B.”
May 19, 2019
Ian Stewart posted a reply to What is the value of y? in the Data Sufficiency forum
“Each statement is clearly insufficient alone. Using both, from Statement 1 we can factor since we have a difference of squares: (x + y)(x - y) = 5 From Statement 2, x+y and x-y are both integers, and if x and y are each positive integers, x+y is greater than 1. Since x+y is also clearly a ...”
May 18, 2019
Ian Stewart posted a reply to In the rectangular coordinate system shown above, does the in the Data Sufficiency forum
“If a line has a negative slope, that line is falling as it moves to the right. So it is rising as it moves to the left, and eventually it will rise high enough to be in quadrant II. So Statement 1 is sufficient. Statement 2 tells us one point on the line but nothing about how the line rises or ...”
May 18, 2019
Ian Stewart posted a reply to An art gallery has only paintings and sculptures. Currently, in the Problem Solving forum
“If 1/3 of the non-displayed things are paintings, 2/3 of them are sculptures. So if 200 are sculptures, we have 300 non-displayed things in total. Since 1/3 of things are on display, the ratio of displayed to not is 1 to 2, so we have 150 things on display, and 150+300 = 450 things in total.”
May 18, 2019
Brent@GMATPrepNow posted a reply to In the figure above, if A, B, and C are the areas, respectiv in the Data Sufficiency forum
“Key concept: We''re told that the area of the BLUE circle = the area of the RED circle https://i.imgur.com/AZaIFeU.png This means we can say: A + B = B + C Now onto the question..... Target question: What is the value of B + C ? Statement 1: A + 2B + C = 24 Rewrite this as: (A + B) ...”
May 17, 2019
GMATGuruNY posted a reply to (n+1)!f(n) = (n-1)!. What is the value of f(1) + f(2) + … in the Problem Solving forum
“f(n) = (n-1)!/(n+1)! f(1) = 0!/2! = 1/2 f(2) = 1!/3! = 1/6 f(3) = 2!/4! = 1/12 f(4) = 3!/5! = 1/20 f(1) + f(2) = 1/2 + 1/6 = 2/3 f(1) + f(2) + f(3) = 2/3 + 1/12 = 3/4 f(1) + f(2) + f(3) + f(4) = 3/4 + 1/20 = 4/5 The sum of the first 2 terms = 2/3. The sum of the first 3 terms = 3/4. ...”
May 17, 2019
GMATGuruNY posted a reply to A 3-digit positive integer consists of non zero digits. If in the Problem Solving forum
“Alternate approach: Integers with exactly 2 digits the same = Total integers - Integers with all 3 digits the same - Integers with all 3 digits different. Total integers: Number of options for the hundreds digit = 9. (Any digit but 0.) Number of options for the tens digit = 9. (Any digit ...”
May 16, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #7: - The Table Method Video : https://www.youtube.com/watch?v=lYfTiRIG_k4 Cheers, Brent”
May 16, 2019
GMATGuruNY posted a reply to What is the value of x? in the Data Sufficiency forum
“Statement 1: Squaring both sides, we get: x² + y² + 2xy = x² + y² - 2xy 4xy = 0 xy = 0 Case 1: x=0, with the result that y can be any value Case 2: y=0, with the result that x can be any value Since Case 2 allows x to be any value, INSUFFICIENT. Statement 2: Here, y can be any ...”
May 16, 2019
GMATGuruNY posted a reply to Each of A, B and C represents a one-digit integer. AB and BA in the Problem Solving forum
“325 = 100*3 + 10*2 + 5 648 = 100*6 + 10*4 + 8 Generally: Three-digit integer XYZ = 100X + 10Y + Z Since BA + AB + AB = CAA, we get: (10B+A) + (10A+B) + (10A+B) = 100C + 10A + A 12B + 21A = 100C + 11A 12B + 10A = 100C 12B + 10A = MULTIPLE OF 100 Since B and A are digits, the left side will ...”
May 16, 2019
GMATGuruNY posted a reply to The federal immigration station on Ellis Island - GMATPrep in the Sentence Correction forum
“Yes. E: Of all immigrants...the station processed nearly three quarters of them. Here, the red modifier is redundant with the blue modifier. Generally, COMMA + having + VERBed serves to express an action that happens before the action in the preceding clause. E: The federal immigration ...”
May 15, 2019
Ian Stewart posted a reply to The age of a group of people follows a distribution, which in the Problem Solving forum
“95% of the distribution is within two standard deviations of the mean, so 95% of the distribution lies between A - 2SD and A + 2SD. So all of those values are less than A+2SD. The other 5% of the distribution is more than two standard deviations from the mean. Since the distribution is symmetric, ...”
May 15, 2019
Brent@GMATPrepNow posted a reply to If Mary always takes the same route to work, how long did it in the Data Sufficiency forum
“Target question: How long did it take Mary to get to work on Friday? Statement 1: It took Mary 20 minutes to get to work on Thursday. Clearly, we cannot use this information to answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: Mary''s average speed ...”
May 15, 2019
GMATGuruNY posted a reply to In the xy-coordinate system, rectangle ABCD is inscribed in the Problem Solving forum
“x²+y² = r² is the equation for a circle with its center at the origin and a radius of r. Thus, x²+y² = 25 is a circle with a center at the origin and a radius of 5. The information in the prompt yields the following figure: https://i.postimg.cc/xJCgjxbd/rectangle-in-circle.png OB is a ...”
May 15, 2019
Ian Stewart posted a reply to The median of n consecutive odd integers is 30. If the fifth in the Problem Solving forum
“This question makes no sense - they are misusing terminology. If you talk about a list of "consecutive" odd integers, say, then the second thing in the list follows the first thing, in sequence - the second term must be larger than the first term. But here they intend the sequence of ...”
May 14, 2019
Ian Stewart posted a reply to In the xy-coordinate system, rectangle ABCD is inscribed in the Problem Solving forum
“If a circle has the equation x^2 + y^2 = r^2, then it is a circle centered at the origin, with radius r. So our circle here is a circle of radius 5, centered at (0, 0). So, if a diagonal of the inscribed rectangle lies on the x-axis, the coordinates of its endpoints must be (-5, 0) and (5, 0). We ...”
May 14, 2019
Brent@GMATPrepNow posted a reply to x-4=z y-x=8 8-z=t For the system of equations given, what in the Data Sufficiency forum
“Target question: What is the value of z? Statement 1: x = 7 Scanning the three given equations, we see that equation i is all we need to determine the value of z i) x - 4 = z Replace x with 7 to get: 7 - 4 = z So, z = 3 Since we can answer the target question with certainty, statement 1 ...”
May 14, 2019
GMATGuruNY posted a reply to A retail store employs only clerks and managers and the in the Problem Solving forum
“Last year''s payroll = (number of employees)(average hourly wage) = 20*13 = 260. This year 4 clerks are hired, increasing the number of employees to 24. Since the average hourly wage this year = 14, we get: This year''s payroll = (number of employees)(average hourly wage) = 24*14 = 336. ...”
May 14, 2019
Brent@GMATPrepNow posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum
“KEY CONCEPT: 30-60-90 triangles are known as special right triangles, and we know quite a bit about this kind of triangle Target question: What is the length of segment JL ? Statement 1: JK = 10 https://i.imgur.com/sKEFT1R.png Compare ΔJKL with the BASE 30-60-90 triangle. Their ...”
May 13, 2019
Ian Stewart posted a reply to 50 students of a certain class took a test. How many of them in the Data Sufficiency forum
“Using both Statements, it''s possible all 50 students got a score of ''82'', or it''s possible that 25 of them got ''81'' and 25 of them got ''83'', among other possibilities. So the answer is E.”
May 13, 2019
Ian Stewart posted a reply to A jar contains exactly 100 marbles; each marble contains in the Data Sufficiency forum
“If we have 100 marbles, and each marble is made up of 2 colours, we have 200 colours in total. Using either Statement alone, we haven''t accounted for very many of the colours, so we could have quite a few half-blue marbles or we could have none, and our probability of picking half-blue marbles ...”
May 13, 2019
Ian Stewart posted a reply to Cotto Toy Store sells Product X and Product Y at two in the Data Sufficiency forum
“Neither Statement is sufficient alone, because if the initial price of X is enormously larger than the initial price of Y, using either Statement alone, the discounted price of X will remain larger, and similarly if the initial price of Y is vastly larger than that of X, so will be Y''s discounted ...”
May 13, 2019
Ian Stewart posted a reply to Maria can either buy a basket that contains P pounds of in the Data Sufficiency forum
“The basket costs $16.50, and the p pounds of apples cost $0.95p. We want to know which of those figures is larger. Statement 1 is irrelevant, since we don''t care how many apples are in the basket -- we already know the basket costs $16.50. What we need is information about the p pounds of ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to A line that passes through (–1, –4) and (3, k) has a slo in the Problem Solving forum
“Slope of line between the points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1) So, we can write: k = [k - (-4)]/[3 - (-1)] Simplify: (k + 4)/4 = k Multiply both sides by 4 to get: k + 4 = 4k Subtract k from both sides to get: 4 = 3k Divide both sides by 3 to get: 4/3 = k Answer: C Cheers, ...”
May 13, 2019
Ian Stewart posted a reply to What percent of the children in the class are holding a in the Data Sufficiency forum
“The answer is instantly C or E, since we''ll need to know about both boys and girls. Using both statements, we have a standard weighted average situation. If k% of boys and m% of girls are holding a popsicle, then somewhere between k% and m% of the group as a whole is holding a popsicle, where the ...”
May 13, 2019
Ian Stewart posted a reply to S is a set of points in the plane. How many distinct in the Data Sufficiency forum
“We clearly need to know how many points we have, since if we have, say, only 2 points, we can''t draw any triangles, but if we have many points that aren''t all in a line, we can draw at least one triangle. So Statement 1 is indispensable. But knowing we have exactly 5 points is not sufficient, ...”
May 13, 2019
Ian Stewart posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum
“In general, if you know all three angles in a triangle (which we do here, since from two angles we can find the third using the fact that a triangle''s angles sum to 180), and you know one of the triangle''s sides, the other two sides are completely determined, so it must somehow be possible to work ...”
May 13, 2019
Ian Stewart posted a reply to Automobile A is traveling at two-thirds the speed that Autom in the Data Sufficiency forum
“Each Statement gives the same type of relationship between the two speeds, so the answer will be C, D or E. If we let a and b be the two speeds of the cars, we know that a = 2b/3. Using Statement 1 alone, you might be able to see by inspection that the speeds are 20 and 30. Or we can use ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum
“This question relies on our ability to determine the VALUE of any 2-digit number. For example, what is the VALUE of 83? For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just ...”
May 13, 2019
GMATGuruNY posted a reply to According to public health officials in the Sentence Correction forum
“Incorrect: More babies were born in 1900 than they were born in 1800. Here, the usage of they implies that the SAME BABIES born in 1900 were also born in 1800 -- a nonsensical meaning. Generally: When a comparison begins with MORE/FEWER + SUBJECT + VERB, the implied clause after than should NOT ...”
May 13, 2019
GMATGuruNY posted a reply to An auto dealer sells each car at either $20,000 or $30,000. in the Data Sufficiency forum
“Statements combined: Case 1: 30 $30,000 cars are marked up 30%'' 20 $20,000 cars are marked up 20% Case 2: 10 $30,000 cars are marked up 30% 20 $20,000 cars are marked up 30% 20 $30,000 cars are marked up 20% In Case 1, the more expensive $30,000 cars are all sold at the higher profit ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to If n is an integer greater than 10, then the expression (n^2 in the Problem Solving forum
“-----ASIDE--------------------- There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be ...”
May 12, 2019
GMATGuruNY posted a reply to OG 13 #9 in the Sentence Correction forum
“When a statistic decreases in value, we use lower rather than less. Incorrect: The temperature was less in the second experiment than in the first. Correct: The temperature was lower in the second experiment than in the first. Most of the country’s biggest daily newspapers had lower ...”
May 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are the lengths of the legs of a right triangle, in the Data Sufficiency forum
“ Given: x and y are the lengths of the legs of a right triangle We have something like this: https://i.imgur.com/VxCexHO.png Target question: What is the value of xy? Statement 1: The hypotenuse of the triangle is There are infinitely-many different right triangles that meet this ...”
May 11, 2019
Brent@GMATPrepNow posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum
“Question rephrased: In how many different ways can we arrange the letters WWWLLD -------------ASIDE-------------------------------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the If there are n objects where A of them are ...”
May 11, 2019
GMATGuruNY posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum
“Alternate approach: There are 6 slots in the season: 3 wins, 2 losses and 1 draw. From the 6 slots, the number of ways to choose 3 to be occupied by the 3 wins = 6C3 = (6*5*4)/(3*2*1) = 20. From the 3 remaining slots, the number of ways to choose 2 to be occupied by the 2 losses = 3C2 = ...”
May 11, 2019
GMATGuruNY posted a reply to OG 13 #9 in the Sentence Correction forum
“Here, greater serves to modify not costs but PROPORTION. Conveyed meaning: The PROPORTION in the presidential campaign of 1992 was greater than the PROPORTION in any previous election. When comparing elements with regard to WEIGHT, we generally use not lower but LESS. Adam weighs LESS than ...”
May 11, 2019
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1 In this case, (a-b)/6 = C.”
May 11, 2019
GMATGuruNY posted a reply to If a, b, and c are positive integers, what is the remainder in the Data Sufficiency forum
“Statement 1: No information about b. INSUFFICIENT. Statement 2: No information about a. INSUFFICIENT. Statements combined: Case 1: c=1, with the result that a=1³=1 and b=(1-2)³=-1 In this case, (a-b)/6 = C.”
May 11, 2019
Brent@GMATPrepNow posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum
“We can also solve the question using one variable Given: Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. Let G = the number of years Green worked at Firm X So, G - 4 = the number of years Smith worked at Firm X (since ...”
May 10, 2019
Brent@GMATPrepNow posted a reply to In the below addition A, B, C, D, E, F, and G represent the in the Problem Solving forum
“If we add two 2-digit numbers and the sum is a 3-digit number, then the 3-digit number must start with a 1. So, E = 1 In order for the sum to be a 3-digit number, A+C must be greater than 9 So, we have two options: EITHER A and C are 5 and 6, OR A and C are 4 and 6 If A and C are 5 and 6, ...”
May 10, 2019
GMATGuruNY posted a reply to According to surveys by the National Institute on Drug Abuse in the Sentence Correction forum
“Proposed revision: as many young adults as the 1997 survey reported Conveyed meaning: The 1997 survey reported many young adults. This meaning seems illogical. The 1997 survey reported a NUMBER. It did not report the young adults themselves.”
May 10, 2019
GMATGuruNY posted a reply to Ellipsis question in the Sentence Correction forum
“OA: Today, the same amount of acreage produces twice as many apples as it did in 1910. The phrase in blue conveys that the amount of acreage producing apples today is the SAME as the amount that produced apples in 1910. For example: If 100 acres produced apples in 1910, then 100 acres are ...”
May 10, 2019
GMATGuruNY posted a reply to An art gallery has only paintings and sculptures. Currently, in the Problem Solving forum
“This is an EITHER/OR group problem. Every piece of art is EITHER a painting OR a sculpture. Every piece of art is EITHER displayed OR not displayed. For an EITHER/OR group problem, we can use a GROUP GRID (also known as a double-matrix) to organize the data. Let P = paintings, S = ...”
May 10, 2019
Brent@GMATPrepNow posted a reply to If xyz ≠ 0, what is the value of in the Data Sufficiency forum
“Target question: What is the value of (x⁴z²)/(z²y²)? This is a good candidate for rephrasing the target question. Since z ≠ 0, we know that z² ≠ 0 So, we can safely take (x⁴z²)/(z²y²) and divide top and bottom by z² to get: x⁴/y² REPHRASED target question: What is the value ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Is quadrilateral PQRS a parallelogram? in the Data Sufficiency forum
“Target question: Is quadrilateral PQRS a parallelogram? If you recognize that each statement on its own is not sufficient, we can jump straight to . . . Statements 1 and 2 combined There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two: Case a: PQRS could ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to A lecture course consists of 595 students. The students are in the Problem Solving forum
“In order to have an EQUAL number of students in each section, the number of students per section MUST BE A FACTOR of 595 Let''s do some prime factorization 595 = (5)(7)(17) From the prime factorization, we can see that answer choice A, B, D and E are all factors of 595 Answer: C Cheers, ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to If a and b are constants, is the expression in the Data Sufficiency forum
“Target question: Is the expression defined for x = –2? This is a great candidate for rephrasing the target question. If x = -2, then the expression becomes (-2)+b/√(-2+a) There are two ways in which the expression(-2)+b/√(-2+a) is NOT defined: case i) If a = 2, then the fraction''s ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Is x = y? in the Data Sufficiency forum
“Target question: Is x = y? Statement 1: 2x/3 - y/3 = 1/3 Multiply both sides by 3 to get: 2x - y = 1 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, it is the case that x = y ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to The figure above represents a box that has the shape of a in the Data Sufficiency forum
“Target question: What is the volume of the box? IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to In the figure above, PQRT is a rectangle. What is the length in the Data Sufficiency forum
“Let''s assign some variables to some of the lengths... https://i.imgur.com/BpaiRKm.png Target question: What is the value of x? Statement 1: The area of region PQRS is 39 and TS = 6. Region PQRS is a TRAPEZOID Area of trapezoid = (height)(base1 + base2)/2 So, we get: (x)(y + z)/2 = 39 ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico Ci in the Problem Solving forum
“Here''s how I would answer this in my head Average speed = total distance/total time = 1200/2.5 = 2400/5 = 4800/10 = 480 Answer: D Cheers, Brent”
May 9, 2019
Ian Stewart posted a reply to In an integer division operation, the divisor is x, the quot in the Data Sufficiency forum
“You don''t need to know what a "dividend" is on the GMAT, and if this were a real GMAT question it would declare that all of the numbers are positive. In this question, we''re dividing z by x, and getting a quotient of y and a remainder of r. So z = xy + r Using either Statement ...”
May 8, 2019
GMATGuruNY posted a reply to The sum of two numbers is 1 and their product is -1. What is in the Problem Solving forum
“x³ + y³ = (x+y)(x²+y²-xy) Since x+y=1, we get: (x+y)² = 1² x² + y² + 2xy = 1 Substituting xy=-1 into x² + y² + 2xy = 1, we get: x² + y² + 2(-1) = 1 x² + y² = 3 Substituting x+y=1, x²+y²=3 and xy=-1 into x³ + y³ = (x+y)(x²+y²-xy), we get: x³ + y³ = (1)(3-(-1)) = ...”
May 8, 2019
Brent@GMATPrepNow posted a reply to What amount did Jean earn from the commission on her sales in the Data Sufficiency forum
“Target question: What amount did Jean earn from the commission on her sales in the FIRST HALF of 1988 ? Statement 1: In 1988 Jean''s commission was 5 percent of the total amount of her sales. We don''t know her total sales amount in 1988, AND we don''t know what happened in the FIRST HALF of ...”
May 8, 2019
GMATGuruNY posted a reply to According to surveys by the National Institute on Drug Abuse in the Sentence Correction forum
“Correct! The OA to SC71 in the OG11 includes a similar construction: The cameras of the Voyager II spacecraft detected six small, previously unseen moons circling Uranus, doubling...the number of satellites now known to orbit the distant planet.”
May 7, 2019
Brent@GMATPrepNow posted a reply to Six shipments of machine parts were shipped from a factory o in the Data Sufficiency forum
“We might be able to solve this one faster by first converting the fractions to decimals. S1=0.25 S2=0.2 S3=0.17 (approx) S4=0.15 S5=0.13 (approx) S6=0.1 Statement 1: S2 and S4 were shipped on the first truck. First truck has 0.2 + 0.15 = 0.35 Since the first truck holds more than 0.5, ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum
“\ Target question: Is a^5 > 4^b Statement 1: a³ = -27 Solve to get: a = -3 So, a^5 = (-3)^5 = -243 Since 4^b will be POSITIVE for all values of b, the answer to the target question is NO, a^5 is definitely NOT greater than 4^b Since we can answer the target question with certainty, ...”
May 7, 2019
GMATGuruNY posted a reply to GMATPrep SC in the Sentence Correction forum
“Here, much and the increase are redundant, since both words refer to an amount. Proposed revision: The number of people flying first class on domestic flights rose sharply in 1990, twice the increase of the previous year. Implied comparison: The NUMBER OF PEOPLE flying in 1990 was twice ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum
“Let''s assume that we''re creating subcommittees. We want to place 6 people in the following spaces: _ _ _ | _ _ _ First, we place Michael in one subcommittee; it makes no difference which one: M _ _ | _ _ _ Now place Anthony. We can see that there are 5 spaces remaining. 2 spaces ...”
May 7, 2019
Ian Stewart posted a reply to For any sequence of \(n\) consecutive positive integers, in the Problem Solving forum
“If you take the sequence 1, 2, the sum of the even integers is 2 and the sum of the odd integers is 1, so \(S_e > S_o\) and item 1 can be true. If you take the sequence 2, 3, the sum of the even integers is 2 and the sum of the odd integers is 3, so \(S_e < S_o\), and item 3 can be true. ...”
May 7, 2019
Ian Stewart posted a reply to \(A\) and \(B\) are the endpoints of the longest line that in the Problem Solving forum
“The longest line you can draw in a circle is a diameter, so AB is a diameter of the circle. If X is the center of the circle, then AX is a radius. The question tells us AX is 3, so the radius of the circle is 3. If you draw a diagram, and look at triangle ACX, two of the sides of that triangle, ...”
May 7, 2019
Ian Stewart posted a reply to If \(x\) is a positive integer, is \(x\) a prime integer? in the Data Sufficiency forum
“Statement 1 tells us x is one less than some prime number. If that prime is 3, then x=2, and x is prime, but if that prime is 5, x=4, and x is not prime, so Statement 1 is not sufficient. Statement 2 tells us x is 5 greater than some prime number. If that prime is 2, then x=7, and x is prime, but ...”
May 7, 2019
Ian Stewart posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum
“4^b is always positive, no matter what b is. If a^3 = -27, then a is negative and so is a^5. So it''s certainly true that a^5 < 4^b, because negative numbers are smaller than positive numbers. So Statement 1 is sufficient. Statement 2 is not sufficient; while we know b is either 4 or -4, we ...”
May 7, 2019
GMATGuruNY posted a reply to If each child in a group of children received either one or in the Data Sufficiency forum
“Let x = the number of children receiving 2 candies each and y = the number of children receiving 1 candy each. Thus: Total number of candies = 2x + y. Question stem, rephrased: What is the value of x? Statement 1: Of every 4 children, 1 receives 2 candies and 3 each receive 1 candy. ...”
May 7, 2019
GMATGuruNY posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum
“A 3-person committee that includes Michael will be composed of Michael and two other people chosen from the remaining five members. From 5 members, the number of ways to choose 2 = 5C2 = 10. Of these 10 pairs, the number that will include Anthony = 4. (Since there are 4 other people who could ...”
May 7, 2019
GMATGuruNY posted a reply to A bucket full worns in the Problem Solving forum
“Let the number of worms = 60. Since the rat eats 1/6 of the 60 worms -- in other words, 10 worms -- in 5 hours, the rat''s rate = w/t = 10/5 = 2 worms per hour. 1/4 of the 60 worms = 60/4 = 15 worms. Since the rat''s rate = 2 worms per hour, the time for the rat to eat 15 worms = w/r = 15/2 = 7.5 ...”
May 7, 2019
GMATGuruNY posted a reply to A book has 1000 pages numbered 1, 2, 3, …, and so on. How in the Problem Solving forum
“Ignore page 1000, since it does not include the digit 2. To make the calculation easier, consider the remaining pages numbered as 3-digit integers, beginning with 000 and ending with 999: 000, 001, 002...997, 998, 999 There are 1000 options between 000 to 999, inclusive. Since each option is ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to If x is 8/3 percent of y, y is what percent of x? in the Problem Solving forum
“x percent = x/100 So, 8/3 percent = (8/3)/100 = (8/3)/(100/1) = (8/3)(1/100) = 8/300 GIVEN: x is 8/3 percent of y, We can write: x = 8/300 of y In other words: x = (8/300)(y) or......: x = 8y/300 y is what percent of x? Take: x = 8y/300 Multiply both sides by 300 to get: 300x = 8y ...”
May 7, 2019
Ian Stewart posted a reply to A six-sided mosaic contains 24 triangular pieces of tile in the Data Sufficiency forum
“If we know each triangle is equilateral with sides of length 9, and we know how many triangles we have, of course we can find the area of all of them, so Statement 1 is sufficient. That we can fit the mosaic in some rectangle limits how large the mosaic might be, but we have no idea how much ...”
May 6, 2019
GMATGuruNY posted a reply to The equation (M + 6)/36 = (p – 7)/21 relates two temperatu in the Problem Solving forum
“If M=30 and P=28, both sides of (M + 6)/36 = (P – 7)/21 are equal to 1. The correct answer must yield a valid equation for M=30 and P=28. When the question stem includes the phrase "which of the following," the correct answer is likely to be D or E. E: M = (12/7)P – 18 If M=30 ...”
May 6, 2019
GMATGuruNY posted a reply to What is the remainder when the product of the first 10 prime in the Problem Solving forum
“What is the remainder when 30 is divided by 4? One approach: 1. Break the dividend 30 into factors: 30 = 5*6 2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2 3. Multiple the resulting remainders: 1*2 = 2 Step 3 indicates that 30 divided by 4 will yield a remainder of 2. ...”
May 6, 2019
Ian Stewart posted a reply to Mr. Wayne bungee jumps from the top of a building straight in the Problem Solving forum
“In 15-3 = 12 seconds, he passes 20 - 5 = 15 floors. If each floor is 3 meters, he covers a distance of 45 meters. So his speed is 45/12 = 15/4 = 3.75 m/s. Of course if each floor is 3 meters high, it''s not clear what it means to ''pass a floor'' (when during the 3 meters do we consider the ...”
May 5, 2019
Ian Stewart posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum
“If we have a two digit number AB, where A is the tens digit and B the units digit, then the number is equal to 10A + B. So here, if A and B represent digits, our numbers are AB and BA. These are equal to 10A + B and 10B + A, and their sum is equal to 11A + 11B. This sum is clearly divisible by ...”
May 5, 2019
Ian Stewart posted a reply to In 1994, Company X recorded profits that were 10% greater in the Data Sufficiency forum
“We already know the ratio of the company''s profits in 1994 to profits in 1992, since we''re told the percent changes from year to year in the stem, so Statement 2 just restates information we already know, and is useless. If in 1994 the company profits were $100,000 greater than in 1993, and ...”
May 5, 2019
GMATGuruNY posted a reply to If a jury of 12 people is to be selected randomly from a in the Problem Solving forum
“Question rephrased: What is the probability that at least 8 men will be selected to serve on the 12-member jury? P(good outcome) = 1 - P(bad outcome). Here, a BAD outcome means selecting a jury with FEWER than 8 men. Of the 10 men and 5 women in the jury pool, 3 people must be selected NOT ...”
May 5, 2019
Ian Stewart posted a reply to The 9 squares above are to be filled with x's and o's in the Data Sufficiency forum
“From Statement 1, we know we have at least 5 O''s, and therefore at most 4 X''s. From Statement 2, we know we have at least 4 X''s, in the four corners. Neither statement is sufficient, but using both, if we have at least 4 X''s and at most 4 X''s, we must have exactly 4 X''s, and the two ...”
May 5, 2019
Ian Stewart posted a reply to In the figure above, triangle PQR has angle measures as in the Data Sufficiency forum
“If PQ = QR, the triangle is isosceles, and we have two equal angles opposite PQ and QR. So we have two 58 degree angles (x = 58), and since the sum of the three angles in a triangle is 180, we can find the third angle y and answer the question. In a triangle, the longest side is opposite the ...”
May 5, 2019
Ian Stewart posted a reply to When Tom works alone he chops 2 lbs salad in 3 minutes, and in the Problem Solving forum
“Getting the same time, 6 minutes, for both: Tom chops 4 lbs in 6 minutes Tammy chops 9 lbs in 6 minutes So when they work for the same amount of time, the ratio of the amount Tammy chops to the amount Tom chops is 9 to 4, and since 9 is 125% greater than 4, the answer is 125%. The 65 lbs in ...”
May 4, 2019
Ian Stewart posted a reply to What is the sum of all values of that satisfy the equation in the Problem Solving forum
“We can divide by 4 and get zero on both sides: 4x^2 + 16 = 32x x^2 + 4 = 8x x^2 - 8x + 4 = 0 When we factor the left side above, the factorization will look like (x - a)(x - b), where a and b are the two solutions to the quadratic. The numbers a and b will multiply to 4 (since 4 = (-a)(-b) = ...”
May 4, 2019
Ian Stewart posted a reply to Teachers in United States high schools teach an average in the Problem Solving forum
“Standard deviation is the square root of variance (a fact you almost certainly will not need to know on the GMAT), so the standard deviation here is 10, two standard deviations is thus 20, and 60 and 100 are the two values that are two standard deviations away from the mean of 80. Only 60 is an ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum
“A quick solution is to assign some values to the highest paid and lowest paid workers Let $10,000 = the lowest salary LAST YEAR Let $40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = $30,000 If the annual salary of each of the 100 employees this ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum
“Hey BTGmoderatorDC, You posted this question 2 months ago: https://www.beatthegmat.com/last-year-the-range-of-the-annual-salaries-of-the-100-t306593.html Cheers, Brent”
May 4, 2019
Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum
“Approach #2: Algebra Let x = the width of the rectangle So, 2x = the length of the rectangle If the perimeter is 10, we can write: x + x + 2x + 2x = 10 Simplify: 6x = 10 Solve: x = 10/6 = 5/3 So, the width (x) is 5/3 And the length (2x) is 10/3 Answer: B Cheers, Brent”
May 4, 2019
Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum
“We COULD use algebra to solve this question. However, it''s probably faster to just test the answer choices The answer choices give us the length and width of the rectangle. So, the sum of two values will equal HALF the perimeter of the rectangle. Since we want a perimeter of 10, the ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to Three-fourths of the area of a rectangular lawn 30 feet wide in the Problem Solving forum
“Here''s a diagram of the 30 x 40 lawn https://i.imgur.com/6dQyyQ5.png If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet https://i.imgur.com/nRkAVRU.png So, the enclosure is a 30 by 30 square. The PERIMETER = 30 + 30 + 30 + 30 = 120 feet If ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to If rectangle ABCD is inscribed in the circle above, what is in the Problem Solving forum
“Draw a line connecting points A and C. https://i.imgur.com/fQaxM5q.png An important circle property (see video below for more info) tells us that, if we have a 90-degree inscribed angle, then that angle must be containing ("holding") the DIAMETER of the circle. So, we know that AC = ...”
May 4, 2019
Brent@GMATPrepNow posted a reply to In quadrilateral ABCD above, what is the length of AB ? in the Problem Solving forum
“https://i.imgur.com/srEvM6A.png If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem. https://i.imgur.com/L50lEKr.png Either way, we''ll see that the triangle''s ...”
May 4, 2019
Ian Stewart posted a reply to If x represents the number of positive factors of integer y in the Data Sufficiency forum
“A number has an odd number of divisors only if that number is a perfect square. It''s easy to see why: for a number that is not a perfect square, say 6, then all of the divisors can be ''paired up'' into pairs that produce 6 as a product: 1 and 6 2 and 3 so we have an even number of divisors. ...”
May 4, 2019
Ian Stewart posted a reply to If the positive integer \(x\) is rounded to the nearest ten, in the Data Sufficiency forum
“The question is just asking "is the units digit of x greater than 5?" When we divide a positive number by 10, the remainder we get is that number''s units digit, so Statement 1 tells us "the units digit of x is even". It could be 0, 2, 4, 6 or 8, so we can''t answer the ...”
May 4, 2019
GMATGuruNY posted a reply to 7, 9, 6, 4, 5, x If x is a number in the list above in the Data Sufficiency forum
“Given numbers in ascending order: 4, 5, 6, 7, 9 Statement 1: Smallest 3 numbers are 4, 5, and 6. Greatest 3 numbers are 7, 9 and x, where x is any number greater than 7. Thus: Median = average of the 2 middle numbers =(6+7)/2 = 6.5. SUFFICIENT. Rule: For any set that is SYMMETRICAL ...”
May 4, 2019
GMATGuruNY posted a reply to Romeo and Juliet play a dice game in which the two in the Problem Solving forum
“Let P(R) = the probability that Romeo wins and P(J) = the probability that Juliet wins. Since there are only two possible outcomes -- either Romeo wins or Juliet wins -- we get: P(R) + P(J) = 1 Probability that Romeo wins on the first roll = 1/6 Probability that Romeo wins on the third roll ...”
May 3, 2019
Ian Stewart posted a reply to Operation F means “take the square root,” operation G me in the Problem Solving forum
“If we multiply our positive number x by a negative constant c, then take the square root, we get something undefined. And if we multiply x by 0, then take a reciprocal, we get something undefined. So if we''re supposed to be able to apply these functions in any order, just to get something that ...”
May 3, 2019
Ian Stewart posted a reply to In the \(xy-\)plane above, is angle \(BAC\) greater than in the Data Sufficiency forum
“They should be clear in Statement 2 what angles they''re describing - around a point, there are two different angles you can make, the small angle within the triangle, and the large angle around the outside of the triangle (the one that would sum to 360 with the angle inside the triangle). But as ...”
May 3, 2019
Ian Stewart posted a reply to At a restaurant, five friends each purchased a sandwich. in the Data Sufficiency forum
“Presumably they mean to ask about the sum of the prices of the sandwiches, and not about the sum of the sandwiches themselves. If Statement 1 is true, all we can say is that the sum of the prices exceeded 5*13 = $65, so that''s not sufficient. If Statement 2 is true, all we can say is that the ...”
May 3, 2019
Brent@GMATPrepNow posted a reply to A paint mixture was formed by mixing exactly 3 colors of in the Data Sufficiency forum
“Target question: How many gallons of green paint were used? Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used. In other words, we ...”
May 2, 2019
Brent@GMATPrepNow posted a reply to If 2.00X and 3.00Y are 2 numbers in decimal form with thousa in the Data Sufficiency forum
“ Given: 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y Target question: Is 3(2.00X) > 2(3.00Y)? This is a good candidate for rephrasing the target question. Since X is the thousandths digit, we can write: 2.00X = 2 + X/1000 Since Y is the thousandths ...”
May 2, 2019
GMATGuruNY posted a reply to Tickets for all but 100 seats in a 10,000-seat stadium were in the Problem Solving forum
“If all 10,000 tickets are sold, we get: 20% sold for $1 each = 2000*1 = 2,000 80% sold for $2 each = 8000*2 = 16,000 Total revenue = 2000+16000 = 18,000 Since 100 tickets are not actually sold, the total revenue must be a bit less than 18,000. The correct answer is B.”
May 2, 2019
GMATGuruNY posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we ...”
May 2, 2019
GMATGuruNY posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent the minimum number of socks that must be pulled. When the correct answer choice is plugged in, the probability of NOT picking a matching pair will be LESS than 1/2 (implying that the probability of picking a matching pair will be MORE than 1/2). Since we ...”
May 2, 2019
Ian Stewart posted a reply to Tony owns six unique matched pairs of socks. All twelve sock in the Problem Solving forum
“We can work out the probability he continues to get unmatched socks, and once that probability falls below 1/2, we''ll know he has a greater than 1/2 chance of getting at least one pair of matched socks. The first sock he picks doesn''t matter. The next sock has a 10/11 chance of not matching the ...”
May 2, 2019
Ian Stewart posted a reply to After the first two terms in a sequence of numbers, each in the Data Sufficiency forum
“If the sum of the first 3 terms is 6, then according to the definition of the sequence, the 4th term is 6. But then the fifth term is just the sum of the first 3 terms plus the 4th term, so is 6+6 = 12. Statement 1 is sufficient. If the 4th term is 6, then by the definition of the sequence, the ...”
May 2, 2019
Ian Stewart posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum
“If Jones has worked twice as many years as Green, and has also worked 5 years longer than Green, then Green has worked 5 years and Jones has worked 10. So Statement 2 is sufficient. We can deduce from Statement 1 that Jones has worked 5 years longer than Green, so Statement 1 is also sufficient, and ...”
May 2, 2019
GMATGuruNY posted a reply to Train A leaves the station at 5:00, and travels north at 50 in the Data Sufficiency forum
“Statement 1: From 5pm to 6pm, A travels on its own for 1 hour at a rate of 50 mph, with the result that A travels ahead 50 miles. Since B''s rate is unknown, we cannot determine when B catches up to A. INSUFFICIENT. Statement 2: Since A''s 50-mph rate is 5/6 of B''s rate, we get: 50 = ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to If n^m leaves a remainder of 1 after division by 7 for all in the Problem Solving forum
“The most important piece of information is here: "for all positive integers n that are not multiples of 7" Since 2 is not a multiple of 7, then it must be the case that, for a particular value of m, 2^m leaves a remainder of 1 after division by 7 Let''s check the answer choices.... ...”
May 1, 2019
Ian Stewart posted a reply to At a community center, three separate pumps- A, B, and C in the Data Sufficiency forum
“If C alone fills 3/10 of the pool in 126 minutes, it fills the whole pool in (10/3)(126) = 1260/3 = 420 minutes, or 7 hours. So C alone would fill the pool at 3pm, even with no help from A or B, and Statement 1 is sufficient. If A+B together fill 1/8 of the pool in 55 minutes, they fill the whole ...”
May 1, 2019
Ian Stewart posted a reply to The total price of 5 pounds of regular coffee in the Data Sufficiency forum
“Since we''re never given any information about price per pound, the numbers in "5 pounds" and "3 pounds" are just a distraction. All we''re doing here is mixing some regular coffee and some decaf coffee. Say all the regular coffee costs $R and all the decaf costs $D. The stem ...”
May 1, 2019
GMATGuruNY posted a reply to x^2 + 4x + 1 = 0. What is the value of x^2 + 1/x^2? in the Problem Solving forum
“x² + 4x + 1 = 0 Dividing both sides by x, we get: (x² + 4x + 1)/x = 0/x x + 4 + 1/x = 0 x + 1/x = -4 Squaring both sides, we get: (x + 1/x)² = (-4)² x² + 1/x² + 2(x)(1/x) = 16 x² + 1/x² + 2 = 16 x² + 1/x² = 14 The correct answer is C.”
May 1, 2019
Ian Stewart posted a reply to Is the average (arithmetic mean) of 5 different positive in the Data Sufficiency forum
“If the five numbers are, as Statement 1 and the stem tell us, five different positive multiples of 10, the smallest values we could possibly have are: 10, 20, 30, 40, 50 That''s an equally spaced list, so its average is equal to its median, so the average of the list above is 30. But that''s ...”
May 1, 2019
Ian Stewart posted a reply to A certain painting job requires a mixture of yellow, green, in the Data Sufficiency forum
“From Statement 1, 1/4 of the mixture is green paint, and since we know we have 12 quarts of paint in total, we must have 3 quarts of green paint. So Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about what fraction of the mixture is white paint.”
May 1, 2019
Brent@GMATPrepNow posted a reply to If x is an integer greater than 0, what is the remainder in the Data Sufficiency forum
“Target question: What is the remainder when x is divided by 4 ? Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What number is 6 more than x + y ? in the Data Sufficiency forum
“Target question: What is the value of x + y + 6? Statement 1: y is 3 less than x. We can write: y = x - 3 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9 ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Is the average (arithmetic mean) of the numbers x, y, and z in the Data Sufficiency forum
“Target question: Is the average (arithmetic mean) of the numbers x, y, and z greater than z? This is a good candidate for rephrasing the target question. Rewrite the question as "Is (x + y + z)/3 > z?" Multiply both sides by 3 to get: "Is x + y + z > 3z?" Subtract z ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum
“Target question: How many objects are in the box? Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green. We can solve this using the Double Matrix Method. This technique can be used for most questions featuring a population in which ...”
May 1, 2019
Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Target question: What is the remainder when the positive integer n is divided by 5 ? Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to Is n equal to zero? in the Data Sufficiency forum
“Target question: Is n equal to zero? Statement 1: The product of n and some nonzero number is 0 (n)(non-zero number) = 0 This means n must be 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The sum of n and 0 is 0 If n + 0 = 0, we can ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“ Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to How many hours does it take Jennifer to run y miles if she r in the Problem Solving forum
“time = distance/rate So, time = y/x Answer: B Cheers, Brent”
April 30, 2019
Brent@GMATPrepNow posted a reply to If x = 5 – 4k and y = 5k – 3, then for what value of k d in the Problem Solving forum
“We want: x = y Replace values with their equivalents: 5 - 4k = 5k - 3 Add 4k to both sides: 5 = 9k - 3 Add 3 to both sides: 8 = 9k Divide both sides by 9 to get: 8/9 = k Answer: B Cheers, Brent”
April 30, 2019
GMATGuruNY posted a reply to For all his professed disdain of such activities, Auden was in the Sentence Correction forum
“When a sentence begins with for all + POSSESSIVE, for all = DESPITE. OA: For all his professed disdain of such activities, Auden was an inveterate literary gossip. Conveyed meaning: Despite his professed disdain of such activities, Auden was an inveterate literary gossip. E: In spite of ...”
April 30, 2019
GMATGuruNY posted a reply to Is x+y>0? in the Data Sufficiency forum
“Statement 1: Here, x and y must have the SAME SIGN. If x and y are both positive, then x+y > 0. If x and y are both negative, then x+y < 0. INSUFFICIENT. Statement 2: The inequality implies that x and y are both NONZERO. Since the square of a nonzero value must be positive, we can ...”
April 30, 2019
GMATGuruNY posted a reply to Last year, the average price of eight different products in the Data Sufficiency forum
“We can determine this year''s average price if we know the difference between this year''s revenue and last year''s. Statements combined: Case 1: Last year the 5 products in Statement 1 had an average price of $10, for a total of $50 in revenue In this case, the increase in revenue yielded by ...”
April 30, 2019
Ian Stewart posted a reply to If \(\frac{4^7+4^8+4^9+4^{10}}{5}\) is \(x\) times 4^7, what in the Problem Solving forum
“Just factor out 4^7 from the sum in the numerator: (4^7 + 4^8 + 4^9 + 4^10)/5 = x*4^7 4^7(1 + 4 + 4^2 + 4^3)/5 = x*4^7 and now if we divide by 4^7 on both sides, we have 1 + 4 + 4^2 + 4^3 = 5x 85 = 5x 17 = x”
April 30, 2019
Ian Stewart posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum
“We can just check each of the four arithmetic operations to see when each Statement will be true. If r = s, we can replace ''s'' with ''r'', so for Statement 1: r+r = 2r r-r = 0 r*r = r^2 r/r = 1 and it''s only when the operation is subtraction that we get 0 as a result, and the operation ...”
April 30, 2019
Ian Stewart posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum
“Statement 1 tells us that n is equal to 13, so of course we can answer any question about n, and Statement 1 is sufficient. The remainder you get when you divide by 4 has no relationship to the remainder you get when you divide by 5, so Statement 2 is useless. For example, n could be 5, and then ...”
April 30, 2019
Ian Stewart posted a reply to In a certain first grade classroom, the average height is in the Data Sufficiency forum
“The sum of the 5 girls'' heights is 5x, and the sum of the 8 boys'' heights is 8y, so the average height is (5x + 8y)/13. So if we can find the value of 5x + 8y, we can answer the question. From Statement 1, dividing by 3 on both sides, we find 15x + 24y = 1755 5x + 8y = 1755/3 so we can ...”
April 30, 2019
Ian Stewart posted a reply to Last year, the average price of eight different products in the Data Sufficiency forum
“The answer is instantly C or E, because using either statement alone, we don''t know anything about some of the products. Using both Statements, it''s possible, say, that five of the products cost $0.10 each, and the other three cost more than $600 each. If the five cheap products increased in ...”
April 30, 2019
Ian Stewart posted a reply to A drawer contains 12 socks, of which 8 are black and 4 are in the Data Sufficiency forum
“We have 9 socks left. If, as Statement 1 tells us, the ratio of black to white socks is 2 to 1, then 2/3 of the remaining socks are black, and thus 6 are black, so Statement 1 is sufficient. Statement 2 is not sufficient because we have no information about the third sock that was removed, so the ...”
April 30, 2019
GMATGuruNY posted a reply to A basketball coach has won 65 percent of the 400 games she in the Problem Solving forum
“Total games = (400 games already played) + (100 additional games) = 500. Required number of wins = 70% of 500 = 350. Current number of wins = 65% of 400 = 260. Additional wins needed = 350-260 = 90. The correct answer is D.”
April 30, 2019
GMATGuruNY posted a reply to What is the remainder when 1044*1047*1050*1053 is in the Problem Solving forum
“What is the remainder when 30 is divided by 4? One approach: 1. Break the dividend 30 into factors: 30 = 5*6 2. Divide the divisor 4 into each factor: 5/4 = 1 R1, 6/4 = 1 R2 3. Multiple the resulting remainders: 1*2 = 2 Step 3 indicates that 30 divided by 4 will yield a remainder of 2. ...”
April 30, 2019
Brent@GMATPrepNow posted a reply to If a school district paid a total of $35 per desk for x desk in the Data Sufficiency forum
“ Given: School district paid a total of $35 per desk for x desks and a total of $30 per table for y tables So, the TOTAL amount paid = 35x + 30y. Target question: What was the total amount that the district paid for these desks and tables?? Statement 1: The total amount the district ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to In a sequence of numbers in which each term is 2 more than in the Data Sufficiency forum
“ Given: Sequence of numbers is such that each term is 2 more than the preceding term Target question: What is the value of term_4? Statement 1: The last term is 90. We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . . ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is the integer p divisible by 5 ? in the Data Sufficiency forum
“Target question: Is the integer p divisible by 5? Statement 1: p is divisible by 10. If p is divisible by 10, we can write: p = 10k, for some integer k. Rewrite this as: p = (5)(2)(k) This tells us that p is a multiple of 5, which means p must be divisible by 5 Since we can answer the ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If R, S, and T are points on a line in the Data Sufficiency forum
“ Given: R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S There are 4 possible scenarios that meet the above conditions: https://i.imgur.com/kOeqUfZ.png Target question: How far is S from T? Statement 1: R is between S and T. When we check the 4 ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum
“ Given: m and n are integers Target question: What is the value of m + n ? Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0. Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn At this point, we ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum
“ Given: a and b are integers, and b > 0 Target question: Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question. Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is the sum of two integers divisible by 10 ? in the Data Sufficiency forum
“Target question: Is the sum of two integers divisible by 10 ? Statement 1: One of the integers is even. We only have information about ONE number. Statement 1 is NOT SUFFICIENT Statement 2: One of the integers is a multiple of 5. We only have information about ONE number. Statement 2 ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum
“ Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers. Since p < r < s, we know that r = the mean = the median. In other ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Three children inherited a total of X dollars. If the oldest in the Data Sufficiency forum
“ Given: Three children inherited a total of X dollars. The oldest child inherited $7,000 more than the youngest child, and the youngest child inherited $9,000 less than the middle child Let y = the amount the YOUNGEST child received So, y + 7000 = the amount the OLDEST child received And y + ...”
April 29, 2019
Ian Stewart posted a reply to If a and b are integers and a is even, what is the value in the Data Sufficiency forum
“Using both Statements, we might have a=2 and b=7, or we might have a = -2000 and b = -7000, among other possibilities, and we can easily get different values for a-b, so the answer is E.”
April 29, 2019
Ian Stewart posted a reply to The inflation index for the year 1989 relative to the year in the Data Sufficiency forum
“We know that the ratio of the price of the mixer in 1989 to the price in 1970 was 3.56 to 1. Notice then that for every dollar the mixer cost in 1970, the price increased by $2.56. So if the actual increase was $102.40, the cost in 1970 must have been 102.40/2.56, and Statement 1 is sufficient. ...”
April 29, 2019
Ian Stewart posted a reply to K is a set of integers such that if the integer r is in K in the Data Sufficiency forum
“If we know r is in K, then we know r+1 is in K. So if 50 is in K, we know that 51 is in K, but then we know 52 is in K, and 53 is in K, and so on, so 100 will be in K. So Statement 1 is sufficient. From Statement 2, we know 150 is in K, so we know 151, 152, 153 etc are also in K. But we don''t ...”
April 29, 2019
Ian Stewart posted a reply to A total of 20 amounts are entered on a spreadsheet that has in the Data Sufficiency forum
“If you have 4 values, and R is their average, then 4R is their sum, from the definition of an average (just rewrite average = sum/n so you have ''sum'' on one side). So here, 4R(1) is the sum of the four values in row 1, 4R(2) is the sum of the four values in row two, and so on, and thus 4[ R(1) ...”
April 29, 2019
Ian Stewart posted a reply to If m is an integer, is m/102 an integer? in the Data Sufficiency forum
“Prime factorize: 102 = 2*51 = 2*3*17 So we can be certain m/102 is an integer if we can be certain m is divisible by 2, 3 and 17. Statement 1 tells us 165m is divisible by 99, or that 165m/99 is an integer. So (33)(5m)/(33)(3) is an integer, and 5m/3 is an integer. That means the ''3'' in the ...”
April 29, 2019
Ian Stewart posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum
“We can rewrite the question: Is (a-1)/(b+1) = a/b ? Is ab - b = ab + a ? Is -b = a? from which we can see that Statement 2 tells us exactly what we want, while Statement 1 does not (if Statement 1 is true, the answer may be ''yes'', if b = 2 and a = -2, but can also be no for any other ...”
April 29, 2019
Ian Stewart posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum
“The average of an equally spaced set is equal to the median of that set, so here, if p, r, s are consecutive integers in increasing order, their average is simply r, so r = x and the question is just asking if we can find r. Notice also that the sum of the three integers is therefore 3r (because by ...”
April 29, 2019
Ian Stewart posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum
“If you expand the left side of Statement 1, we have (x + m)(x + n) = x^2 + 5x + mn x^2 + (m+n)x + mn = x^2 + 5x + mn and now most of the terms can be subtracted from both sides, leaving us with (m + n)x = 5x and dividing by the nonzero x, we find m+n = 5, so Statement 1 is sufficient. ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is x<y? in the Data Sufficiency forum
“Target question: Is x < y? Statement 1: z< y No information about x Statement 1 is NOT SUFFICIENT Statement 2: z < x No information about y Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined The combined statements tell us that x and y are both greater than z ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to What is the value of a^4 - b^4? in the Data Sufficiency forum
“Target question: What is the value of a⁴ - b⁴? NOTE: a⁴ - b⁴ is a difference of square, which we can factor. a⁴ - b⁴ = (a² - b²)(a² + b²) So, we can REPHRASE the target question as... REPHRASED target question: What is the value of (a² - b²)(a² + b²)? Statement 1: ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Which of the following could be the equation of line m? in the Problem Solving forum
“First off, we can eliminate answer choice D, since y = 2 is the equation of a HORIZONTAL line, and the given line is NOT horizontal. Next, we can eliminate answer choice E, since x = -2 is the equation of a VERTICAL line, and the given line is NOT vertical. Now notice that line m has a ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum
“ Given: S is a set of odd integers and 3 and –1 are in S Target question: Is –15 in S ? Statement 1: 5 is in S So far, set S looks like this: {-1, 3, 5, . . . .} So, -15 may or may not be in set S Since we cannot answer the target question with certainty, statement 1 is NOT ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If r and s are positive integers... in the Data Sufficiency forum
“ Given: r and s are positive integers Target question: Is r + s even? Statement 1: r is even. Since we have no information about s, we cannot determine whether r + s is even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: s is ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to When positive integer k is divided by 5, the remainder is 2. in the Problem Solving forum
“When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Is the integer x a 3-digit integer? in the Data Sufficiency forum
“Target question: Is the integer x a 3-digit integer? Statement 1: x is the square of an integer. Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 10² = 100. In this case, the answer to the target question is YES, x IS a 3-digit ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum
“ Given: term1 = 0 and term2 = 1 Target question: Does term5 equal 2? Once we scan the two statements, we can probably jump straight to . . . Statements 1 and 2 combined There are several possible sequences that satisfy BOTH statements. Here are two: Case a: {0, 1, 2, 0, 2,...}. In ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum
“Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is the sum of four particular integers even? Statement 1: Two of the integers are odd and two are even. ...”
April 28, 2019
GMATGuruNY posted a reply to What is the units digit of the number z? in the Data Sufficiency forum
“Statements combined: Case 1: z=19, with the result that z is between both 17 and 20 and 18 and 21 In this case, the units digit of z is 9. Case 2: z=18.1, with the result that z is between both 17 and 20 and 18 and 21 In this case, the units digit of z is 8. Since the units digit can be ...”
April 28, 2019
GMATGuruNY posted a reply to The number line shown contains three points R, S, and T in the Problem Solving forum
“Let R=-3, S=3 and T=6, implying that r=|-3|=3, s=|3|=3, and t=|6|=6. Average of R, S, and T = (-3+3+6)/3 = 2. The correct answer must yield 2 when r=3, s=3 and t=6. Only E works: (s + t - r)/3 = (3+6-3)/3 = 6/3 = 2 The correct answer is E.”
April 28, 2019
GMATGuruNY posted a reply to Peter and Tom shared the driving on a certain trip. in the Problem Solving forum
“Let the total distance = 5 miles and the time for each driver = 1 hour. Since Peter drives 2/5 of the total distance -- 2 miles -- in 1 hour, Peter''s speed = d/t = 2/1 = 2 miles per hour. Since Tom drives the remaining distance -- 3 miles -- in 1 hour, Tom''s speed = d/t = 3/1 = 3 miles per ...”
April 28, 2019
Ian Stewart posted a reply to S is a set of integers such that i) if a is in S, then in the Data Sufficiency forum
“Using Statement 1 alone, if ''1'' is in the set, then from rule i), we can deduce that -1 is in the set. But then using rule ii), we can''t generate any new values besides 1 and -1. So there are only two values, 1 and -1, that we can be certain are in the set, and we have no way to know if -4 is in ...”
April 28, 2019
Ian Stewart posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum
“Statement 1 isn''t sufficient, since it just tells us one other value in the set. Statement 2 also isn''t sufficient alone -- while using it we can determine many other values in the set (all the positive and negative powers of 3 are in the set), we have no way to know if -15 is in the set, since ...”
April 28, 2019
Ian Stewart posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum
“Statement 1 tells us exactly what kind of integers we have, so using the familiar even/odd rules, we can work out if the sum will be even or odd (since odd+odd is even, and even+even is even, the sum will turn out to be even, though since it''s a DS question, we don''t actually care what the answer ...”
April 28, 2019
Ian Stewart posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum
“Statement 1 tells us that the fifth term is either 0 or 2. There''s no other information anywhere in the question that tells us anything about the fifth term in the sequence, so using both statements, we have two possibilities, and the answer is E.”
April 28, 2019
Brent@GMATPrepNow posted a reply to If 90/k is an integer, is k an integer? in the Data Sufficiency forum
“ Given: 90/k is an integer Target question: Is k an integer? Statement 1: k > 1 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 10. Notice that 90/k = 90/10 = 9, which is an integer. In this case, the answer to the target ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to For a recent play performance, the ticket prices were $25 in the Data Sufficiency forum
“Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled $10,500 In other ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to The arithmetic mean of a data set is 46 and the standard in the Problem Solving forum
“-----------ASIDE----------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to In the town of Z, the town lion roars on some days and not in the Data Sufficiency forum
“Target question: What is the probability that on that day, either the town lion roared or it rained? This is a good candidate for rephrasing the target question. This is an OR probability. The OR probability rule says, P(A or B) = P(A) + P(B) - P(A and B) So, P(rained or roared) = P(rained) + ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to If 20 percent of x is 5y, and y = 7, what is 60 percent in the Problem Solving forum
“GIVEN: 20 percent of x = 5y This means: 40 percent of x = 10y And: 60 percent of x = 15y Since y = 7, we can write: 60 percent of x = 15(7) = 105 Answer: A”
April 27, 2019
Brent@GMATPrepNow posted a reply to Is x^2 > 15? in the Data Sufficiency forum
“Target question: Is x² > 15? Statement 1: x > -4 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -1. In this case, x² = (-1)² = 1. So, the answer to the target question is NO, x² is NOT greater than 15 Case b: x = ...”
April 27, 2019
GMATGuruNY posted a reply to Ten theater students are to begin work on a set for a musica in the Problem Solving forum
“(50 days)/(60 days) = 5/6. To finish the job in 5/6 of the normal time, the crew requires 6/5 of the normal number of students -- an increase of 1/5: (1/5)(10) = 2 more students. The correct answer is A.”
April 27, 2019
Ian Stewart posted a reply to If \(n\) and \(m\) are positive integers, what is the in the Data Sufficiency forum
“If you divide a number by 10, the remainder you get is just the number''s units digit. So the question is just asking "what is the units digit of \(3^{(4n+2)}+m\) ?" There are other units digit/exponent methods that are more flexible, but I''ve explained those in other posts, so I''ll ...”
April 26, 2019
Brent@GMATPrepNow posted a reply to If digit \(h\) is the hudredths' digit in the decimal in the Data Sufficiency forum
“ Given: Digit h is the hundredths digit in the decimal d=0.2h6 Target question: What is the value of d, rounded to the nearest TENTH? Statement 1: d < 1/4 In other words, 0.2h6 < 0.25 This means h = 0, 1, 2, 3 or 4 If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest ...”
April 26, 2019
Brent@GMATPrepNow posted a reply to In the rectangular coordinate system, line \(k\) is defined in the Data Sufficiency forum
“KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line. Given: Line k is defined by the equation x - 2y + n = 0 Target question: What is the value of n? Statement 1: The x-intercept of line k is 8 In other words, ...”
April 26, 2019
GMATGuruNY posted a reply to OG Most of the country's biggest daily newspapers in the Sentence Correction forum
“Plural terms such as profits, revenues, costs, etc. refer to NUMERICAL VALUES. When comparing plural terms that refer to numerical values, we generally do not use more but instead use -ER comparatives such as higher, lower, greater, etc. Thus, the blue sentence above is correct; the red sentence ...”
April 26, 2019
Brent@GMATPrepNow posted a reply to If z is a three-digit positive integer, what is the value in the Data Sufficiency forum
“ Given: z is a three-digit positive integer Target question: What is the value of the tens digit of z ? Statement 1: The tens digit of z - 91 is 3 Let''s examine two EXTREME cases z - 91 = 30 z - 91 = 39 NOTE: These are extreme cases, because 30 is the smallest 2-digit number ...”
April 25, 2019
Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, 2/3 are either pigs or in the Data Sufficiency forum
“Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...”
April 25, 2019
GMATGuruNY posted a reply to Suppose x = a/b (b≠0). Which of following is equivalent to in the Problem Solving forum
“Let a=2 and b=1, with the result that x = a/b = 2/1 = 2 and that (a²+ab)/(a²+b²) = (4+2)/(4+1) = 6/5. The correct answer must yield 6/5 when x=2. Only A works: (x²+x)/(x²+1) = (4+2)/(4+1) = 6/5 The correct answer is A.”
April 25, 2019
GMATGuruNY posted a reply to Probability Question in the Problem Solving forum
“The approach above counts the following: Cases that include 11: 1122, 1133, 1144, 1155, 1166 Cases that include 22: 2211, 2233, 2244, 2255, 2266 Cases that include 33: 3311, 3322, 3344, 3355, 3366 Cases that include 44: 4411, 4422, 4433, 4455, 4466 Cases that include 55: 5511, 5522, ...”
April 25, 2019