# winniethepooh

Ian Stewart posted a reply to If a fair die is rolled three times, what is the probability in the Problem Solving forum
“There''s a 5/6 chance we don''t get a ''3'' on one roll, so a (5/6)^3 = 125/216 chance we don''t get a ''3'' on any of our three rolls. So the probability we do get at least one ''3'' is 1 - (125/216) = 91/216.”
Yesterday
Ian Stewart posted a reply to In a series of four cricket matches, the average number of in the Problem Solving forum
“If Jill''s average is the same as Jack''s in 4 games, then their sum is the same. Jill''s sum is 160, so Jack''s sum must be 160. Jack''s median score is the average of his two middle scores, so if his median score is 30, the sum of his two middle scores is 60. His smallest and largest scores ...”
Yesterday
GMATGuruNY posted a reply to Is x > y ? in the Data Sufficiency forum
“If A, then B does not imply If B, then A. True statement: If John is in Times Square, then John is in New York. The following statement is NOT necessarily true. If John is in New York, then John is in Times Square. Is x > y? Statement 1: 5x > 3y Statement 2: 4x > 7y Each ...”
Yesterday
GMATGuruNY posted a reply to Is x > y ? in the Data Sufficiency forum
“I received a PM requesting that I post a response. The issue at hand is how to combine the two inequalities. Visually-oriented test-takers might find it helpful to plot the values on a number line. Statement 1: (2/5)x > (3/8)y x > (5/2)(3/8)y x > (15/16)y Statement 2: (3/7)x ...”
Yesterday
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.”
July 17, 2019
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 ...”
July 17, 2019
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 ...”
July 16, 2019
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 ...”
July 16, 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
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
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
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 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
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
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
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
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 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 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 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 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 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 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 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 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 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 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 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
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
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
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
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
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
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
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
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
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 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 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 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 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
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
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
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
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
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
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
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
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
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
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
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
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 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
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$$, the in the Data Sufficiency forum
“Using Statement 1, n can be 13, 38, 63, and 88. Using Statement 2 alone, we''ll have an infinite number of values of n, separated by 100, the LCM of 25 and 20. Using both Statements, n must be 63, and the answer is C.”
May 24, 2019
Ian Stewart posted a reply to What is the remainder when $$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
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
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 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 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 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 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 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 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
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
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
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
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
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
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
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
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
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
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 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
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
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
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
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
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
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
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
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
GMATGuruNY posted a reply to On account of a law in the Sentence Correction forum
“The OA is correct because it contains no grammatical errors and conveys a logical meaning. OA: With the cost of wireless service plummeting, many people are now using their mobile phones. Here, the action in blue is accompanied by the plummeting cost of wireless service. This meaning is perfectly ...”
April 24, 2019
Ian Stewart posted a reply to If the positive integer x divisible by 200? in the Data Sufficiency forum
“If we prime factorize everything: The question asks if x is divisible by 2^3 * 5^2 From S1: x^2 is divisible by 2^3 * 5^4. For x^2 to be divisible by 2^3, it will need to be true that x itself is divisible by at least 2^2, since if x were only divisible by 2^1, then x^2 would only be divisible ...”
April 23, 2019
Ian Stewart posted a reply to A number when divided successively by 4 and 5 leaves in the Problem Solving forum
“The question means something different from what it actually says, but I can guess what it''s trying to say. When we take our number, "n", and divide it by 4, we get a remainder of 1. So n is exactly 1 greater than some multiple of 4, and we have: n = 4q + 1 It''s here where the ...”
April 22, 2019
Ian Stewart posted a reply to What is the area of the shaded region in the figure shown? in the Data Sufficiency forum
“Draw a vertical line starting from point E, up to the line BC. That line will divide the large rectangle (ABCD) into two smaller rectangles. Line BE cuts one of those smaller rectangles in half along the diagonal, while line EC cuts the other one in half along the diagonal. So half of each smaller ...”
April 22, 2019
Ian Stewart posted a reply to What is the value of x? in the Data Sufficiency forum
“From Statement 1, x must be 5. From Statement 2, either x-3 = 2, or x-3 = -2, which gives us two different values for x (5 and 1). So the answer is A.”
April 22, 2019
Ian Stewart posted a reply to At a community event, the total number of men, women, and in the Data Sufficiency forum
“If the ratio of men to women to children is 15 to 32 to 17, then (since that ratio is reduced) the total number of people must be a multiple of 15+32+17 = 64. If the total is also less than 120, it can only be exactly 64, so we have exactly 15 men, and Statement 1 is sufficient. Statement 2 is ...”
April 22, 2019
GMATGuruNY posted a reply to Probability Question in the Problem Solving forum
“All possible rolls: Since there are 6 number options for each roll, we get: 6*6*6*6 = 1296 Case 1: Exactly 2 rolls are the same (such as 1123) From 4 rolls, the number of ways to choose a pair to yield the same number = 4C2 = (4*3)/(2*1) = 6. Number options for this pair = 6. (Any of the 6 ...”
April 22, 2019
GMATGuruNY posted a reply to If j > 1, is integer j a prime number? in the Data Sufficiency forum
“Statements combined: Since dividing by 3 or 2 leaves a remainder of 1, j must be 1 more than a multiple of 3 and 2: j = (3*2)a + 1 = 6a + 1, where a is a positive integer Options for j: 7, 13, 19, 25... If j=7, then the answer to the question stem is YES. If j=25, then the answer to the ...”
April 21, 2019
GMATGuruNY posted a reply to From a group of 5 managers (Joon, Kendra, Lee, Marnie and in the Problem Solving forum
“Approach 1; P = (good pair)/(all possible pairs) Good pair = Marnie and Noomi = 1 option. All possible pairs = the number of ways to select 2 managers from 5 options = 5C2 = (5*4)/(2*1) = 10 options. Thus: P = 1/10 = 0.1 Approach 2: P(M or N is selected first) = 2/5. (Of the 5 managers, 2 ...”
April 21, 2019
GMATGuruNY posted a reply to While it costs about the same in the Sentence Correction forum
“Here, the phrase in blue implies that people were trying to drive on the freeway but that the process was made challenging by the rain. This meaning is logical. Here, the phrase in red implies that nuclear plants are trying to generate electricity but that the process is made more expensive ...”
April 20, 2019
GMATGuruNY posted a reply to Discussion of greenhouse effects has usually in the Sentence Correction forum
“An effect is a CHANGE brought about by an event. The Earth ALWAYS has a temperature. Since temperature does not constitute a change, it cannot be an effect. In the OA, EXTREMES are the change brought about by greenhouse emissions. This meaning is logical. The temperature of the Earth is not ...”
April 20, 2019
GMATGuruNY posted a reply to What is the value of |x|? in the Data Sufficiency forum
“Statement 1: Case 1: x=0, with the result that -|x| = - |0| = 0 In this case, |x| = 0. Case 2: x=-1, with the result that -|-1| = -1 In this case, |x| = 1. Since |x| can be different values, INSUFFICIENT. Statement 2: Thus, x=2 or x=-2. In each case, |x|=2. SUFFICIENT. The correct ...”
April 20, 2019
GMATGuruNY posted a reply to Mary's income is 60 percent more than Tim's income, and in the Problem Solving forum
“Let J=100. Since Tim''s income is 40% less than Juan''s, T = 100 - (40% of 100) = 100 - 40 = 60. Since Mary''s income is 60% greater than Tim''s, M = 60 + (60% of 60) = 60 + 36 = 96. What percent of Juan''s income is Mary''s income? M/J = 96/100 = 96%. The correct answer is C.”
April 20, 2019
Ian Stewart posted a reply to A certain money market account that had a balance of $48,000 in the Problem Solving forum “If it earns$360 in a month, it earns $360 *12 in a year, if there''s no compounding. Dividing by the amount invested, we''ll get the interest rate for the year: (12)(360)/48000 = 1*360/4000 = 36/400 = 9/100 = 9%” April 19, 2019 Ian Stewart posted a reply to If x is an integer, then which of the following statements in the Problem Solving forum “Lots of ways to do this, for example: x^2 - x - 1 = x(x-1) - 1 Notice x(x-1) is the product of two consecutive integers, so it is the product of one odd and one even integer, and must therefore be even. When we subtract 1 from this product, we get an odd number, so x(x-1) - 1 is odd.” April 19, 2019 Ian Stewart posted a reply to A number of oranges are to be distributed evenly among a in the Data Sufficiency forum “Statement 1 is automatically true, so it really only tells us that it is possible to divide the number of baskets by 2. But we might have 2 baskets with 10 oranges each, or 20 baskets with 1 orange each, for example, so that information is not sufficient. If Statement 2 is true, then when we ...” April 19, 2019 Ian Stewart posted a reply to From a group of $$J$$ employees, $$K$$ will be selected, at in the Data Sufficiency forum “Using only Statement 1, we might be picking only from 15 employees in total, in which case it''s not likely, but also not nearly impossible, that Lisa and Philip sit together. But we might be picking from 15,000,000 employees in total, and the probability might be almost zero that we even pick Lisa ...” April 19, 2019 GMATGuruNY posted a reply to Verb-ing doubt in the Sentence Correction forum “NOUN + VERBing implies that the VERBing is a restrictive modifier. The purpose of a restrictive modifier is to SPECIFY the type of noun being discussed. Here, the restrictive modifier in blue implies the following: There are many types of planets. The sentence is not referring to all these ...” April 18, 2019 GMATGuruNY posted a reply to If x and y are positive integers and in the Data Sufficiency forum “Statement 1: x=2 $$2^y =2^{2y-3}$$ Since each side has the same base, the two exponents must be equal: y = 2y-3 3 = y Since the values of x and y are known, the value of $$x^y$$ can be determined. SUFFICIENT. Statement 2: Thus, x=2. Same information as in Statement 1. Since Statement ...” April 17, 2019 GMATGuruNY posted a reply to There are 10 employees in an office. The table shows how in the Problem Solving forum “List of 10 pet values implied by the chart: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3 Since the answer choices are all 3 or greater, the addition of the manager''s pet value will yield the following list of 11 values: 0, 0, 1, 1, 1, 2, 2, 3, 3, 3, M Since the new average must be equal to the median value ...” April 17, 2019 GMATGuruNY posted a reply to Computer-based activities in the Critical Reasoning forum “In a strengthen CR, the OA SUPPORTS THE PASSAGE. In an inference CR, the PASSAGE SUPPORTS THE OA. Here, the OA supports the passage. The result is a strengthen CR. Since the OA supports the conclusion, its negation naturally will weaken the conclusion.” April 16, 2019 GMATGuruNY posted a reply to OG Most of the country's biggest daily newspapers in the Sentence Correction forum “This is the comparison conveyed by the green sentence above. Here, each blue portion has a subject (the company) and a verb (had) and thus constitutes a clause. The result is a logical comparison. This is the comparison implied by the incorrect red sentence above. The first blue portion ...” April 16, 2019 GMATGuruNY posted a reply to Three salespeople, Dan, Matt, and Nicole, earned annual in the Problem Solving forum “D:M:N = 3:5:8. The sum of the parts of the ratio = 3+5+8 = 16. The values in red indicate the following: Nicole''s fraction of the total = 8/16 = 1/2. Since Nicole''s$28,000 is 1/2 of the total, the total = $56,000. The correct answer is E.” April 15, 2019 GMATGuruNY posted a reply to Together, 15 type A machines and 7 type B machines can in the Problem Solving forum “Let the job = 44 units. Since 15A+7B take 4 hours to complete the 44-unit job, the rate for 15A+7B = w/t = 44/4 = 11 units per hour. Since 8B+15C take 11 hours to complete the 44-unit job, the rate for 8B+15C = w/t = 44/11 = 4 units per hour. Adding together 15A+7B=11 and 8B+15C=4, we get: ...” April 15, 2019 GMATGuruNY posted a reply to Mark has fewer than 9 coins. Each coin is either a quarter in the Data Sufficiency forum “Statement 1: 25Q + 10D = 170 5Q + 2D = 34 To minimize the number of coins, we must maximize the value of Q. If Q=6, then D=2, with the result that 5Q + 2D = (5*6) + (2*2) = 34. In this case, the total number of coins = 6+2 = 8. If the value of Q decreases, then the total number of coins ...” April 15, 2019 GMATGuruNY posted a reply to 12^(1/2) + 108^(1/2) + 48^(1/2) = in the Problem Solving forum “√12 + (√9 * √12) + (√4 * √12) = √12 + 3√12 + 2√12 = 6√12 = 6 * √4 * √ 3 = 12√3 The correct answer is A.” April 15, 2019 GMATGuruNY posted a reply to If n is a positive integer greater than 6, what is the in the Data Sufficiency forum “Approach 1: Since n is greater than 6, and the statements refer to n², make a list of perfect squares greater than 6²: n² = 49, 64, 81, 100, 121, 144, 169, 196, 225. Subtracting 1 from these values, we get the following options for n² - 1: n² - 1 = 48, 63, 80, 99, 120, 143, 168, 195, ...” April 15, 2019 GMATGuruNY posted a reply to Which of the following is equivalent to in the Problem Solving forum “Let x=2 and y=1, with the result that (x+y)/3 - (x-y)/4 = 1 - 1/4 = 3/4. The correct answer must yield 3/4 when x=2 and y=1. Only D works: (7y+x)/12 = (7*1 + 2)/12 = 9/12 = 3/4 The correct answer is D.” April 15, 2019 GMATGuruNY posted a reply to In a certain office, 50 percent of the employees are college in the Data Sufficiency forum “Let T = the total number of employees. Since 60% of the employees are over 40, we get: Over 40 = 0.6T 30% of those over 40 -- in other words, 30% of the expression in blue -- have master''s degrees. Thus: Over 40 with master''s = 0.3(0.6T). To calculate the value of the expression in ...” April 14, 2019 GMATGuruNY posted a reply to Dwight and Mose decide to build a new barn on their farm, in the Problem Solving forum “Every time Dwight does 1/4 of the remaining work, 3/4 of the work remains. Every time Mose does 1/6 of the remaining work, 5/6 of the work remains. When Mose starts his third shift, Dwight has completed 3 shifts, while Mose has completed 2 shifts. Thus, the remaining work at the start of Mose''s ...” April 14, 2019 GMATGuruNY posted a reply to In a law firm, 72% of the employees are associates and 54% in the Problem Solving forum “Let the total number of employees = 100, implying that the total number of associates = 72% of 100 = 72 and that the number of senior associates = 54% of 100 = 54. The prompt should make clear that every associate is either a junior associate or senior associate, yielding the following equation: ...” April 14, 2019 GMATGuruNY posted a reply to A library branch originally contained 18360 volumes, 30% of in the Problem Solving forum “Since the answer choices are PERCENTS, the total number of books can be ANY POSITIVE VALUE. 30% = 3/10, implying a denominator of 10. Let the total number of books = the product of the three denominators 10, 3 and 3 = 10*3*3 = 90. Since 30% of the books are fiction, the number of fiction books ...” April 12, 2019 GMATGuruNY posted a reply to Heavy commitment by an executive in the Sentence Correction forum “that-clause includes its own subject and verb and thus does not require an additional agent. In the blue that-clause above, the subject for will meet (verb) is a system of import relief laws. Since it is clear that A SYSTEM will meet the strategic needs, no additional agent is required. An ...” April 11, 2019 GMATGuruNY posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum “Since Mary is behind Kate by 250 meters -- half the circumference of the track -- she will catch up to Mary when she has traveled 250 meters more than Kate. To catch up to Kate a second time, Mary must then travel one more lap than Kate -- in other words, 500 meters more than Kate. Implication: ...” April 11, 2019 GMATGuruNY posted a reply to Heavy commitment by an executive in the Sentence Correction forum “The bad weather makes it difficult to work outdoors. Here, the infinitive in blue is not immediately preceded by an agent: the sentence does not specify WHO is intended TO WORK. The implication is that the agent for the blue infinitive is not a specific person but people IN GENERAL, as follows: ...” April 11, 2019 GMATGuruNY posted a reply to How many rectangles are found in the lattice below? in the Problem Solving forum “https://i.postimg.cc/Z0xg3MXX/lattice.png To form a rectangle, we must combine as HORIZONTAL LENGTH with a VERTICAL LENGTH: Horizontal length: Number of ways to choose a horizontal length of 1: AB, BC, CD, DE, EF = 5 Number of ways to choose a horizontal length of 2: AC, BD, CE, DF = 4 ...” April 9, 2019 GMATGuruNY posted a reply to If x is a positive integer, is the remainder 0 when in the Data Sufficiency forum “$$3^x + 1$$ will yield a remainder of 0 when divided by 10 if it has a units digit of 0. 3¹ --> units digit of 3. 3² --> units digit of 9. (Since the product of the preceding units digit and 3 = 3*3 = 9.) 3³ --> units digit of 7. (Since the product of the preceding units digit and ...” April 9, 2019 GMATGuruNY posted a reply to If d is a positive integer and f is the product of the first in the Data Sufficiency forum “30! = 30*29*28*....*3*2*1. Statement 1: To determine the greatest possible value for d, we need to know the number of 10''s contained within 30! Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 30! will yield a 10. The prime-factorization of 30! is composed ...” April 9, 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 + ...” April 9, 2019 GMATGuruNY posted a reply to If the median and average (arithmetic mean) of a set of 4 di in the Data Sufficiency forum “In ascending order, let the four numbers = a, b, c, d. Since the average of the 4 numbers = 10, we get: (a+b+c+d)/4 = 10 a+b+c +d = 40 Since the median of the 4 numbers = 10, we get: (b+c)/2 = 10 b+c = 20 Subtracting the blue equation from the red equation, we get: (a+b+c+d) - (b+c) = 40-20 ...” April 8, 2019 GMATGuruNY posted a reply to Mixture A is 15 percent alcohol, and mixture B is 50 percent in the Problem Solving forum “A = 15% alcohol B = 50% alcohol The MIXTURE of A and B = 30% alcohol To determine the ratio of A to B, use ALLIGATION -- a very efficient way to handle mixture problems. Step 1: Plot the 3 percentages on a number line, with the percentages for A and B (15% and 50%) on the ends and the ...” April 7, 2019 GMATGuruNY posted a reply to A museum sold 30 tickets on Saturday. Some of the tickets so in the Data Sufficiency forum “Let G = the number of general tickets. Since a total of 30 tickets are sold, the number of special exhibit tickets = 30-G. Since general tickets =$10 each and special exhibit tickets = $70 each, we get: Total revenue = 10G + 70(30-G) = 10G + 2100 - 70G = 2100 - 60G. Statement 1: 1570 < ...” April 7, 2019 GMATGuruNY posted a reply to If 500 is the multiple of 100 that is closest to X and 400 in the Data Sufficiency forum “Statements combined: Case 1: X=460, with the result that 500 is the multiple of 100 closest to X Y=360, with the result that 400 is the multiple of 100 closest to Y In this case, X+Y=820, so the multiple of 100 closest to X+Y is 800. Case 2: X=490, with the result that 500 is the multiple of ...” April 7, 2019 Ian Stewart posted a reply to Harry and Ron work for the same company but earn different in the Data Sufficiency forum “Say Harry earns$H, and has $E in expenses, while Ron earns$R, and spends $S. Then Harry saves H-E dollars, and Ron saves R-S dollars. Statement 1 tells us: H + S > R + E H - E > R - S or in other words, Harry''s savings exceed Ron''s savings. Now, it''s not clear what is meant ...” April 6, 2019 Ian Stewart posted a reply to n is a positive integer greater than 2. If y = 9^0 + 9^1+ in the Data Sufficiency forum “If you look at the units digits of various powers of 9, you''ll see they alternate between 1 and 9: 9^0 ends in 1 9^1 ends in 9 9^2 ends in 1 9^3 ends in 9 and so on. So if we add 9^0 + 9^1 + 9^2 + ... + 9^n, we''ll get something ending in 0 when n is even, and something ending in 1 when n ...” April 6, 2019 GMATGuruNY posted a reply to One legacy of Madison Avenue's in the Sentence Correction forum “Generally, a when-clause refers to an action performed at a particular moment: When Mary entered the room, John smiled. Here, the usage of when implies that the action in blue happened at a particular moment. An as-clause refers to an action performed over an extended period of time: Adam sang ...” April 6, 2019 GMATGuruNY posted a reply to The 32 species that make up the dolphin family are closely r in the Sentence Correction forum “There is no reason to repeat which in the OA. Even if more than one verb is attributed to COMMA + WHICH, the usage of one which should suffice.” April 6, 2019 GMATGuruNY posted a reply to In a nationwide poll, N people were interviewed. If 1/4 in the Problem Solving forum “Let N=12. Number who answered yes to question 1 = (1/4)12 = 3. Number who also answered yes to question 2 = (1/3)3 = 1. Number who didn''t answer yes to both questions = 12-1 = 11. This is our target. Now we plug N=12 into the answers to see which yields our target of 11. Only E works: ...” April 6, 2019 April 6, 2019 Ian Stewart posted a reply to Is BG > EC? in the Data Sufficiency forum “BG is the height of triangle ABC (when we use AC as our base), and EC is the height of triangle DEF (when we use DF as our base). It''s confusing to use all those capital letters, so let''s use ''h'' for the height BG, and ''j'' for the height EC. We also have three important lengths along the ...” April 6, 2019 Ian Stewart posted a reply to If a certain positive integer is divided by 9, the ..... in the Data Sufficiency forum “Statement 1 tells us our number is 30 greater than some multiple of 45, so our number is equal to 45q + 30, for some integer q. But 45q + 30 = 5(9q + 6), which is clearly divisible by 5, so the remainder is 0 when we divide our number by 5, and Statement 1 is sufficient, even without using any ...” April 6, 2019 Ian Stewart posted a reply to In the figure above, if the length of MO is 10 in the Data Sufficiency forum “If you knew that the seemingly-vertical line of length ''h'' was at right angles to the line MO, then it would be easy, with both statements, to use Pythagoras to find the lengths of all of the sides. But without knowing if we have a right angle there, we can''t do much, and the answer is E. ...” April 5, 2019 GMATGuruNY posted a reply to Is x < 0? in the Data Sufficiency forum “Statement 1: x³ < -1 The cube of x will be negative only if x itself is negative. Thus, x < 0. SUFFICIENT. Statement 2: x³ + x < -1 x(x² + 1) < -1 Since the square of a value cannot be negative, x² ≥ 0, with the result that the factor in blue must be POSITIVE. ...” April 5, 2019 GMATGuruNY posted a reply to A pizza shop sold small pizzas for$4.5 in the Problem Solving forum
“The GMAT would list the answer choices in ascending or descending order, as follows: We can PLUG IN THE ANSWERS, which represent the number of small pizzas. The average cost per pizza = 5050/500 ≈ $10. Since the average cost ($10) is much closer to the price of a large pizza ($12.50) than ...” April 5, 2019 GMATGuruNY posted a reply to Fossils of feathered dinosaurs - GMAT prep Exam pack 1 in the Sentence Correction forum “A general truth is something that is true not just at a particular moment but is true IN GENERAL. Mary plays the saxophone. Here, the portion in blue expresses a general truth about Mary. To express a GENERAL TRUTH, we use the simple present tense. The SC above is intended to express a general ...” April 2, 2019 GMATGuruNY posted a reply to While making a non-stop trip, a bus averaged m mph for the in the Data Sufficiency forum “Distance traveled in the first 5 hours = 5m. Distance traveled in the remaining 4 hours = 4n. Average speed for the entire 9-hour trip = (5m + 4n)/9. To determine the average speed for the entire trip, we need to know the value of 5m+4n. Question stem, rephrased: What is the value of 5m+4n? ...” April 2, 2019 GMATGuruNY posted a reply to OG13 - Q20 in the Sentence Correction forum “The OA does not make a comparison. to double X = to increase X by 100% OA: Personal spending in the Julv-September quarter would more than double the...growth rate. Conveyed meaning: Personal spending in the July-September quarter would increase the growth rate by more than 100%.” April 2, 2019 GMATGuruNY posted a reply to OG12, Q18 in the Sentence Correction forum “OA: Plants are more efficient than fungi at acquiring carbon, in the form of carbon dioxide. Here, the modifier in green is an adverb in that it describes UNDER WHAT CIRCUMSTANCE the preceding blue action happens. Under what circumstance ARE plants MORE EFFICIENT at acquiring carbon? Under the ...” April 2, 2019 GMATGuruNY posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum “Let B = Barry''s rate and W = the walkway''s rate. The distance can be ANY VALUE. Let the distance = 240 meters. WITH the walkway, the time = 30 seconds: Here, Barry and the walkway WORK TOGETHER, so we ADD their rates: B+W = d/t = 240/30 = 8 meters per second. AGAINST the walkway, the ...” April 1, 2019 Ian Stewart posted a reply to What is the value of 10^x · 10^y? in the Data Sufficiency forum “I imagine there''s a typo in the question somewhere, because as written, the statements aren''t consistent, and the answer is not D (it would be A). It seems more likely the question is meant to say something like: What is $$10^x 10^y$$ ? 1. 2^(x+y) = 16 2. 5^(x+y) = 625 Since 10^x * 10^y ...” April 1, 2019 Ian Stewart posted a reply to Barry walks from one end to the other of a 30-meter long in the Problem Solving forum “If s is his speed, and w the speed of the walkway, then when he walks with the walkway, his net speed is s+w, and when he walks against the walkway, his net speed is s-w. Using the familiar S = D/T equation for both cases, we have: s+w = 30/30 = 1 s-w = 30/120 = 1/4 and adding these two ...” April 1, 2019 Ian Stewart posted a reply to For any given x and any positive integer n in the Problem Solving forum “For any sequence question, it is usually a good idea to work out the first few terms until you understand the structure of the sequence. Here, if s_n = x^(2n - 1) then plugging in n =1, 2 and 3 we find: s_1 = x^1 s_2 = x^3 s_3 = x^5 and so on. We want to multiply these terms together, ...” April 1, 2019 Ian Stewart posted a reply to For positive integers n, the integer part of the nth term in the Problem Solving forum “The digits long after the decimal point are not going to matter here, since they only make a minuscule contribution to the sum, and we only need a rough estimate. If we work out the first seven terms, truncating each to one decimal place, we have: 1.2 2.4 3.6 4.8 5.1 6.1 7.1 When we ...” April 1, 2019 Ian Stewart posted a reply to Is xy > 0? in the Data Sufficiency forum “xy > 0 will be true if x and y have the same sign, so if both are positive, or if both are negative. x^2 is always positive or zero, so Statement 1 tells us almost nothing (it only tells us x is not zero). In Statement 2, we can divide by y^2 on both sides, because we know y^2 is positive (so ...” April 1, 2019 Ian Stewart posted a reply to Is the slope of line z positive? in the Data Sufficiency forum “If two lines are perpendicular, their slopes are negative reciprocals, so if one line has a slope of m, the other has a slope of -1/m. So from Statement 1, if line m has a slope of -1/4, the perpendicular line z must have a slope of 4, and Statement 1 is sufficient. Knowing about one point on a ...” April 1, 2019 GMATGuruNY posted a reply to 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=? in the Problem Solving forum “2⁸ = 256 2⁷ = 128 Thus: 2⁸ + 2⁷ + 2⁶ + 2⁵ + 2⁴ + 2³ + 2² + 2 + 2 = 256 + 128 + (around 100) ≈ 500. Only A is viable: 2⁹ = 512. The correct answer is A.” April 1, 2019 Ian Stewart posted a reply to Points (a, b) and (c, d) lie on line L in the coordinate in the Data Sufficiency forum “When you subtract y-coordinates of two points, you''re just finding the distance between them purely in the vertical direction. That''s sometimes called the "rise". Similarly when you subtract x-coordinates of two points, you''re finding the purely horizontal distance between them, ...” March 31, 2019 Ian Stewart posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum “Using both statements, k can be 2, and thus prime, or -1, and not prime, so the answer is E.” March 31, 2019 Ian Stewart posted a reply to Alice bought a certain number of 30 cent stamps, 35 cent in the Data Sufficiency forum “Using Statement 2 alone, if she bought x stamps at 30 cents, and x stamps at 40 cents, she spent 70x cents in total just on those stamps. If she only spent 420 cents overall, then x clearly is no greater than 6. But if she also bought some 35 cent stamps, x must be strictly less than 6. And ...” March 31, 2019 Ian Stewart posted a reply to If $$n$$ is a positive integer and $$r$$ is the remainder in the Data Sufficiency forum “n-1, n and n+1 are three consecutive integers. If, as Statement 1 tells us, n is odd, then n-1 and n+1 are both even -- in fact, they are consecutive even numbers. If you take any two consecutive even integers, one of them will always be a multiple of 4, so Statement 1 guarantees that (n-1)(n+1) is ...” March 31, 2019 Ian Stewart posted a reply to How many hours did it take Helen to drive from her house to in the Data Sufficiency forum “Statement 1 is clearly insufficient. Using Statement 2, maybe her speed was 8 km/hr, and the total distance was 16 km, so took 2 hours. Then if her speed was 8 km/hr greater, so was 16 km/hr, she would have saved an hour. But we know there must also be a solution where her speed was 72 km/hr, ...” March 31, 2019 Ian Stewart posted a reply to In the diagram above, O is the center of the circle and ACDE in the Data Sufficiency forum “If you connect a diameter of a circle to a point C on the circle, you always form a right angle at C, so Statement 2 tells us nothing new, and is useless. Using only Statement 1, since we know we have a right triangle, and we know two of its sides (the hypotenuse is twice the radius, so is 4), we ...” March 31, 2019 Ian Stewart posted a reply to In the figure above, all angles are right angles. If the len in the Data Sufficiency forum “The perimeter of the figure is identical to the perimeter of a rectangle with sides a and b (if you just draw the two lines in the top right corner that you''d need to draw to make that rectangle, you''ll see that you''re adding a line of length v to the top side, and a line of length u to the ...” March 31, 2019 GMATGuruNY posted a reply to Cars emerging from a motorway arrive at a junction that in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the number of cars in the left lane. Answer choice C: 1700 If 700 cars per hour were diverted from the left lane to the right lane, the number of cars entering the right lane per hour would be twice as big as the number of cars entering the left lane ...” March 30, 2019 GMATGuruNY posted a reply to A 3-character alpha-numeric code does have the following in the Problem Solving forum “Number of options for the first character = 8. (Of the 10 digits, any digit but 0 or 9.) Number of options for the second character = 24. (Of the 26 letters in the alphabet, any but a or z.) Number of options for the third character = (number of options for the first character) + (number of ...” March 29, 2019 GMATGuruNY posted a reply to The ratio of boys to girls in Class A is 3 to 4. The ratio in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the number of girls in Class A. Since b:g = 3:4, the number of girls must be a multiple of 4. Eliminate B, C and D. Answer choice A: g = 8. Since b:g = 3:4 = 6:8, b=6. Since Class A has one more boy and two more girls than Class B, in Class B, ...” March 29, 2019 GMATGuruNY posted a reply to 100 students appeared for two tests-Maths and English. For in the Data Sufficiency forum “100 = Only Math + Only English + Both + Neither For every student who passed in both the tests, 8 students passed only in Maths and 9 students passed only in English. Let B = both, implying that Only Math = 8B and that Only English = 9B. Thus: 100 = 8B + 9B + B + Neither 100 = 18B + Neither ...” March 28, 2019 GMATGuruNY posted a reply to An optometrist charges$150 per pair for soft contact lenses in the Problem Solving forum
“Since $150 soft lenses and$85 hard lenses yield $1690 in revenue, we get: 150S + 85H = 1690 30S + 17H = 238 The sum on the left side must yield a units digit of 8. Since 17*4 = 68, it is likely that H=4: 30S + 17*4 = 338 30S + 68 = 238 30S = 170 S=9 S=9 and H=4 satisfy the condition ...” March 28, 2019 GMATGuruNY posted a reply to OG-12 SC Q-43 Laos has a land area in the Sentence Correction forum “D: Laos has a land area comparable to the size of Great Britain, but only four million in population, and many are members of hill tribes ensconced in the virtually inaccessible mountain valleys of the north. Error 1: The intent here is to compare the LAND AREA of Laos to the LAND AREA of Great ...” March 28, 2019 GMATGuruNY posted a reply to Which of the following is the solution set for the inequalit in the Problem Solving forum “We can PLUG IN THE ANSWERS, which represent the range of x. A: -1 < x < 0 Plugging x=-0.5 into the given inequality, we get: 0 < |-0.5| - 2(-0.5) < 3 0 < 0.5 + 1 < 3 0 < 1.5 > 3 Since x=-0.5 is a valid solution, the correct answer must include x=-0.5 within its ...” March 28, 2019 GMATGuruNY posted a reply to A straight highway connects two cities P and Q, and goes via in the Data Sufficiency forum “Statement 1: For every 2 hours spent at 30 mph and 1 hour spent at 50 mph, 3 hours are spent at 60 mph. Average speed per 6 hours = (2*30 + 1*50 + 3*60)/6 = 290/6. SUFFICIENT. Statement 2: Case 1: NQ = 180 miles, PM = 60 miles and MN = 50 miles Since NQ is traveled at 60 mph, the time for ...” March 27, 2019 GMATGuruNY posted a reply to Geometry in the Problem Solving forum “https://i.postimg.cc/N2Ky6DSp/square-divided-into-triangles.png Each triangle in the figure above is an isosceles right triangle with sides 1, 1 and √2. Shaded region = 4 triangles. Largest square = 16 triangles. Thus: (shaded region)/(largest square) = 4/16 = 1/4. The correct answer is ...” March 27, 2019 GMATGuruNY posted a reply to A music festival took place over two days, Saturday and in the Data Sufficiency forum “Anyone who attended the festival must have attended only Saturday, only Sunday, or both days. Let the total number of attendees = 100. Statement 1: 40% of attendees attended both days. No way to determine how many attendees attended only Saturday. INSUFFICIENT. Statement 2: 70% of attendees ...” March 26, 2019 GMATGuruNY posted a reply to Boat World sells a certain boat and a certain trailer. What in the Data Sufficiency forum “Let b = boat and t = trailer. What is the value of t? Statement 1: b = 7500+t No way to solve for t. INSUFFICIENT. Statement 2: b+t = 15000 No way to solve for t. INSUFFICIENT. Statements combined: Since we have two variables (b and t) and two distinct linear equations (b=7500+t and ...” March 26, 2019 GMATGuruNY posted a reply to p, q, and r are different prime numbers. What is the value o in the Data Sufficiency forum “Statement 1: (pq)² = 36 pq = 6 Case 1: p=2 and q=3 Case 2: p=3 and q=2 Since q can be different values, INSUFFICIENT. Statement 2: (qr)² = 225 qr = 15 Case 1: q=3 and r=5 Case 2: q=5 and r=3 Since q can be different values, INSUFFICIENT. Statements combined: Only one case ...” March 26, 2019 GMATGuruNY posted a reply to √r + 2/√r = 4. What is the value of r + 4/r? in the Problem Solving forum “(a+b)² = a² + b² + 2ab √r + 2/√r = 4 (√r + 2/√r)² = 4² (√r)² + (2/√r)² + 2(√r)(2/√r) = 16 r + 4/r + 4 = 16 r + 4/r = 12 The correct answer is A.” March 26, 2019 Ian Stewart posted a reply to There are x people and y chairs in a room where x and y are in the Data Sufficiency forum “This question doesn''t make any sense, at least if the OA is A. I can guess the logic they use to justify ''A'' as the right answer -- using only Statement 1, there are only two primes that sum to 12, namely 5 and 7. If we want to seat 5 people in 7 chairs, there are 7*6/2! = 21 ways to choose the ...” March 25, 2019 GMATGuruNY posted a reply to How many trailing zeroes would be found in 63! upon in the Problem Solving forum “TRAILING 0''s = the number of 0''s at the end of a large product. 63! = 63*62*61*....*3*2*1. Since 10=2*5, EVERY COMBINATION OF 2*5 contained within the prime-factorization of 63! will yield a 0 at the end of the integer representation of 63!. The prime-factorization of 63! includes FAR ...” March 25, 2019 GMATGuruNY posted a reply to A certain NYC taxi driver has decided to start charging a in the Problem Solving forum “Let r=100 cents. For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars. Let x = 2 miles. Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars. With a 50% discount, the cost in dollars = 3. This is our target. Now we plug x=2 and r=100 into the answers to see which ...” March 25, 2019 GMATGuruNY posted a reply to 60% of all students in a class commute by public in the Problem Solving forum “Use a DOUBLE-MATRIX to organize the data. Let P = public transportation, NP = not public transportation, S = science, NS = not science. 60% of all students in a class commute by public transportation. 30% of the students aspire to be scientists. The following matrix is yielded: ...” March 25, 2019 GMATGuruNY posted a reply to GPREP SC-8 in the Sentence Correction forum “Proposed revision: The sandpipers...are a result of residential and industrial development. This meaning is nonsensical. BIRDS cannot be a RESULT. This line of reasoning is valid: In D and E, the referent for in the northeastern United States is unclear.” March 24, 2019 Ian Stewart posted a reply to Time and work in the Problem Solving forum “You can do this mathematically - if you suppose it takes t minutes for A to print n pages, you can then get the same time for each machine: A prints 2n pages in 2t minutes B prints n pages in 2t minutes so A+B together print 3n pages in 2t minutes and A+B together print n pages in 2t/3 ...” March 24, 2019 GMATGuruNY posted a reply to If P and Q are positive integers, and if P > 1, does P = in the Data Sufficiency forum “Statement 1: Case 1: P=2 and Q=2, with the result that P divides evenly into Q In this case, P=Q, so the answer to the question stem is YES. Case 2: P=2 and Q=4, with the result that P divides evenly into Q In this case, P≠Q, so the answer to the question stem is NO. INSUFFICIENT. ...” March 24, 2019 GMATGuruNY posted a reply to Is it true that x > 0? in the Data Sufficiency forum “Statement 1: Case 1: x=0 In this case, the answer to the question stem is NO. Case 2: x≠0, allowing us to divide both sides by x x²/x = 2x/x x = 2 In this case, the answer to the question stem is YES. INSUFFICIENT. Statement 2: Case 1: x=0 In this case, the answer to the question ...” March 24, 2019 Ian Stewart posted a reply to A number of ties are individually packaged in unmarked boxes in the Data Sufficiency forum “It makes no logical sense to ask a DS question like this, because it''s not clear what information would be sufficient to find the "maximum number" of something. That''s easy to see if you imagine a different question: There are 25 boxes, and each box contains one colored tie. What is ...” March 23, 2019 Ian Stewart posted a reply to At a particular business school which requires applicants to in the Data Sufficiency forum “You can say "the average score of admitted applicants was 15 points higher than of rejected applicants" or you can say "the difference between the average score of accepted applicants and rejected applicants was 15 points" but you can''t say both things in the same sentence. The ...” March 23, 2019 GMATGuruNY posted a reply to Events A and B are independent and have equal probabilities in the Data Sufficiency forum “Statement 1: P(at least one event occurs) = 1 - P(neither event occurs) Thus: P(at least A or B) = 1 - P(neither A nor B) Since P(at least A or B) = 0.84, we get: 0.84 = 1 - P(neither A nor B) P(neither A nor B) = 0.16 P(not A) * P(not B) = 0.16. Since it is given that P(A) = P(B), P(not ...” March 23, 2019 GMATGuruNY posted a reply to In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, in the Problem Solving forum “Third-side rule: The third side a triangle must be LESS THAN THE SUM OF and GREATER THAN THE DIFFERENCE OF the other two sides. Here, all the sides must be INTEGER values. In triangle ANS, AS=10 and NS=5. Thus, third side AN must be an integer value less than 10+5 = 15 and greater than 10-5 = ...” March 23, 2019 Ian Stewart posted a reply to Find the range of values of $$x$$ that satisfy the in the Problem Solving forum “(x+1)(x-2) > 4 x^2 - x - 2 > 4 x^2 - x - 6 > 0 (x-3)(x+2) > 0 So either x-3 and x+2 are both positive, which will be true when x > 3, or both x-3 and x+2 are negative, which will be true when x < -2.” March 22, 2019 Ian Stewart posted a reply to If $$xy \neq 0$$ and $$2x + 3y$$ is equal to 175 percent in the Problem Solving forum “If we''re taking 175% of something, we''re multiplying it by 1.75, or by 7/4. So 2x + 3y = (7/4)(8x) 2x + 3y = 14x 3y = 12x 1/4 = x/y” March 22, 2019 Ian Stewart posted a reply to The largest bonus that Felix can receive this year is equal in the Data Sufficiency forum “His smallest bonus is 30% of 20% of his salary, so, multiplying, is 6% of his salary. Statement 1 tells us his smallest bonus, and since we know that''s 6% of his salary, we can find his salary. Statement 2 tells us the difference in his largest and smallest bonuses, and since 20% - 6% = 14%, that ...” March 22, 2019 Ian Stewart posted a reply to Paul, a painter, paints only flowers or cats in his notebook in the Data Sufficiency forum “Am I missing something? Statement 2 tells us the exact answer to the question. I assume it means to ask how many *cat* pictures in charcoal there are. Since we know the 39 pictures mentioned in the stem consist precisely of flower-pencil, flower-charcoal, and cat-charcoal pictures, then once we ...” March 22, 2019 GMATGuruNY posted a reply to Express 2^20-2^19-2^18-2^17 as a power of 2. in the Problem Solving forum “Test an analogous case with easier values: 2⁴ - 2³ - 2² - 2¹ = 16 - 8 - 4 - 2 = 2¹ The matching blue portions imply the following: 2²⁰ - 2¹⁹ - 2¹⁸ - 2¹⁷ = 2¹⁷ The correct answer is C.” March 22, 2019 GMATGuruNY posted a reply to If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? in the Problem Solving forum “(r + 1/r)² = 5 r + 1/r = √5 (r + 1/r)² = 5 r² + 1/r² + 2(r)(1/r) = 5 r² + 1/r² + 2 = 5 r² + 1/r² = 3 Multiplying the blue equation and the red equation, we get: (r² + 1/r²)(r + 1/r) = 3√5 r³ + (r²)(1/r) + (1/r²)(r) + 1/r³ = 3√5 r³ + (r + 1/r) + 1/r³ = 3√5 ...” March 21, 2019 GMATGuruNY posted a reply to A dessert recipe calls for 50% melted chocolate and 50% in the Problem Solving forum “Chocolate percentage in the incorrect sauce: 40%. Chocolate percentage in the pure chocolate: 100%. Chocolate percentage in the mixture: 50%. Let I = the incorrect sauce and C = the pure chocolate. The following approach is called ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS. ...” March 21, 2019 GMATGuruNY posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill in the Problem Solving forum “Downhill speed - uphill speed = (x+10) - (x-8) = 18. Implication: The downhill speed is 18 mps greater than the uphill speed. We can PLUG IN THE ANSWERS, which represent the downhill speed. Since the downhill speed is 18 mps greater than the uphill speed, the correct answer must be GREATER ...” March 21, 2019 GMATGuruNY posted a reply to Jeremiah invests his savings of$120,000 by dividing it in the Problem Solving forum
“On the GMAT, compounded interest is typically just a bit more than simple interest. Since the answer choices are all greater than 2% -- the percentage given in the prompt -- they must represent the HIGHER interest rate, with 2% representing the LOWER interest rate. Lower rate: Since 3/4 of ...”
March 21, 2019
GMATGuruNY posted a reply to If m and n are positive integers, is m+n divisible by 15? in the Data Sufficiency forum
“Rule: MULTIPLE OF X + MULTIPLE OF X = MULTIPLE OF X MULTIPLE OF X + NON-MULTIPLE OF X = NON-MULTIPLE OF X 225 = 9*25 Statements combined: Case 1: m=9 and n=25*15, with the result that m is a multiple of 9, n is a multiple of 15, and mn = 9*25*15 = 225*15 = multiple of 225 In this case, m+n ...”
March 21, 2019
GMATGuruNY posted a reply to What is the smallest positive integer n such that n / 420 ca in the Problem Solving forum
“A fraction will yield a terminating decimal if the prime-factorization of its denominator contains only 2''s and/or 5''s. n/420 = n/(2*2*3*5*7). For a terminating decimal to be yielded, the prime factors in red must CANCEL OUT with n, leaving only 2''s and 5''s in the denominator. Thus, the ...”
March 21, 2019
GMATGuruNY posted a reply to The consultant explained that companies in the Sentence Correction forum
“Generally, a one-word adverb such as tirelessly will not be positioned between a verb and its direct object. Incorrect: Companies lobby tirelessly government officials. Here, tirelessly (adverb) is awkwardly positioned between lobby (verb) and government officials (direct object). Correct: ...”
March 20, 2019
GMATGuruNY posted a reply to one another vs. others? in the Sentence Correction forum
“Some grammarians -- including me -- reserve each other for two elements and one another for more than two. Other grammarians consider the two modifiers interchangeable. A club has exactly three members: Ann, Beth, and Carol. The sentence above implies the following: Ann, Beth and Carol ...”
March 20, 2019
GMATGuruNY posted a reply to If arc PQR above is a semicircle, what is the length of diam in the Data Sufficiency forum
“An INSCRIBED ANGLE is formed by two chords. Thus, angle PQR is an inscribed angle. An inscribed angle that intercepts the diameter is a RIGHT ANGLE. Thus, angle PQR is a right angle, implying that triangle PQR is a RIGHT TRIANGLE. http://s15.postimage.org/xozmfjdh3/PQR.jpg In the figure ...”
March 20, 2019
GMATGuruNY posted a reply to Reiko drove from point A to point B at a constant speed, and in the Data Sufficiency forum
“Test the THRESHOLD. Since we want to know whether the speed from A to B is greater than 40mph, the threshold here is 40mph. Statement 1: Reiko''s average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour. Let the distance in each direction = 40 ...”
March 19, 2019
GMATGuruNY posted a reply to Danny spends $360 buying his favorite dolls. If he buy only in the Problem Solving forum “Since a small doll costs$1 less than a large doll, the answer choices imply the following options for the price of a small doll: 4 5 6.2 7 8 Given that all of the values in the prompt are INTEGERS, the price of a small doll is almost certain to be a factor of 360. Only the values in blue ...”
March 18, 2019
Ian Stewart posted a reply to If $defines a certain operation, is p$ q less than 20? in the Data Sufficiency forum
“Statement 1 tells us that we want to know if 2p^2 - q is less than 20, which we can''t tell with no information about p or q. Statement 2 is clearly not sufficient alone, because we have no idea what this "$" operation does. Using both Statements, we can clearly evaluate p$q = 2p^2 - q and ...”
March 18, 2019
Ian Stewart posted a reply to List S and List T each contain 5 positive integers, and for in the Data Sufficiency forum
“Since we know three values in List S, and we know the mean, and thus the sum, of all five values in List S, then if we''re given a fourth value in list S, we can find the fifth missing value. So from Statement 1 alone, we know exactly what List S contains. Similarly, from Statement 2 alone, we know ...”
March 18, 2019
Ian Stewart posted a reply to Is xy an integer? (1) x is the ratio of the area of a squar in the Data Sufficiency forum
“Strange question - you obviously need to know about both x and y, so neither statement could be sufficient alone. But Statement 1 gives us the value of x, and Statement 2 gives us the value of y, so of course we can answer any question in the universe about x and y using both Statements, and the ...”
March 18, 2019
GMATGuruNY posted a reply to Of the 25 cars sold at a car dealership, some had auto trans in the Data Sufficiency forum
“The following cases satisfy both statements: Case 1: 2 cars have neither 1 car has both antilock breaks and automatic transmission 22 cars have only automatic transmission. Case 2: 2 cars have neither 22 cars have both antilock breaks and automatic transmission 1 car has only automatic ...”
March 18, 2019
GMATGuruNY posted a reply to A box contains 3 red balls, 4 green balls, 5 yellow balls, 6 in the Problem Solving forum
“Determine the WORST-CASE-SCENARIO -- for each color of ball, the MAXIMUM number that can be removed WITHOUT removing 5 of the same color: 3 red 4 green 4 yellow 4 blue 4 white Sum = 3+4+4+4+4 = 19 Implication: It is possible to remove 19 balls without selecting 5 of the same color. ...”
March 18, 2019
Ian Stewart posted a reply to A carpenter worked alone for 1 day on a job that would take in the Problem Solving forum
“Once the first day is done, 6/7 of the job is left. We then know that the two workers together do 6/7 of a job in 4 days. So now we know these two things: Carpenter A does 1 job in 7 days Carpenters A+B together do 6/7 jobs in 4 days We can now get the same time for both: A does 4 jobs ...”
March 17, 2019
Ian Stewart posted a reply to What is the smallest positive integer $$x$$ such that in the Problem Solving forum
“Prime factorize the 450: 450 = 50*9 = 2 * 3^2 * 5^2 To get a perfect cube, we need to multiply by a number that will make every exponent in the prime factorization into some multiple of 3. So the smallest thing we can multiply by is 2^2 * 3^1 * 5^1 = 60, since that will give us 2^3 * 3^3 * ...”
March 17, 2019
Ian Stewart posted a reply to What is the remainder when the positive integer $$n$$ is in the Data Sufficiency forum
“If you know remainder arithmetic ("modular arithmetic"), this is a three-second question, because if you''re dividing by k, then "k+1" is the same as "1", so (k+1)^3 is the same as 1^3, and our remainder is 1 using Statement 1. But that won''t make any sense to most ...”
March 17, 2019
Ian Stewart posted a reply to If a light bulb is selected at random from a shipment, what in the Data Sufficiency forum
“When you''re only selecting one thing from a group, a probability is just a ratio. If you''re asked, say, "if you pick a random student from a class, what is the probability you pick a woman?", that is the same question as "what fraction of the students are women?" So the ...”
March 17, 2019
Ian Stewart posted a reply to The next number in a certain sequence is defined by in the Data Sufficiency forum
“If our sequence contains positive values, and if we''re multiplying by some positive constant (different from one) to produce each subsequent term, the sequence is either constantly increasing (if the constant is greater than 1) or constantly decreasing. (if the constant is less than 1). Either ...”
March 17, 2019
Ian Stewart posted a reply to If $$xyz < 0$$, is $$x < 0$$? in the Data Sufficiency forum
“If xyz < 0, then at least one of x, y or z must be negative. Notice that means that the smallest of the three numbers is certainly negative, because negative numbers are always smaller than positive numbers. Statement 1 tells us x < y, but maybe they''re both positive and z is negative. ...”
March 17, 2019
Ian Stewart posted a reply to $$n$$ is an integer greater than or equal to $$0$$. in the Data Sufficiency forum
“t_0 = 3 t_1 = 3 + 1 t_2 = 3 + 1 + 2 t_3 = 3 + 1 +2 + 3 t_4 = 3 + 1 + 2 + 3 + 4 and so on, so t_n is just equal to 3 plus the sum of the first n positive integers. The sum of the first n positive integers is just (n)(n+1)/2 (it''s the number of terms, n, times the average term, which, since ...”
March 17, 2019
GMATGuruNY posted a reply to To fill an order, a manufacturer had to produce 1000 tools in the Data Sufficiency forum
“Prompt: Total production = 1000n Statement 1: Total production for the first 5 days = 5*600 = 3000 Statement 2: Total production for the last 4 days = 4*1500 = 6000 Case 1: n=9, with no days between the first 5 days and the last 4 days Total production = 1000n = 1000*9 = 9000 Total ...”
March 17, 2019
GMATGuruNY posted a reply to What is the sum of all values of that satisfy the equation 4 in the Problem Solving forum
“For any quadratic in the form x² + bx + c = 0: Product of the roots = c Sum of the roots = -b Given equation: 4x² + 16 = 32x 4x² - 32x + 16 = 0 x² - 8x + 4 = 0 In the resulting quadratic, b=-8. Thus: Sum of the roots = -(-8) = 8. The correct answer is E.”
March 17, 2019
GMATGuruNY posted a reply to Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} in the Problem Solving forum
“One approach: Show that four of the five answers do NOT have to be true. P--> a=1, b=2, c=3, d=5, e=6, f=7, g=4 Range = 7-1 = 6, median = 4, mean = (1+2+3+5+6+7+4)/7 = 28/7 Q --> a=1, b=2, c=3, d=5, e=6, f=7 Range = 7-1 = 6, median = (3+5)/2 = 4, mean = (1+2+3+5+6+7)/6 = 24/6 = 4 ...”
March 17, 2019
GMATGuruNY posted a reply to If n is a positive integer and r is the remainder when in the Data Sufficiency forum
“What is the remainder when (n+1)(n-1) is divided by 8? Statement 1: Since n is odd, both n-1 and n+1 are EVEN, implying that (n-1)(n+1) = the product of two consecutive even integers. Given any two consecutive even integers, one will be a multiple of 4, while the other will be an even ...”
March 16, 2019
GMATGuruNY posted a reply to The sum of the weekly salaries of 5 employees is $3,250. If in the Problem Solving forum “Since each salary increases by 10%, the sum increases by 10%. 10% of 3250 = 325. Average increase per employee = (total increase)/(number of employees) = 325/5 = 65. The correct answer is E.” March 16, 2019 Ian Stewart posted a reply to Two cyclists, A and B, are 145 miles apart on a straight roa in the Problem Solving forum “In the first half hour, A covers 10 miles. So at 2pm, the cyclists are 135 miles apart. Together they will cover this distance in 3 hours, since they meet at 5pm. Since A covers 60 miles in that time, B must cover the rest, or 75 miles, and so B''s speed must be 25 mph.” March 15, 2019 Ian Stewart posted a reply to The number $$A$$ can be expressed as $$p*q$$ where $$p$$ and in the Data Sufficiency forum “p and q almost always represent prime numbers in math, so I don''t like their choice of letters here. Statement 1 tells us p is divisible by 8, but not by 16. So for pq to be divisible by 16, we need q to be even, something we don''t know, so Statement 1 is not sufficient alone. Statement 2 gives a ...” March 15, 2019 GMATGuruNY posted a reply to A rectangle has sides x and y and diagonal z. What is the pe in the Data Sufficiency forum “Always look for special triangles such as 3-4-5 and 5-12-13. Statement 2: Case 1: https://i.postimg.cc/V0JX8Hqv/rectangle-with-x-y-and-z-1.png Case 2: https://i.postimg.cc/DWCWwPyX/rectangle-with-x-y-and-z-2.png Since each case will yield a different perimeter, INSUFFICIENT. Statement ...” March 15, 2019 GMATGuruNY posted a reply to combinations in the Problem Solving forum “The portion in red is incorrect: it should be not 4C1 but 2C1. If we select two upper case letters from two sets of twins, we must then select one lower case letter from the OTHER TWO SETS OF TWINS, yielding only two options for the lower case letter. For example: If we select A and B for the two ...” March 15, 2019 GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “Good catch. In my solution, the lone exception (N=29) is now noted.” March 14, 2019 Ian Stewart posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don''t get a digit sum of ...” March 14, 2019 GMATGuruNY posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “Statement 1: Any integer whose digits sum to a multiple of 3 must itself be a multiple of 3. Since N has a digit sum of 11, N+1 must have a digit sum of 12. One exception: If N=29, then N+1 = 30, which has a digit sum of 3. Since the digit sum of N+1 must be a multiple of 3 -- either 12 or 3 -- ...” March 14, 2019 Ian Stewart posted a reply to A rectangle has sides x and y and diagonal z. What is the pe in the Data Sufficiency forum “Statement 1 is not sufficient, since the sides could be anything. Statement 2 also isn''t sufficient, because you''ll have different perimeters when, say, the quadrilateral is a square and when it isn''t. Using both statements, squaring the equation in statement 1, we learn x^2 + y^2 - 2xy = ...” March 14, 2019 Ian Stewart posted a reply to Are 40% of the employees attending the annual company picnic in the Data Sufficiency forum “The wording of the question is strange (is it asking if exactly 40% are men, or at least 40%?) but regardless, with no information about how many men or women work at the company, the question clearly can''t be answered even using both statements. If equal numbers of men and women work for the ...” March 14, 2019 GMATGuruNY posted a reply to If √x+√y=7 and √x-√y=5, what is the value of xy? in the Problem Solving forum “Adding the two equations, we get: 2√x = 12 √x = 6 x = 36 Substituting √x = 6 into √x+√y=7, we get: 6 + √y = 7 √y = 1 y = 1 Thus: xy = 36*1 = 36 The correct answer is C.” March 14, 2019 GMATGuruNY posted a reply to If f(x)=ax^2+bx+c, where a, b and c are integers, is b=0? in the Data Sufficiency forum “Statement 1: Since (49, 0) and (-49, 0) are both solutions, the quadratic must be as follows: f(x) = (x-49)(x+49) = x² - 49² In the resulting quadratic, b=0. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: If x-49 is a factor of the equation, then f(49) = 0. Case ...” March 14, 2019 GMATGuruNY posted a reply to Ashley and Vinnie work on a sales staff with 8 other in the Problem Solving forum “From the 10 people, 5 will be selected. Thus, P(Ashley is selected) = 5/10. From the 9 remaining people, 4 will be selected. Thus, P(Vinnie is selected) = 4/9. To combine these probabilities, we multiply: 5/10 * 4/9 = 2/9. The correct answer is C. Similar problem: ...” March 14, 2019 GMATGuruNY posted a reply to A cosmetics company would like to market a six-item gift in the Problem Solving forum “From 10 items, the number of ways to choose a bundle of 6 = 10C6 = (10*9*8*7*6*5)/(6*5*4*3*2*1) = 210. Subtracting the 49 bundles already eliminated from consideration, we get: 210-49 = 161. The correct answer is B.” March 13, 2019 GMATGuruNY posted a reply to Set M is composed of the positive even integers up to 100. in the Problem Solving forum “For any EVENLY SPACED SET: Count = (biggest - smallest)/(increment) + 1. Average = (biggest + smallest)/2. Sum = (count)(average). The INCREMENT is the difference between successive values. Even integers between 2 and 100, inclusive: Here, the integers are EVEN, so the increment = 2. Count ...” March 13, 2019 GMATGuruNY posted a reply to A set of 51 different integers has a median of 30 and a in the Problem Solving forum “Range = biggest - smallest Smallest = biggest - range Since the range = 60, we get: Smallest = biggest - 60 To minimize the smallest integer, we must minimize the biggest integer. Since the median of the 51 distinct integers = 30, there must be 25 integers above 30, with the other 25 ...” March 13, 2019 GMATGuruNY posted a reply to What is the sum of the integers from 1 to 999, inclusive? A in the Problem Solving forum “For any set of consecutive integers: Count = biggest - smallest + 1. Average = (biggest + smallest)/2. Sum = (count)(average). In the set above: Count = 999 - 1 + 1 = 999. Average = (999 + 1)/2 = 500. Sum = (999)(500) = (1000-1)(500) = 500000-500 = 499500. The correct answer is B.” March 13, 2019 GMATGuruNY posted a reply to Peter and Tom shared the driving on a certain trip. If Peter in the Problem Solving forum “Let the time for each driver = 1 hour. Let the total distance = 5 miles, implying that Peter''s distance = (2/5)(5) = 2 miles and that Tom''s distance = 5-2 = 3 miles. Since Peter drives 2 miles in 1 hour, Peter''s rate = 2 mph. Since Tom drives 3 miles in 1 hour, Tom''s rate = 3 mph. Thus: ...” March 13, 2019 GMATGuruNY posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum “To form a diagonal, we must choose 2 vertices. But any pair of vertices that forms a side of the polygon cannot serve to form a diagonal. Thus: Number of diagonals = (number of ways to choose 2 vertices) - (number of sides of the polygon) When the prompt includes the phrase which of the ...” March 12, 2019 GMATGuruNY posted a reply to Alice, Bob, Cindy, Darren, Eddie, Fabian sit on six chairs a in the Problem Solving forum “To count circular arrangements: 1. Place someone in the circle 2. Count the number of ways to arrange the REMAINING people Once Alice has been placed in the circle: Number of options for Bob = 1. (Must be in the seat opposite Alice) Number of options for Cindy = 4. (Any of the 4 remaining ...” March 12, 2019 GMATGuruNY posted a reply to If x and y are positive integers, x/y=? in the Data Sufficiency forum “Statement 1: Case 1: x=2 and y=1, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 2/1 = 2. Case 2: x=1 and y=2, with the result that 2^(x+y) * 3^(xy) = 2³3² = 72 In this case, x/y = 1/2 = 1/2. Since x/y can be different values, INSUFFICIENT. Statement 2: Here, x=2 ...” March 12, 2019 GMATGuruNY posted a reply to Roman City in the Critical Reasoning forum “E: mosaic designs with which artisans who lived in various parts of the Roman Empire were familiar. Here, the two blue portions constitute an adjective serving to modify designs. Question: What KIND of designs? Answer: Designs WITH WHICH ARTISANS WERE FAMILIAR. Put another way: Artisans were ...” March 11, 2019 GMATGuruNY posted a reply to Carmen currently works 30 hours per week at her part-time jo in the Data Sufficiency forum “Rate and time have a RECIPROCAL relationship. If the hourly rate DOUBLES, then the same income will be yielded in 1/2 the total time. Statement 1: Actual hourly rate = 225/30 =$7.50, implying that an additional $1.50 per hour will increase the hourly rate to$9. (increased hourly ...”
March 11, 2019
GMATGuruNY posted a reply to schistosomiasis and malaria. in the Critical Reasoning forum
“M --> more than 50% of all disease cases over the past 5 years S --> 40% of all disease cases 5 years ago, 30% of all disease cases now For each answer choice: Try to devise a case that aligns with the information in the passage but CONTRADICTS the answer choice, thus proving that the ...”
March 9, 2019
Ian Stewart posted a reply to A certain game board is in the shape of a non-convex polygon in the Data Sufficiency forum
“Statement 1 is always true, so is useless, while Statement 2 obviously gives you one equation in one unknown, so is sufficient. But test takers don''t need to know anything about ''exterior angles'' for the GMAT, nor what a ''non-convex polygon'' is, not to mention that Statement 2 is problematic ...”
March 9, 2019
GMATGuruNY posted a reply to Verbal Review 18 : Kudzu, an Asian vine in the Sentence Correction forum
“Generally, COMMA + SINCE after a clause serves to express a CAUSAL relationship. An OA in GMATPrep: Prospecting for gold was a relatively easy task, since erosion put gold literally within reach of anybody with a pan. Here, the clause in blue serves to express what CAUSED prospecting to be a ...”
March 9, 2019
GMATGuruNY posted a reply to If p is a positive integer, is 2p + 1 prime? in the Data Sufficiency forum
“Statements combined: Case 1: p=11 --> p is prime, but its units digits is not prime In this case, 2p+1 = 2*11 + 1 = 23. Since 23 is prime, the answer to the question stem is YES. Case 2: p=19 --> p is prime, but its units digit is not prime In this case, 2p+1 = 2*19 + 1 = 39. Since 39 ...”
March 9, 2019
GMATGuruNY posted a reply to If a certain reel of film runs at 5/6 of a frame per second, in the Problem Solving forum
“2580 frames * (1 second)/(5/6 frame per second) * (1 minute)/(60 seconds) = 2580/50 = a little over 50 minutes. The correct answer is B.”
March 9, 2019
GMATGuruNY posted a reply to When positive integer x is divided by positive interger y, in the Problem Solving forum
“When one positive integer is divided by another, we typically represent what is left over as a REMAINDER or as a DECIMAL. There is a relationship between the two representations: Remainder/Divisor = Decimal. When 5 is divided by 2: Remainder representation: 5/2 = 2 R1 Decimal ...”
March 8, 2019
GMATGuruNY posted a reply to The R students in a class agree to contribute equally to buy in the Problem Solving forum
“Let y=$10 and R=10 students, with the result that the original share per student = ($10)/(10 students) = $1. Let x=9, implying that the number of students decreases by 9 to 1. New share per student = ($10)/(1 student) = $10. Increase in share per student = 10-1 =$9. The correct answer must ...”
March 8, 2019
Ian Stewart posted a reply to In the figure shown, point O is the center of the circle and in the Data Sufficiency forum
“This is exactly identical to a GMATPrep question: https://gmatclub.com/forum/in-the-figure-shown-point-o-is-the-center-of-the-semicircle-89662.html”
March 7, 2019
GMATGuruNY posted a reply to Is the average (arithmetic mean) of x, y, and z equal to the in the Data Sufficiency forum
“Statement 1: In other words, y is HALFWAY BETWEEN x and z, implying that x, y and z are EVENLY SPACED. For any evenly spaced set, the average = the median. Thus, the answer to the question stem is YES. SUFFICIENT. Statement 2: x+z = 2y (x+z)/2 = y Implication: y is the average of x and z ...”
March 7, 2019
GMATGuruNY posted a reply to What is the remainder when -12 is divided by -5? in the Problem Solving forum
“This problem is not relevant to the GMAT. On the GMAT, problems involving remainders are constrained to POSITIVE INTEGERS. From the Math Review in the OG: If x and y are positive integers, there exist unique integers q and r, called the quotient and remainder, respectively, such that y = xq + r ...”
March 7, 2019
Ian Stewart posted a reply to At a particular moment, a restaurant has x biscuits and y pa in the Data Sufficiency forum
“It makes no sense to ask a DS question in this way. If y is a "number of patrons" in a real GMAT DS question, then y stands for a single unknown value; it doesn''t stand for a variable. You can''t ask "how many values of y are possible?" in DS, because it''s not clear what ...”
March 7, 2019
Ian Stewart posted a reply to Each of the items in a box is either a ball or a cube and ea in the Problem Solving forum
“The above solution isn''t right. If we have 100 objects, we have 72 cubes. If 54 of these are blue, the rest, or 18, are red. The question asks "What percent of the cubes are red?", and we have 18 red cubes and 72 cubes in total, so the answer is 18/72 = 1/4 = 25%.”
March 6, 2019
Ian Stewart posted a reply to What is the sum of all of the integers in the chart above? in the Problem Solving forum
“In each column, if we list the numbers in increasing order, we get an equally spaced list with a multiple of 100 in the middle. So, for example, the second column contains the numbers: -204, -202, -200, -198, -196 The sum of an equally spaced list is just equal to the average (which, in an ...”
March 6, 2019
Ian Stewart posted a reply to Eight friends go to watch a movie but only 5 tickets were in the Problem Solving forum
“I don''t like the wording of the question, because it''s not altogether clear if order should matter. But that''s the intention, so we have 8 choices for which person goes in the first seat, 7 for the next seat, and so on, and multiplying our choices gives the answer of (8)(7)(6)(5)(4).”
March 6, 2019
Ian Stewart posted a reply to Among the members of the Malmo family, there are three times in the Problem Solving forum
“It''s a pure ratio/percent problem, so we can freely make up a number, and since we''re asked for a percent in the end, I''d just use 100. Then we have: 50 have blue eyes, of whom: 40 have blue eyes and no glasses 10 have blue eyes and glasses We also know that the ratio of ...”
March 5, 2019
Ian Stewart posted a reply to If j and k are positive integers where k > j, what is the in the Data Sufficiency forum
“Statement 1 says, in words, "k is 5 greater than some multiple of of j". If j > 5, then that''s just another way of saying "the remainder is 5 when we divide k by j". But we don''t know if j > 5, using only Statement 1. If j=2, say, then it''s impossible for the remainder ...”
March 5, 2019
GMATGuruNY posted a reply to A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum
“Given that the area and the answer choices are all integers, the triangle is probably a Pythagorean Triple. The only Pythagorean Triple with an area of 30 is 5-12-13. In the given equation, test c=5, with the result that c+7 = 12: x/5 + y/12 - 1 = 0 If x=0, then y=12, implying a y-intercept ...”
March 5, 2019
GMATGuruNY posted a reply to Joey works at a clothing store and receives an employee in the Problem Solving forum
“Since the discount = 10% = 1/10, and the resulting discount price is an integer value, the regular price must be a dollar value that is a multiple of 10. The correct answer is E.”
March 5, 2019
GMATGuruNY posted a reply to When 32 is divided by k, the remainder is k-3. What is the in the Data Sufficiency forum
“Dividing 32 by k leaves a remainder of k-3. In other words, 32 is equal to k-3 more than a multiple of k: 32 = ak + (k-3), where a is a nonnegative integer and k is an integer such that k≥3. Simplifying 32 = ak + (k-3), we get: 35 = ak + k 35 = k(a+1) The resulting equation implies that ...”
March 5, 2019
GMATGuruNY posted a reply to If x and y are positive integers and (x-y)^2+y^2=25, which o in the Problem Solving forum
“Identify two perfect squares that sum to 25: 1, 4, 9, 16... The two values in blue sum to 25. If y=3 and x=7, then (x-y)² = (7-3)² = 16 and y² = 9, with the result that (x-y)² + y² = 25. The correct answer is B.”
March 5, 2019
Ian Stewart posted a reply to In how many ways can 16 different gits be divided among four in the Problem Solving forum
“If you know that in any counting situation, when the order of k things doesn''t matter, you can first pretend order does matter and then divide by k!, then you can just: imagine putting all 16 gifts in a row, which you can do in 16! ways. Give the first four gifts to the oldest child, the next four ...”
March 4, 2019
Ian Stewart posted a reply to When 900 is divided by positive integer d, the remainder is in the Data Sufficiency forum
“Each Statement is clearly insufficient alone, because using only one statement, we know almost nothing about one of the two unknowns in the inequality in the question. Using Statement 1, we know when 900 is divided by d, the remainder is 1. That means that 900 is exactly 1 larger than some ...”
March 3, 2019
Ian Stewart posted a reply to In five football games thus far this season, Barry has run f in the Problem Solving forum
“The wording here is problematic for a few reasons - it needs to mention that yard totals must be integers (that''s not going to be intuitive or obvious to someone who doesn''t follow football), it should say ''yards per game'', and it should certainly not ask what Barry needs to do to "keep his ...”
March 3, 2019
Ian Stewart posted a reply to The positive two-digit integers x and y have the same digits in the Problem Solving forum
“If AB is a two digit number, where A is the tens digit and B the units digit, then the number is equal to 10A + B. Here we are adding AB and BA, which is the same as adding 10A+B and 10B + A. Adding those we get 11A + 11B, which clearly has 11 as a factor.”
March 3, 2019
GMATGuruNY posted a reply to OG Before 1988, insurance companies in California in the Sentence Correction forum
“Generally, COMMA + VERBing serves to modify the nearest preceding action and the agent of this action. Given this rule, I received a PM requesting that I justify the usage of COMMA + needing in the OA: Insurance companies in California were free to charge whatever rates the market would bear, ...”
March 3, 2019
Ian Stewart posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum
“Anyone interested in my GMAT math books or problem sets can contact me at the email address below.”
March 2, 2019
Ian Stewart posted a reply to If y is a positive integer, is y prime? in the Data Sufficiency forum
“This is a near-exact replica of an official question. Statement 1 is clearly not sufficient, because there is an infinite number of primes. I think Statement 2 is supposed to read: 11! - 12 < y < 11! - 2 That''s also not sufficient, because each number in that interval has an obvious ...”
March 2, 2019
GMATGuruNY posted a reply to In a certain school, there are 160 boys and 240 girls. If 15 in the Problem Solving forum
“Left-handed boys = 15% of 160 = 24. Left-handed girls = 25% of 240 = 60. (total left-handed)/(total students) = (24+60)/(160+240) = 84/400 = 21/100 = 21%. The correct answer is C.”
March 2, 2019
Ian Stewart posted a reply to Is the standard deviation of Set A greater than or equal to in the Data Sufficiency forum
“If you multiply all of the values in a set by some constant k, you will multiply the mean, median, range and standard deviation of that set by k. So here, if we multiply everything in set A by 1/4, we will make the standard deviation 1/4 of its previous value. Since standard deviation is always zero ...”
March 2, 2019
GMATGuruNY posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum
“$$(2^{(1-x)})^2$$ = $$2^{2-2x}$$ = $$2^2/2^{2x}$$ = $$4/2^{2x}$$ We need to know the value of $$2^{2x}$$: $$2^{4x}=3,600$$ $$(2^{2x})^2=3,600$$ $$2^{2x}= 60$$ Substituting $$2^{2x}= 60$$ into $$4/2^{2x}$$, we get: 4/60 = 1/15 The correct answer is B.”
March 2, 2019
Ian Stewart posted a reply to Is the area of Circle A greater than the area of Circle B? in the Data Sufficiency forum
“Strange question. The ratio of circumference to diameter for every circle in the universe is π, so Statement 1 tells you nothing. Circle A''s radius is half its own diameter, so if it is also half of B''s diameter, they have the same radius, and thus the same area, so Statement 2 is sufficient ...”
March 2, 2019
Ian Stewart posted a reply to In a certain school, there are 160 boys and 240 girls. If 15 in the Problem Solving forum
“This is a weighted average problem, where 15% and 25% are the averages of each group. We can draw a number line with the three averages: ---15------------A------25--- Since the ratio of boys to girls is 2 to 3, the overall average A will divide the total distance above in a 3 to 2 ratio, so ...”
March 2, 2019
Ian Stewart posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum
“Alternatively: 2^(4x) = 3600 2^(2x) = 60 2^x = √60 So (2^(1-x))^2 = (2 / 2^x)^2 = (2/√60)^2 = 4/60 = 1/15”
March 2, 2019
Ian Stewart posted a reply to If $$2^{4x}=3,600$$, what is the value of $$(2^{(1-x)})^2$$? in the Problem Solving forum
“2^(4x) = 3600, so (2^2)^2x = 3600, and 4^(2x) = 3600. Taking square roots, 4^x = 60. We want to find the value of (2^(1-x))^2 = (2^2)^(1-x) = 4^(1-x) = 4^1 * 4^(-x) Since 4^x = 60, 4^(-x) is equal to 1/60, so 4^1 * 4^(-x) = 4 * (1/60) = 4/60 = 1/15”
March 2, 2019
GMATGuruNY posted a reply to Car B starts at point X and moves clockwise around a circula in the Problem Solving forum
“π ≈ 3. Car B is traveling for more than 10 hours, so answer choices D and E are too small, and A is unlikely. The correct answer is either B or C. Circumference of track = 20π ≈ 60 miles. In 10 hours, distance for B = 2*10 = 20 miles. 60-20 = 40 miles between A and B. A and B now ...”
March 2, 2019
GMATGuruNY posted a reply to Which of following satisfies the inequality (2x-49)(x^2+6x+1 in the Problem Solving forum
“The two factors must have DIFFERENT SIGNS. Each of the answer choices will yield a positive value for x² + 6x + 10. Thus, the correct answer must yield a negative value for 2x-49. Only A is viable: (2*24) - 49 = -1. The correct answer is A.”
March 1, 2019
GMATGuruNY posted a reply to Andrew bought pizzas for his swim team. Pepperoni pizzas in the Problem Solving forum
March 1, 2019
GMATGuruNY posted a reply to The three squares above share vertex A with AF = FE and AE = in the Problem Solving forum
“Let AF=FE=1, with the result that AE=ED=2: https://i.postimg.cc/2qmj2KbL/probability-and-three-squares.png As the figure illustrates: shaded region = 1+1+1 = 3 ABCD = 4*4 = 16 shaded/ABCD = 3/16 The correct answer is D.”
March 1, 2019
GMATGuruNY posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum
“Use the following equation: (machines)(time) / output = (machines)(time) / output In the equation above: Machines and time are INVERSELY PROPORTIONAL. As the number of machines increases, the amount of time required to produce the same output decreases. Machines and output are DIRECTLY ...”
February 28, 2019
GMATGuruNY posted a reply to The restorative power of sleep is graphically approximated b in the Problem Solving forum
“Multiplying the equation by -1, we get: y = x² - 16x - 36 y = (x-18)(x+2) The restorative power -- the value of y -- is equal to 0 when x=18 or x=-2. Since the time cannot be a negative value, only x = 18 hours is viable. The correct answer is E.”
February 28, 2019
GMATGuruNY posted a reply to In June 1989, what was the ratio of the number of sales tran in the Data Sufficiency forum
“What is (June X)/(June Y)? Statement 1: In June 1989, Salesperson X made 50 percent more sales transactions than Salesperson Y did in May 1989. (June X)/(May Y) = 150/100 = 3/2. INSUFFICIENT. Statement 2: In June 1989, Salesperson Y made 25 percent more sales transactions than in May ...”
February 28, 2019
GMATGuruNY posted a reply to How many whole numbers between 100 and 400, inclusive, conta in the Problem Solving forum
“(integers with the digit 2) = (all integers between 100 and 399, inclusive) - (integers without the digit 2) All integers between 100 and 399, inclusive: For any set of consecutive integers, count = biggest - smallest + 1. In this case: count = 399-100+1 = 300 Integers without the digit 2: ...”
February 27, 2019
GMATGuruNY posted a reply to A square playground has the same area as a rectangular in the Problem Solving forum
“We can PLUG IN THE ANSWERS, which represent a side of the square. Since the dimension of the rectangular playground are INTEGER values, the correct answer is probably also an integer. When the correct answer is plugged in, the square and the rectangle will have the same area. D: 50, implying ...”
February 27, 2019
GMATGuruNY posted a reply to Two hoses are pouring water into an empty pool. Hose 1 alone in the Problem Solving forum
“Let the pool = 12 gallons. Since Hose 1 takes 6 hours to fill the 12-gallon pool, the rate for Hose 1 = w/t = 12/6 = 2 gallons per hour. Since Hose 2 takes 4 hours to fill the 12-gallon pool, the rate for Hose 2 = w/t = 12/4 = 3 gallons per hour. Since the combined rate for the two hoses = 2+3 = ...”
February 27, 2019
GMATGuruNY posted a reply to What is the value of a+b? in the Data Sufficiency forum
“Statements combined: Adding the two equations, we get: a² + b²+ 2ab - 2a - 2b = 63 (a+b)² - 2(a+b) = 63 (a+b)(a+b-2) = 63 Let x = a+b. Substituting x=a+b into (a+b)(a+b-2) = 63, we get: (x)(x-2) = 63 x² - 2x - 63 = 0 (x-9)(x+7) = 0 x=9 or x=-7 Since x=a+b, it is possible that ...”
February 26, 2019
GMATGuruNY posted a reply to On a Saturday night, each of the rooms at a certain motel in the Problem Solving forum
“If 10 rooms are rented for $40 instead of$60 -- a decrease of $20 per room -- the total decrease = 10*20 =$200. Since the value in blue constitutes a 25% reduction in the total rent, it must be equal to 1/4 of the total rent: 200 = (1/4)R 800 = R. The correct answer is B.”
February 26, 2019
GMATGuruNY posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum
“How many umbrellas can it afford to sell at the below-cost rate of b dollars per umbrella and still make a 100% profit? If c=1 and r=2 -- implying that the cost per umbrella = $1 and that the retail price per umbrella =$2 -- then 100% profit will be yielded only if ALL of the umbrellas are sold at ...”
February 26, 2019