# andrew.coleman

Ian Stewart posted a reply to Line DB divides Rectangle ABCD into two equal triangles. Is in the Data Sufficiency forum
“Even if we had enough information using both Statements to be sure ABD was a 30-60-90 triangle, we still wouldn''t know if angle ABD was 30 degrees or 60 degrees, so the answer must be E (and we can''t even be sure it''s a 30-60-90, because the side of length 2 might not be the hypotenuse of ABD).”
Yesterday
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.”
July 18, 2019
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 ...”
July 18, 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
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
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
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
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
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 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 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 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
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
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
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
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
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?$$ in the Data Sufficiency forum
“It''s also possible that z is negative, so z can also be equal to -3 or -5. That doesn''t change the answer to the question though. I''d find it useful to rephrase the question by dividing by 300 on both sides: we want to know "is z > 5?"”
July 1, 2019
Ian Stewart posted a reply to Sequence A is defined by the equation An = 3n + 7 in the Data Sufficiency forum
“I wouldn''t solve this problem by generating a formula -- we know exactly what our sequence is. The sequence is 10, 13, 16, 19, etc. Every term is positive, so as you add more and more terms, the sum gets larger and larger. If we know the sum of the first n terms is 275, there can thus only be one ...”
June 29, 2019
Ian Stewart posted a reply to What is the X intercept of non horizontal line m? in the Data Sufficiency forum
“Our line has an equation y = mx + b, where m is the slope, b the y-intercept. To find the x-intercept of a line, we find the value of x when y=0. If we plug in y=0 here, we find 0 = mx + b x = -b/m Statement 1 tells us m = 4b, and if we substitute that for m above, we learn that x = ...”
June 29, 2019
Ian Stewart posted a reply to Data sufficiency in the GMAT Math forum
“If x > 1, then 1/x is between 0 and 1. So 1 + (1/x) will be between 1 and 2, and answers C and E are both possible (for C, x = 7/2, and for E, x = 7). If there''s a typo in D, and instead it''s meant to read "15/11", then D is also possible (x = 11/4). It''s only if the question tells ...”
June 28, 2019
Ian Stewart posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum
“This is not a "series". It is a "sequence". A series is a sum of a sequence, and this question has nothing to do with summing a sequence. It would be understandable for a test taker to be confused by the wording here (I was at first), because test takers aren''t expected to know ...”
June 28, 2019
Ian Stewart posted a reply to Is $$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
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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
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
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
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
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 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$$ is rounded to the nearest ten, in the Data Sufficiency forum “The question is just asking "is the units digit of x greater than 5?" When we divide a positive number by 10, the remainder we get is that number''s units digit, so Statement 1 tells us "the units digit of x is even". It could be 0, 2, 4, 6 or 8, so we can''t answer the ...” May 4, 2019 Ian Stewart posted a reply to Operation F means “take the square root,” operation G me in the Problem Solving forum “If we multiply our positive number x by a negative constant c, then take the square root, we get something undefined. And if we multiply x by 0, then take a reciprocal, we get something undefined. So if we''re supposed to be able to apply these functions in any order, just to get something that ...” May 3, 2019 Ian Stewart posted a reply to In the $$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
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
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
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
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
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
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
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
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
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 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 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 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 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 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 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 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 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 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 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$$. in the Data Sufficiency forum “t_0 = 3 t_1 = 3 + 1 t_2 = 3 + 1 + 2 t_3 = 3 + 1 +2 + 3 t_4 = 3 + 1 + 2 + 3 + 4 and so on, so t_n is just equal to 3 plus the sum of the first n positive integers. The sum of the first n positive integers is just (n)(n+1)/2 (it''s the number of terms, n, times the average term, which, since ...” March 17, 2019 Ian Stewart posted a reply to Two cyclists, A and B, are 145 miles apart on a straight roa in the Problem Solving forum “In the first half hour, A covers 10 miles. So at 2pm, the cyclists are 135 miles apart. Together they will cover this distance in 3 hours, since they meet at 5pm. Since A covers 60 miles in that time, B must cover the rest, or 75 miles, and so B''s speed must be 25 mph.” March 15, 2019 Ian Stewart posted a reply to The number $$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 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 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 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 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 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 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 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 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 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 Ian Stewart posted a reply to Guidance Appreciated: Scored ~100 Points Lower than PT's in the GMAT Strategy forum “There is some variance in GMAT scores, as there is in the scores on any multiple choice test, but that variance is small. If you scored in the 690-710 range on several GMATPrep tests, your level essentially has to be in the 690-710 range right now. It''s very unlikely, though not impossible, ...” August 9, 2017 Ian Stewart posted a reply to Kim and Sue each bought some roses and some in the Data Sufficiency forum “The table is missing from the post above, but it just says that roses cost$1 each, and daisies cost $0.50 each. If Kim and Sue buy the same number of flowers in total, the person who spends more will be the person who bought more of the expensive flowers, so we really want to know: did Kim buy ...” August 9, 2017 Ian Stewart posted a reply to Melting cube! in the Problem Solving forum “A cube has 6 faces, so if the length of one edge of a cube is k, each of the six faces has area k^2, and the total surface area of the cube is 6k^2. So the number ''6'' appears in the solution to this problem for two completely different reasons -- you''ll always multiply by 6 when you calculate ...” August 3, 2017 Ian Stewart posted a reply to An operation Ф is defined by the equation x Ф y in the Problem Solving forum “Ha, I just did a quick mental estimate when I read the question and thought "that''s way bigger than any of the answer choices", but I forgot to divide by the 4! So I thought most of the right hand side must be in the denominator, and interestingly if change the question as I did, flipping ...” August 2, 2017 Ian Stewart posted a reply to An operation Ф is defined by the equation x Ф y in the Problem Solving forum “Great question, but I think there''s a typo with the signs - I think it should read: x Ф y = x²/ ( 4 + xy - y² ) and brackets would probably help to make clear that most of the right hand side is in a denominator. edit: I was mistaken - the question is perfect as is, but I''ll leave this ...” August 2, 2017 Ian Stewart posted a reply to Negatives as odd numbers in the Data Sufficiency forum “Yes, negative numbers can also be odd or even: The odd numbers are: ... -5, -3, -1, 1, 3, 5, .... The even numbers are: ... -4, -2, 0, 2, 4, ... If you''ve learned rules for odd and even numbers (rules like: odd + odd = even), those rules apply to all odd and even numbers, regardless of ...” July 30, 2017 Ian Stewart posted a reply to OG The average score on a test taken by 10 students in the Problem Solving forum “The two groups are equal in size (5 students each), so the overall average score will just be the ordinary average of the scores of each group, because each group is equally important. If x is the average of two things, then 2x is the sum of those two things. So if y is the average we want to find, ...” July 28, 2017 Ian Stewart posted a reply to Jonathan buys c chairs and t tables for his newly set up res in the GMAT Math forum “He saves$10 on each chair, and $12 on each table. So using Statement 1, we know 10c + 12t = 100 Dividing by 2, 5c + 6t = 50 If you have an equation where you are adding or subtracting two integers on one side, and getting some result on the other side, and two of the terms share some ...” July 28, 2017 Ian Stewart posted a reply to If the y-intercept of a line is greater than 2 in the Data Sufficiency forum “The line meets the y-axis above the origin. Using Statement 1, we know (2, 3) is on the line. Here it''s best to draw different diagrams, placing the y-intercept above and below y=3, to see where the x-intercept will be in different cases. If the y-intercept is only very slightly greater than 2, ( ...” July 28, 2017 Ian Stewart posted a reply to Geometry in the GMAT Math forum “If (a, 4) and (a, b+1) are on the same line, and that line isn''t vertical, they must be the same point, because they have the same x-coordinate. So b+1 = 4, and b = 3. We know (4, b) is on the line, so if b = 3, the point (4, 3) is on the line. That means the point must work in the line''s ...” July 25, 2017 Ian Stewart posted a reply to Line Segment in the GMAT Math forum “Yes, you''re supposed to assume that every side of each quadrilateral is of length 4. So each is a rhombus (a parallelogram with four equal sides). Not sure if you wanted a solution, so stop reading now if you want to do the problem on your own, but the angles in each parallelogram must be ...” July 25, 2017 Ian Stewart posted a reply to here are 5 locks and 5 keys and each of the 5 keys matches in the Problem Solving forum “As Matt says, this won''t be relevant to GMAT test takers, so no need to worry about any of this if you''re preparing for the test, but I find it fun to sometimes talk about math problems that are beyond the scope of the test: That is an interesting question, though it does have a fast ...” July 25, 2017 Ian Stewart posted a reply to If u > 0 and v > 0, which is greater in the Data Sufficiency forum “Using Statement 1, if u = 1, then u^v = 1^v = 1 and v^u = v^1 = v So the question "which is greater, u^v or v^u?" becomes "which is greater, 1 or v?" We don''t know if v is greater than 1 (we only know that v > 0) so Statement 1 is not sufficient. But when we use ...” July 25, 2017 Ian Stewart posted a reply to beat this probability Qs in the Problem Solving forum “In an ordinary deck of cards, 1/4 of the cards are hearts. If a magician spreads out a deck of cards on a table, and asks you to pick one, and you pick the second card from the top, I think everyone would agree the probability that card is a heart is 1/4. If instead, the magician picks the top ...” July 23, 2017 Ian Stewart posted a reply to Approach is faulty: Experts please comment in the Problem Solving forum “If you''re asked: "in how many ways can six people be divided into two committees of three, if the order of the two committees does not matter?" (which is not a kind of question I''ve ever seen on the GMAT, incidentally, though I have seen a couple of prep company questions like that) then ...” July 21, 2017 Ian Stewart posted a reply to Approach is faulty: Experts please comment in the Problem Solving forum “Your approach is correct, though you could streamline it a bit by ignoring the second committee, which doesn''t matter here. We have 5C2 ways of picking the other two people on Michael''s committee, and when Anthony is on that committee, we have 4 ways to pick the third person, so the answer is ...” July 21, 2017 Ian Stewart posted a reply to Combination Grouping: Any expert please help in the Problem Solving forum “You have 2 choices for the goalkeeper. Because two of the ten don''t play any other position, you have 8 choices left for the forward. I''d prefer it if the question said so explicitly (see below) but because of the question setup, I''ll assume the order of the two defenders and of the two ...” July 20, 2017 Ian Stewart posted a reply to here are 5 locks and 5 keys and each of the 5 keys matches in the Problem Solving forum “This should be an SC question. They don''t mean "each key matches each lock" (which would mean every key works in any lock you choose). Instead they mean each key matches a different one of the locks. Nor is it clear what a "trial number of attempts" means - is a trial inserting ...” July 20, 2017 Ian Stewart posted a reply to Alice, Bobby, Cindy, Daren and Eddy participate in in the Problem Solving forum “I''m not sure what the phrase "no two or three athletes finish at the same time" is doing in the question - if no two athletes finish at the same time, clearly no three athletes finish at the same time. Anyway, with no restrictions, there are 5! = 120 orders in which they could finish. ...” July 20, 2017 Ian Stewart posted a reply to An army’s recruitment process included n rounds of selecti in the Problem Solving forum “In the first a rounds, we keep 2/5 of applicants; in the next b rounds, we keep 1/2 of applicants, and in the final c rounds we keep 7/10 of applicants. So: (2/5)^a * (1/2)^b * (7/10)^c * 10,000 = 1400 Let''s break these numbers down into primes, get integers on both sides, and cancel what we ...” July 20, 2017 Ian Stewart posted a reply to Which of the following equations has in the Problem Solving forum “That is not correct. If you have this equation: x = (1/3)*y you''re multiplying y by a non-terminating decimal, but you don''t need something to end in zero to get integer solutions; you can have x = 1 and y = 3 for example. The difficulty in C is that we''re multiplying by √5, which is ...” July 19, 2017 Ian Stewart posted a reply to What is the greatest possible number of points in the Problem Solving forum “Same idea as the post above, but using more elementary principles: draw just one circle first. Then draw another - it can intersect the first at 2 points, at most. Then draw a third. It can intersect each of the first two circles at two points, so we can make 4 new intersection points. Similarly the ...” July 19, 2017 Ian Stewart posted a reply to If the square root of p^2 is an integer greater than 1 in the Problem Solving forum “The question doesn''t say that p^2 is an integer greater than 1, which is how I think you''ve interpreted it; it says that the square root of p^2 is an integer greater than 1, which means p is an integer and p^2 is the square of an integer. There is one minor issue with the wording - the ...” July 19, 2017 Ian Stewart posted a reply to If the square root of p^2 is an integer greater than 1 in the Problem Solving forum “You don''t need to know any particular number theory methods to see why a perfect square always has an odd number of divisors. If you look at a number that is not a square first, all of its divisors will be in pairs. Take the number 12, say: 1 * 12 2 * 6 3 * 4 We have six divisors, which ...” July 17, 2017 Ian Stewart posted a reply to # 69 2016 OG problem solving in the Problem Solving forum “N votes were cast in total 40% were by independent voters, so the rest, 60%, were by voters registered with a party. So 60% of N, or 0.6N, votes were cast by voters registered with a party. Ms Robbins received 10% of those votes, so (0.1)*0.6N = 0.06N of those votes. She also received the ...” July 13, 2017 Ian Stewart posted a reply to easy- medium OG 2016 #63 in the Problem Solving forum “f(x) = √x - 10 To find f(t), just replace ''x'' with ''t'' on the right side above: f(t) = √t - 10 We know u = f(t) so u = √t - 10 u + 10 = √t (u + 10)^2 = t” July 13, 2017 Ian Stewart posted a reply to The average of seven numbers in the Problem Solving forum “The first four numbers add to 4(19) = 76. The last four numbers add to 4(24) = 96. If we add those eight numbers, we get 76+96 = 172, but we''re including the middle number twice in that sum. We know if we only include the middle number once, we get 7(20) = 140, because the average of the whole set ...” July 13, 2017 Ian Stewart posted a reply to Question Pack 1 CR Q#1 | Revision in the Critical Reasoning forum “The entire paragraph after "Theatergoer:" is the theatergoer''s argument. You''ve divided that paragraph into two parts, and attributed one part to the theatergoer, and the other part to the author of the CR question. But all of it should be attributed to the theatergoer.” July 11, 2017 Ian Stewart posted a reply to Number Properties question? in the Problem Solving forum “I does not need to be true : just let a = 1, b = 2, c = 3. In fact, I can never be true, because if a < b and a < c, then by adding those two inequalities together, you find that 2a < b + c. For II, we know c > b from the question stem. Subtract a on both sides of that inequality, and ...” July 8, 2017 Ian Stewart posted a reply to Is there an easier way to solve Q 15 diagnostic test OG'16? in the Problem Solving forum “I''d just use quick estimates here - the way I prefer to do this question is: 2*5 = 10 3*7 is roughly 20 11*19 is roughly 10*20 13*17 is roughly 10*20 so the product is roughly 10*20*10*20*10*20 = 8 * 10^6, which is closest to 10^7. I''d never even contemplate doing any precise ...” July 7, 2017 Ian Stewart posted a reply to help in the GMAT Math forum “The squares just take up half the rectangle. There are a few ways to see that. For example, if you divide up the picture into a grid of 8 squares, as I did below, you can see that half of each grid zone is taken up by part of a square, and the other half is taken up by non-square. So the area of ...” July 7, 2017 Ian Stewart posted a reply to Question type confusion in the Critical Reasoning forum “Hey Brent! Hope you''ve been doing well. :) Just drop me a line if you ever want to catch up on Skype.” July 7, 2017 Ian Stewart posted a reply to Question type confusion in the Critical Reasoning forum “This is really a strengthening question. There''s a missing connection between the plan and the goal: plan: "new courses focused on cooking exotic species of fish, alternative grains such as quinoa, and organically produced vegetables." goal: to appeal to students who want "a ...” July 7, 2017 Ian Stewart posted a reply to GMAT Battle Plan in the GMAT Strategy forum “You really can''t rely on prep company tests to give you an accurate estimate of your level. If you can take an official test, you''ll get a clearer idea of how close you are to your goal, and how much time you''ll need to get there. If you were 650+ now, then a six-week timeframe is perfectly ...” August 10, 2015 Ian Stewart posted a reply to High-Level Math Help in the GMAT Math forum “To clear one thing up from a post above - the computer version of the GMAT was calibrated against the paper tests, so the scores are perfectly comparable. GMAT questions are harder now than before (since ACT started developing the test), but you need to get fewer of the questions right to get the ...” August 8, 2015 Ian Stewart posted a reply to Number Line in the Problem Solving forum “Neither statement is sufficient alone, as we''ll see when we combine them. Using both, we know xy < 0, and (xy)(z) < 0, so z must be positive. We also know that x is closer to z than it is to y, and that x and y have opposite signs (because xy < 0). But that still leaves us with possible ...” August 8, 2015 Ian Stewart posted a reply to Planning to take GMAT for first time in the GMAT Strategy forum “I''d be curious to know what you base that on. GMAC''s own research says the opposite: http://www.mba.com/global/the-gmat-blog-hub/the-official-gmat-blog/2013/sep/study-smart-for-your-best-gmat.aspx Notice from the tables that median study time (which is the relevant number if we''re ...” July 7, 2015 Ian Stewart posted a reply to Math Language - 'Factor' in the GMAT Math forum “The phrase "two factors of 10" means "two divisors of 10", so would refer to two numbers in the list: 1, 2, 5, 10. But that phrase is, in some sources, used imprecisely to mean something more like "two factors equal to 10", when the term "factor" is being ...” July 7, 2015 Ian Stewart posted a reply to How many 3s in the Problem Solving forum “You have the right answer - we''d write ''3'' as a units digit exactly 20 times, and as a tens digit exactly 20 times, so we''d write the digit 40 times in total. ''38'' is the answer to a different question: how many whole numbers between 1 and 200 contain the digit ''3''? Because the answer to ...” July 5, 2015 Ian Stewart posted a reply to wine in the Data Sufficiency forum “We can draw a Venn diagram, with one circle for people who like red wine, and one for people who like white wine. If x people like only white wine, the question tells us 3x people like only red wine. So our Venn has the following zones, using ''b'' for the number who like both: like only red: 3x ...” July 3, 2015 Ian Stewart posted a reply to average in the Data Sufficiency forum “We can do the problem algebraically - the question is asking if (w + x + y + z)/4 > y, or in other words if w + x + y + z > 4y. Using Statement 1, we can replace "w+z" in the question with "x+y", so our question becomes: Is w + x + y + z > 4y ? Is x + y + x + y ...” July 3, 2015 Ian Stewart posted a reply to DS in the Data Sufficiency forum “The formula in the question makes this look complicated, but really we''re just making an investment, and applying interest twice (with compounding). There''s no need to even look at the formula. If we know the exact size of the investment, and exactly how much interest we earn in two years, we ...” July 3, 2015 Ian Stewart posted a reply to The number of ways of arranging n students in the Problem Solving forum “If we increase something by 200%, we are multiplying it by 3. There is a conceptual solution here, but it''s more complicated than backsolving, so let''s just test answers. If you have, say, 10 students, 5 boys and 5 girls, there will be two ways to arrange them: BGBGBGBGBG or ...” July 1, 2015 Ian Stewart posted a reply to In the xy coordinate plane, which of the following in the Problem Solving forum “I''d do exactly what Brent did, but maybe it''s useful to see a bit more of the theory here. If we write the equation of any line in the form y = mx + b, then m is the slope of the line, and b is the y-intercept (where the line meets the y-axis). So if we rewrite the equation above in that form, we ...” July 1, 2015 Ian Stewart posted a reply to Data Sufficiency in the Problem Solving forum “This is a GMATPrep question. There are several ways to solve, but if you can label an unknown angle with a letter in a question like this, and then use the basic angles facts to express every other angle in terms of that letter, you''ll be able to answer any similar question, so that''s the approach ...” July 1, 2015 Ian Stewart posted a reply to Selecting door in the Problem Solving forum “It''s not clear what the question means, because the wording is not precise. I''d assume that we can use the same door to enter and leave, and that it matters which door we use to enter, and which we use to leave. Under those assumptions, we have 3 choices for the enter door, and 3 for the exit ...” July 1, 2015 Ian Stewart posted a reply to Explain pls in the Data Sufficiency forum “I do not base my opinions about the scope of the GMAT solely on what is found in the OG, and I do not understand why you''d make that insinuation. I do base those opinions on the 5,000-10,000 official Quant questions I''ve seen. I''ve seen exactly two real questions where a test taker might ...” July 1, 2015 Ian Stewart posted a reply to Algebra in the Data Sufficiency forum “If x=b, then our question becomes: "Does x = 9 - x^2 ? " or rewriting, the question becomes "Does x^2 + x - 9 = 0? " The answer to that question is almost always ''no'' (for example, if x=0, the answer is ''no''). The answer can also be ''yes'', since that quadratic ...” July 1, 2015 Ian Stewart posted a reply to algebra in the Data Sufficiency forum “Statement 2 is not sufficient, because a and b might be, among other possibilities, 2 and 1, or 4 and -1, and ab can have different values. For Statement 1, we have: a = ab - 1 1 = ab - a 1 = a(b-1) So we know that a and b-1 are integers which multiply together to give 1. That can only ...” July 1, 2015 Ian Stewart posted a reply to Geometry in the Data Sufficiency forum “It''s a bit hard to read the diagram, but I assume the length of ZW is given to be 1. Statement 1 is not sufficient, because we have no information about angle b, so about where point Z is, and that information is crucial. If Z and W are very close together, a line of length 1 is very short in ...” July 1, 2015 Ian Stewart posted a reply to time to fill a pool in the Problem Solving forum “Two of the slow outlets would fill the pool in 4.5 hours, and two of the fast outlets would fill the pool in 2.5 hours. Since we have one slow outlet and one fast outlet, the answer must be strictly between 2.5 and 4.5, and D is the only possible answer.” June 26, 2015 Ian Stewart posted a reply to Percent Problem in the Problem Solving forum “When you increase something by 50%, you multiply it by 1.5, or 3/2. So in this question, when we go forward 50 years, the population is multiplied by 3/2. So if instead we want to go back in time 50 years, we''d multiply by 2/3. To go from 810 to 160, we need to multiply by 160/810 = 16/81 = (4/9)^2 ...” June 24, 2015 Ian Stewart posted a reply to RTW (nails) in the Problem Solving forum “I''d normally just solve a problem like this from start to finish, but if you understand what the letters represent here, and know how rates problems work, you can pick the right answer very quickly. A+B together need to do the job in less time than A alone, so x < y. It clearly needs to be ...” June 24, 2015 Ian Stewart posted a reply to weight problem in the Problem Solving forum “Mitch''s solution is obviously fastest, but there is a no-variable solution we can use if the answer choices don''t allow for any trick: if Jake loses 8 pounds, then together they''ll weigh 270 pounds, and if Jake would then weigh twice as much as his sister, the ratio of their weights is 2 to 1, so ...” June 24, 2015 Ian Stewart posted a reply to PS-OG#112 in the Problem Solving forum “''Normal distributions'' are never tested on the GMAT, and test takers should not spend any time studying them. The question in the post above is not about a normal distribution; it just happens to use a number (68%) that we also see when working with normal distributions. The question in the OP is ...” June 22, 2015 Ian Stewart posted a reply to DS in the Data Sufficiency forum “Neither statement is sufficient alone - looking at S2, for example, if one person eats exactly 3 slices, then there are 29 slices left, and 29 people left. So it''s certainly possible that everyone had one slice, but we have no way to know for sure. When we use both statements, we know that 5 ...” June 22, 2015 Ian Stewart posted a reply to GMAT OG, Archaeologist: Researchers excavating a burial site in the Critical Reasoning forum “The argument essentially says: "a cat was buried with a person. Therefore the cat was domesticated." There''s a huge leap in that argument - why does "buried with a person" mean "domesticated"? It''s only a good argument if we know that an animal will be buried ...” June 22, 2015 Ian Stewart posted a reply to 51-60 math in the GMAT Math forum “The highest Quant score you can get is 51. The "0-60" range was used a very long, long time ago, but now the range in Quant and in Verbal is 6-51 only. Your Quant is obviously very strong already, but if you are scoring Q48 on GMATPrep tests with no study, it''s very likely you can ...” June 21, 2015 Ian Stewart posted a reply to CR in the Critical Reasoning forum “Answer A only discusses one point, but the question stem already addresses the other two points. The stem essentially says " X and Y are true, and if X, Y and Z are true, then Q is true." From that, you only need to know if Z is true to determine that Q will be true. Here X, Y and Z ...” June 20, 2015 Ian Stewart posted a reply to Sets in the Data Sufficiency forum “We want to know how many of the 250 students mentioned in the stem are in student government but not in debate (everyone is in at least one of the two groups, so if someone is not in debate, he or she must be in government only). Using Statement 1, we know 80 are not in government, so the rest, ...” June 20, 2015 Ian Stewart posted a reply to Mean,median,SD in the Problem Solving forum “Your understanding is correct, I think, but it''s not clear what the question is asking - is it asking whether the median could change, or whether it must change? Those are very different questions. We know the standard deviation must drop, and the mean must stay the same. The median might stay ...” June 20, 2015 Ian Stewart posted a reply to Word Problem in the Problem Solving forum “I assume those are meant to be fractions, so 3/4 answer no to the first question, and 2/3 of those answer yes to the second question. Then (3/4)Y people answer no to the first question. If 2/3 of these answer yes to the second question, the rest, or 1/3, must answer no. So (1/3)(3/4)Y = (1/4)Y ...” June 19, 2015 Ian Stewart posted a reply to CR in the Critical Reasoning forum “Where is this question from? The answer has to be A, because no other answer is supported at all, but it''s a very strange question, that requires a lot of unfounded assumptions. We know the company''s executives have "abnormally active thyroids", skip breakfast and eat fast food, and do ...” June 19, 2015 Ian Stewart posted a reply to Cat & Owners in the Data Sufficiency forum “I gather we''re meant to assume that cats all have 4 legs, and owners all have 2 legs. Then if we have c cats, and ø owners, Statement 1 tells us that 4c + 2ø = 84 which has a lot of possible positive integer solutions, and Statement 2 tells us that c - ø = 6 which also has a lot of ...” June 19, 2015 Ian Stewart posted a reply to Doubt in the Data Sufficiency forum “If we let c and r be, respectively, the value of the company and rival stock last month, we know they changed as follows: company: c ---> 0.9c rival: r ---> 1.1r The question asks us to find 1.1r/c, or 1.1(r/c), so if we can find r/c, we can answer the question. Statement 1 ...” June 18, 2015 Ian Stewart posted a reply to Explain pls in the Data Sufficiency forum “Just to find a fraction a/b here that works with Statement 2, you need to expand 1/7 to five decimal places, which is not the kind of thing you''d ever need to do on a real GMAT question. So this isn''t a realistic problem, and I wouldn''t worry about it. And one small correction: 1/7 is ...” June 18, 2015 Ian Stewart posted a reply to GMAT Newbie 580GMAT Prep 2 months until the real thing in the GMAT Strategy forum “I agree with the post above that you''re in a good starting position, and you should definitely make a lot of progress with good preparation. Your highest priority now should be to review the basics of math (how to work with fractions and ratios, how to solve simple equations, etc) since that''s a ...” June 18, 2015 Ian Stewart started following yearzack June 17, 2015 Ian Stewart posted a reply to Tough Probability Q in the Problem Solving forum “This is a really tedious question - we want values of x that make x(x+1) divisible by 2^2 * 3^2. Since we''re multiplying consecutive integers, we''re multiplying two numbers with a GCD of 1, so only one of them can possibly be divisible by 3, and we know then that one of x or x+1 is a multiple of ...” June 16, 2015 Ian Stewart posted a reply to DS Geometry in the Data Sufficiency forum “I can count at least three mistakes in that official explanation. Where is it from?” June 16, 2015 Ian Stewart posted a reply to Which one is a better strategy for guessing for verbal? in the GMAT Strategy forum “Improving your overall Verbal pacing would obviously be the best thing to do. If you haven''t already, you should experiment with different strategies, to find which gives you the best balance between speed and accuracy. People are different, and have different skills (read at different speeds, ...” June 16, 2015 Ian Stewart posted a reply to DS Algebra in the Data Sufficiency forum “You can also see why S2 is sufficient using algebra. We can see that when r=s=t=1 we can get a ''yes'' answer to the question. We want to know if it is possible to get a ''no'' answer. That is, we want to know when it will be true that rst > 1. Using S2, we know that st = 2 - r. If we replace ...” June 16, 2015 Ian Stewart posted a reply to A Tough CR Question: Choices seem pretty similar in the Critical Reasoning forum “The argument is essentially: • A has better VO2-max than B after moderate activity • So A will have better VO2-max than B after intensive activity We''re comparing two different situations - moderate activity and intensive activity. We''re assuming the comparison in the first ...” June 15, 2015 Ian Stewart posted a reply to T-1 Month in the GMAT Strategy forum “If you have only one month to test day, I''d not recommend using any tests besides the official ones. Some company tests are decent, but none come all that close to simulating the real thing. The official tests and question pack aren''t expensive, so I''d definitely invest in those if you''ll have ...” June 15, 2015 Ian Stewart posted a reply to Abs Value in the Data Sufficiency forum “Mitch - I think you mean "x < 0" at the end there, and not "x < -2", so you might want to edit your post.” June 14, 2015 Ian Stewart posted a reply to Abs Value 2 in the Data Sufficiency forum “The answer to the question will almost always be yes, but if y can be 0, the answer can be no. So if you let, say, x=2 and y=1, then both statements are true, and the answer to the question is ''yes''. But if you let x=2 and y=0, then both statements are true, and the answer to the question is ...” June 13, 2015 Ian Stewart posted a reply to Abs Value in the Data Sufficiency forum “We can first work out when the answer to the question will be ''yes''. If x^12 - 2x^11 is negative, then x^12 - 2x^11 < 0 We can safely divide by x^10 on both sides without worrying about whether to reverse the inequality, since x^10 cannot be negative (it is an even power of x), so we ...” June 13, 2015 Ian Stewart posted a reply to Budget policy - Weaken Question in the Critical Reasoning forum “We want to identify the "best basis for a criticism of the Central Valley’s budgeting policy as an economically sound budgeting method". So the right answer absolutely needs to give a reason why the policy might not be "economically sound". That''s a vague phrase, more vague ...” June 13, 2015 Ian Stewart posted a reply to Tricky Inference Question. in the Critical Reasoning forum “I agree with you that the "right answer" here is incorrect. We know the company renovated to comply with government regulations. We have no basis to conclude anything at all about the company''s employees -- in fact, we don''t even know the company has any employees. It''s a logical error ...” June 12, 2015 Ian Stewart posted a reply to Gmat Club Math Test in the GMAT Strategy forum “I have an issue with descriptions that make GMAT scoring sound like something other than what it is - that is, descriptions that make it seem that GMAT scoring takes account of factors other than test taker ability. Most of the factors you list simply are not part of the GMAT algorithm. Question ...” June 8, 2015 Ian Stewart posted a reply to What is the number of 7-element subsets of the set in the Problem Solving forum “If you subtract one multiple of 3 from another, you''ll always get a multiple of 3. The sum of the values in the set is 45, which is a multiple of 3. So if we remove two elements which sum to a multiple of 3, we''ll get a 7-element subset which must sum to a multiple of 3. So we really just ...” June 8, 2015 Ian Stewart posted a reply to An automated manufacturing unit employs N experts such in the Problem Solving forum “We may as well assume our lowest salary is 0, our median is 5, and our largest is 10. So our set looks something like this: 0, a, b, c, ..., 5, d, e, f, ... 10 Now if we want to make the mean of this set as large as possible, we want to make every element as large as possible, so that the sum ...” June 8, 2015 Ian Stewart posted a reply to Daily GMAT Math Q - explain in the Problem Solving forum “After we give Bob his$4, we know that he gets 1/3 of what''s left, and Chloe gets 2/3 of what''s left, so Chloe gets twice as much as Bob (not counting Bob''s extra $4). Since Chloe got$32, Bob got $16. We need to add back Bob''s additional$4, so the answer is $20.” June 5, 2015 Ian Stewart posted a reply to Advice on improving from a V42 to a V46? in the GMAT Verbal & Essays forum “There''s a style and logic to the hardest real GMAT Verbal questions that prep company questions do not replicate. I would not advise you use any questions for practice besides official ones. It can be very difficult to improve in Verbal once you''re near the top of the scoring scale, but that ...” June 5, 2015 Ian Stewart posted a reply to Area of non paved area in the Data Sufficiency forum “I disagree with both of you. :) We only need one measurement here, but we do need it. From the diagram, the paving does not extend all the way from the left end of the lawn to the right end. We need to know just how far it extends horizontally. So we need one measurement, but only one. You can ...” June 4, 2015 Ian Stewart posted a reply to First GMAT Exam in July in the GMAT Strategy forum “I''d very rarely advise studying one section and not the other for an extended period of time. It''s too easy to regress in Quant without regular work. I''m not familiar with the study guide you''re using, but if it advises focusing exclusively on Verbal for a long time, I don''t think that''s good ...” June 4, 2015 Ian Stewart posted a reply to Perimeter of rectangle and equilateral triangle. Please help in the Problem Solving forum “Say the equilateral triangle has sides of length x. Its perimeter is 3x. Say the rectangle has dimensions L and W, where W < L. Its perimeter is 2W + 2L. If we''ve assumed W < L, then the rectangle''s perimeter is thus greater than 2W + 2W = 4W. We know that the triangle''s perimeter ...” June 4, 2015 Ian Stewart posted a reply to Data Sufficiency - Standard Deviation problem in the Data Sufficiency forum “Not only does this question test content that can never appear on the GMAT, the question is also just mathematically wrong, as I explained in a post here about five years ago. Ignore this question, and all other questions from the same source about normal distributions. Studying them will be a waste ...” June 4, 2015 Ian Stewart posted a reply to Mistake in GMAT DS videos?! in the Data Sufficiency forum “Let''s first look at a simpler equation more likely to resemble what you''d see on the GMAT: ab = a You cannot just divide by a on both sides here and conclude that b=1, because it might be true that a=0, and you can never divide by 0. If you want to solve this equation by dividing by a, you ...” June 4, 2015 Ian Stewart posted a reply to How much has the GMAT changed since 2011? in the GMAT Strategy forum “The Q and V sections of the test have not changed much, though it might be helpful to note the following: • There is a much bigger supply of official questions for practice. You can now buy two additional GMATPrep tests (in addition to the two free ones), and there''s a large Question Pack you ...” June 1, 2015 Ian Stewart posted a reply to Divisibility Problem in the Data Sufficiency forum “We know PS = QR. This means that PS and QR are exactly the same number. In particular, PS and QR must have exactly the same divisors. We only care about dividing by 5. Statement 2 is clearly not sufficient alone. From Statement 1, we learn that PS is divisible by 5, so QR must be. But we can''t ...” May 30, 2015 Ian Stewart posted a reply to Extremely Confused. in the GMAT Math forum “I don''t want to comment about specific companies, but no company test perfectly replicates the real GMAT. None use the real scoring algorithm, and in some lower quality tests, the style of question is so different from the style of real GMAT questions that the test would barely be measuring GMAT ...” May 30, 2015 Ian Stewart posted a reply to Statistics in the Problem Solving forum “This actually is a real GMAT question, from one of the oldest versions of GMATPrep (though the original wording says "closest to" and not "close to"). It is, however, very different from almost every other standard deviation question I''ve seen. It''s actually unlike almost every ...” May 29, 2015 Ian Stewart posted a reply to Troubling Statistics in the Data Sufficiency forum “The source might say Statement 1 is sufficient, because by ''set'' they might mean the true mathematical definition of ''set'' - in math, a set is a group of distinct things. But if that''s what they mean, there''s really a problem with the question, because real GMAT questions don''t test if you ...” May 29, 2015 Ian Stewart posted a reply to Test in less than a week, expected score? in the GMAT Strategy forum “You should trust your GMATPrep scores more than any other test scores if you want to estimate your level. So as a best guess, your level right now is in the 620-630 range. Assuming you perform to your abilities on test day, and don''t improve between now and then, that would be your expected score. ...” May 29, 2015 Ian Stewart posted a reply to function f(a) in the Data Sufficiency forum “When n is odd, f(n) = 3n - 9, which is an even number. When n is even, f(n) = 2n - 7, which is an odd number. So if we plug in an odd value, we get an even value back, and if we plug in an even value, we get an odd value back. If you notice that the function flips between even and odd, you can ...” May 29, 2015 Ian Stewart posted a reply to low score on second attempt in the GMAT Strategy forum “If you didn''t cancel the 580 score, then it will be on your score report that schools see, at least as long as it''s not from many years ago. Schools see an entire history of your GMAT attempts from the last five years. Schools can have differing policies when test takers have taken the GMAT more ...” May 28, 2015 Ian Stewart posted a reply to Problem solving in the Data Sufficiency forum “If a point is inside the circle, its distance from the circle''s center is less than the radius. The point (-2, 1) is exactly 4 units above the center (-2, -3), so if that point is inside the circle, the radius must be greater than 4. Similarly, if a point is outside a circle, its distance from ...” May 28, 2015 Ian Stewart posted a reply to Area of a triangle in the Problem Solving forum “David - I think you have a couple of typos at the end here, so you might want to edit your post - instead of "32 root3" and "64 root3", I think you meant to write "32 / root3" and "64 / root3".” May 27, 2015 Ian Stewart posted a reply to Area of a triangle in the Problem Solving forum “You can solve even if you don''t know the 30-60-90 ratios. When you draw a height between two equal sides of any isosceles triangle, and in particular in an equilateral triangle, you are always cutting the base exactly in half. So if the length of one side of the equilateral triangle here is x, then ...” May 27, 2015 Ian Stewart posted a reply to Pls explain in the Critical Reasoning forum “This question is testing a logical error known as Survivorship Bias. The writer is discussing hotels built before 1930 that the writer has personally visited, but then draws a conclusion about the quality of workmanship in all hotels built before 1930. But if only the good hotels have survived - if ...” May 26, 2015 Ian Stewart posted a reply to Important Tricks/shortcuts on GMAT Quant in the GMAT Math forum “People use the word ''trick'' to mean a variety of things. Sometimes people mean test-taking ''tricks'' like ''backsolving'' or ''picking numbers''. Sometimes people mean mathematical ''tricks'', like using units digits or divisibility properties to pick a right answer without doing any real ...” May 25, 2015 Ian Stewart posted a reply to Need help in the GMAT Math forum “This is very definitely not a GMAT question - logarithms and trig functions are not part of the GMAT. So GMAT test takers should definitely ignore it. I''m confused looking at the problem, for two reasons - I don''t know why the ''2'' in front of the first log is written as a superscript. I ...” May 25, 2015 Ian Stewart posted a reply to Absolute Values in the Data Sufficiency forum “Statement 2 is sufficient alone. There are two ways to see that - we have 3x - 2 = |x| 3x = |x| + 2 Notice now that |x| + 2 must be a positive number (since we''re adding 2 to something which is zero or greater), so 3x is equal to a positive number, which means x must be positive. If x is ...” May 24, 2015 Ian Stewart posted a reply to x,y are positive integers. Find the number of even factors in the Data Sufficiency forum “Thanks Brent! Hope you''re doing well. :)” May 24, 2015 Ian Stewart posted a reply to x,y are positive integers. Find the number of even factors in the Data Sufficiency forum “If you have a prime factorization, written in the normal way (using exponents), the power on the 2 always tells you the ratio of the number of even factors to the number of odd factors. So for example, if you have this number: 2^5 * 3^4 * 7^3 then because ''5'' is the power on the 2, the ratio ...” May 24, 2015 Ian Stewart posted a reply to Analyzing MGMAT CR Cat in the GMAT Verbal & Essays forum “I would not suggest trying to use a single prep company test to evaluate your level in CR and SC. A lot of company tests provide detailed diagnostic information to test takers, breaking down performance by question type. It''s important to recognize that this kind of information becomes increasingly ...” May 22, 2015 Ian Stewart posted a reply to What to infer from Kaplan /Manhattan /GMATPrep High scores? in the GMAT Strategy forum “You should only be using GMATPrep tests if you want to get a good estimate of your current level. Prep company tests will not give you very accurate estimates for a few reasons, and some of your company test scores don''t make sense. You''d never get a Q51 on the real GMAT with twelve mistakes in ...” May 22, 2015 Ian Stewart posted a reply to Score variation on test day and doing practice exams in the GMAT Strategy forum “That''s not quite true. The ''standard error'' of GMAT scores is about 30 points. If you know statistics terminology, that means your test scores will be normally distributed around your ''true level'' with a standard deviation of 30 points. In concrete terms, if you perform normally on one test, ...” February 27, 2013 Ian Stewart posted a reply to 6 Key Takeaways from the GMAT Test Prep Summit 2013 in the GMAT Strategy forum “I don''t really agree with your take on these things, besides perhaps your comment about the IR section. 2. I certainly think the OG is made up of the best questions that you can find in a book. There are better questions in GMATPrep and GMATFocus (since those questions are more recent, for the ...” February 27, 2013 Ian Stewart posted a reply to Kaplan Percentile Meaning in the GMAT Strategy forum “This is not true. As GMAC''s head of research Lawrence Rudner says: "The GMAC scale scores represent the same ability level over time. Thus, a Quant score of 43 in 2002 represents the exact same level of ability as a Quant score of 43 does in 2011. " You can read the entire article ...” February 21, 2013 Ian Stewart posted a reply to A particular library has 75 books in the Problem Solving forum “I like Anurag''s solution. Another way is as follows: 65% of the number of loaned books were returned. So 65% of the right answer must be an integer, since you can''t return a fraction of a book. So if you multiply the right answer by 65/100 = 13/20, you must get a whole number, and among the answer ...” February 20, 2013 Ian Stewart posted a reply to Number Properties in the Data Sufficiency forum “If k = 2r, then k is even, so the question is just asking if k is an even number. If k is divisible by 26, then k is certainly divisible by 2, so k is even, and Statement 1 is sufficient. If k > 1, and k has no odd divisors besides 1, then the only prime divisor of k must be 2. So using Statement ...” February 19, 2013 Ian Stewart posted a reply to Number Properties in the Data Sufficiency forum “We need information about both j and k, so neither statement is sufficient alone. From Statement 2, we know k = (2^3)(5^3), so k is divisible by exactly two distinct primes, while from Statement 1 we know j is divisible by 2*3*5, so is divisible by at least 3 distinct primes. So the answer is C. ...” February 19, 2013 Ian Stewart posted a reply to Real numbers!!! in the Problem Solving forum “No, that''s not the case. If x = 0, then x^2 is not positive. But as Mitch says, every number on the GMAT is a real number. So if this were a GMAT question, you wouldn''t need any Statements at all to answer this question - the answer must be ''yes'' no matter what the Statements say. Where ...” February 19, 2013 Ian Stewart posted a reply to primes again!!! in the Data Sufficiency forum “Yes, this is really the kind of pedantic discussion (meant in a good way - I like pedantic discussions!) that GMAT instructors might enjoy, but which don''t really matter to test takers. I understand where you''re coming from, but when one possible definition of ''contain'' is ''consist of'', which ...” February 17, 2013 Ian Stewart posted a reply to primes again!!! in the Data Sufficiency forum “This is really an academic discussion, but if I look at the definition of ''contain'' in my Mac dictionary (which is based on the New Oxford American Dictionary), the first two definitions read as follows: contain verb So in the context of this question, the meaning of ''contain'' is ...” February 17, 2013 Ian Stewart posted a reply to primes again!!! in the Data Sufficiency forum “When the question writer can''t be bothered to make clear whether the set must contain more than one element, which is a crucially important issue here, I hardly expect that they are using language so precisely that we need to pay attention to the distinction between ''contains'' and ''consists ...” February 17, 2013 Ian Stewart posted a reply to help in the Data Sufficiency forum “This question makes no logical sense, or at least it doesn''t if the OA is not C. It may be easiest to illustrate why it is nonsensical with a simpler example. If a question reads: An odd integer is an integer k such that k = 2m + 1, where m is an integer. If k and m are integers, is k odd? 1. m ...” February 17, 2013 Ian Stewart posted a reply to primes again!!! in the Data Sufficiency forum “Statement 1 is not sufficient, since the set could be {2, 3}, and the answer is 1/2, or it could be {2, 3, 17}, and the answer is 1/3, among other possibilities. Statement 2 is not sufficient, since the set could be {1, 2, 3}, and the answer is 1/3, or it could be {2, 3, 4}, and the answer is ...” February 17, 2013 Ian Stewart posted a reply to whats is wrong? coordinates in the Data Sufficiency forum “It makes no grammatical or mathematical sense to ask "how many times less" one thing is than another. The question also needs to make clear that the x and y-intercepts of the line are not both at (0,0). So the question is not well-written. I think it means to ask for the ratio between the ...” February 14, 2013 Ian Stewart posted a reply to Salesman probability in the Problem Solving forum “You will never see a GMAT question even remotely like this one, for one thing. For another, there''s no way to answer the question, since the question doesn''t tell you the probability he sells some number of TVs other than 500 or 3000 on Saturday. So the question doesn''t make any sense.” February 14, 2013 Ian Stewart posted a reply to DS question help in the Data Sufficiency forum “In a set, if the largest value is L, and the range is R, then from the definition of the range, the smallest element S is equal to L-R. So here, we want to know if g-r > h - s, or rewriting this, if g+s > h + r. Neither statement is sufficient alone, but if you line up the two inequalities ...” February 13, 2013 Ian Stewart posted a reply to How to calculate score in the GMAT Strategy forum “The GMAT is an adaptive test, and it is not scored like any test you''ve taken before. The number of questions you answer correctly does not have very much to do with your score. What matters is the difficulty level of the questions you can answer, and the difficulty level of the questions you ...” February 13, 2013 Ian Stewart posted a reply to Divisibility and Primes (MGMAT Practice Set Problem) in the Problem Solving forum “I''ll use simpler numbers for illustration, and then perhaps you can return to the questions above and see if they make more sense. If you''re told that x is divisible by 6, so x is divisible by 2*3, then that means 2 and 3 are some of the primes ''inside'' of x. But there may be others; x might ...” February 13, 2013 Ian Stewart posted a reply to y-intercept of line l? in the Problem Solving forum “If you haven''t memorized formulas for x-intercepts (I haven''t), you don''t need them here. We know that the general equation of a line is y = mx + b, where m is the slope, and b is the y-intercept. We need to find the value of b. Neither statement is sufficient alone. From Statement 2, we know ...” February 11, 2013 Ian Stewart posted a reply to IR section related to Q and V? in the GMAT Strategy forum “No, your IR score is entirely separate from your score out of 800. Nothing you do on the IR section will have any effect on either your score out of 800, or on the questions you see during the Quant or Verbal portions of your test.” February 11, 2013 Ian Stewart posted a reply to PS Question help in the Problem Solving forum “After you pick two balls, the sum is either odd, in which case we need the third ball to be even (1/2 chance), or the sum is even, and we need the third ball to be odd (1/2 chance). So no matter what has happened after the first two selections, there will be a 1/2 chance we pick the ''right'' type ...” February 11, 2013 Ian Stewart posted a reply to Percentage DS in the Data Sufficiency forum “If you increase something by M%, you multiply it by (1 + M/100). So here, the price is multiplied by: (1 + M/100)(1 + N/100) = 1 + M/100 + N/100 + MN/10000 So we need to find the value of this expression. Statement 1 alone isn''t much help. Using Statement 2 alone, if we divide both sides by ...” February 11, 2013 Ian Stewart posted a reply to Nice One : Is x negative? in the Data Sufficiency forum “If 0 < x < 1, then x^3 < x^2 < x. If x > 1, then x < x^2 < x^3. So when x is positive, x^2 is never the largest of the three expressions x, x^2 and x^3. Statement 1 tells us that x^3 is not the largest of the three expressions, and Statement 2 tells us x is not the largest ...” February 11, 2013 Ian Stewart posted a reply to ratio problem in the Problem Solving forum “The conventional way to do these problems is to get a common value in each ratio. We know the ratio of 2nd to 4th graders is 8 to 5, and the ratio of 1st to 2nd graders is 3 to 4. If we multiply this second ratio by 2 to get a ratio of 6 to 8, we will have 8 second graders in each ratio, so we know ...” February 10, 2013 Ian Stewart posted a reply to Prime Number in the Data Sufficiency forum “If you chose E, you chose the right answer. If the source thinks the answer is B, the source is simply wrong. Statement 1 means that x^2 has an odd number of divisors. If you look at a number like 9, say, it has three divisors in total: 1, 3 and 9. So 9 is a number which has an odd number of ...” February 10, 2013 Ian Stewart posted a reply to value of Z in the Problem Solving forum “The answer is ''all of the above''. For example if x=0 and y=1, then z is 60. If x=1 and y=0 then z is 30. If x and y are equal, z is 45. And if you put x and y in a 2 to 1 ratio or a 1 to 2 ratio, you''ll get the other two answers. Not a good question, obviously.” February 10, 2013 Ian Stewart posted a reply to Test in the Problem Solving forum “Or for people who use alligation for weighted average questions (I just explained that method in a different post, so I won''t go over the details again) - we are combining x tests with an 80% average with 1 test with a 90% average, and getting an overall average of 82: ...” February 10, 2013 Ian Stewart posted a reply to Capacity in the Data Sufficiency forum “Statement 1 is clearly not sufficient. Statement 2 desperately needs a copy edit ("the total the water in in the pool"?), but mathematically, we know that 3000 gallons corresponds to 3/8 of what is currently in the pool. So there must be 8000 gallons currently in the pool. Since that''s ...” February 10, 2013 Ian Stewart posted a reply to Help Needed !! in the Data Sufficiency forum “The question asks: Is 10^(-x) < 0.01 ? We can rewrite the question so we have powers of 10 on both sides: Is 10^(-x) < 1/100 ? Is 10^(-x) < 10^(-2) and for the answer to be yes, the power on the left side needs to be smaller than the power on the right side, so our question ...” February 10, 2013 Ian Stewart posted a reply to Value in the Data Sufficiency forum “Statement 1 is not sufficient. Statement 2 tells us that 170 is the greatest common divisor of z and 170 -- in other words, it just tells you that z is divisible by 170. That is not sufficient either. Combined, we know that z is divisible by both 3 and 170. So z must be divisible by the LCM of 3 ...” February 10, 2013 Ian Stewart posted a reply to survery result in the Data Sufficiency forum “You can look at Statement 1 algebraically. If m men and w women were surveyed, we know from the stem that: m + w = 1400 We also know from Statement 1 that 0.36m + 0.5w = (0.42)(1400) So we have two distinct linear equations in two unknowns, and we can certainly solve for m and for w ...” February 10, 2013 Ian Stewart posted a reply to Must be Question in the Problem Solving forum “When you raise a nonzero number to an even power, the result is always positive. When you raise a nonzero number to an odd power, its sign doesn''t change. It doesn''t matter whether the power is positive or negative. So here, in answer choice A, the exponent is even, so the result must be ...” February 9, 2013 Ian Stewart posted a reply to divisible by 3 in the Problem Solving forum “This kind of question is more interesting if we can see the answer choices. It obviously could involve a tedious calculation, so I''d at least glance at the answer choices to see if there are any shortcuts available. If the answers are far apart, we could do a rough estimate: if you add all the ...” February 8, 2013 Ian Stewart posted a reply to D S For Number Properties. in the Data Sufficiency forum “That question makes more sense. :) From Statement 1 we know: 10^x = (4^y)(5^z) (2*5)^x = (2^2)^y (5^z) 2^x * 5^x = 2^(2y) * 5^z and because we have prime bases and the exponents must be integers, the powers on the 2 on either side of the equation must be equal, and the powers on the 5 on ...” February 8, 2013 Ian Stewart posted a reply to Unsure topics of Permutations & Combinations & Funct in the Problem Solving forum “I''ve seen some of the topics you list under Permutations and Combinations tested in real GMAT questions, but they certainly are not important. I''ve seen several thousand official GMAT Quant questions, and I think I''ve seen exactly one which tested circular permutations, for example, so the chance ...” February 8, 2013 Ian Stewart posted a reply to Probability trouble! in the Data Sufficiency forum “In case my post above was unclear, it might be easier to see why it is incorrect to simply multiply those two probabilities by looking at a simpler example, since the dice example is not at all intuitive. Suppose a man who lies 1/2 the time flips a coin, and tells you he got Heads. What''s the ...” February 7, 2013 Ian Stewart posted a reply to Probability trouble! in the Data Sufficiency forum “No, you would multiply 3/4 by 1/6 if you wanted to know the probability that he both rolled a six and told the truth about it. That''s not what the question asks. Here, all we know is that he reports that he rolled a six. He may have done so and told the truth, or he may have rolled, say, a two and ...” February 7, 2013 Ian Stewart posted a reply to D S For Number Properties. in the Data Sufficiency forum “There''s something wrong with the question - where is it from? Either it''s badly designed, or Statement 1 is meant to read something more like: 10^x = (4^z)(5^x). As written, it''s impossible for both statements to be true. From Statement 1 we have: 2^x * 5^x = 2^(2x) * 5^z Our exponents ...” February 7, 2013 Ian Stewart posted a reply to Number Properties in the Data Sufficiency forum “From the stem, we know the prime factorization of k must look like (3^a)(7^b), where a and b are positive integers. Now, to count how many divisors a number has, we add 1 to each exponent in its prime factorization and multiply. So k must have (a+1)(b+1) divisors. Since k has 6 divisors, (a+1)(b+1) ...” February 7, 2013 Ian Stewart posted a reply to Problem in the Data Sufficiency forum “Neither statement is sufficient alone. Together, if there are w women, there are w^2 men, and from Statement 1 we know that w^2 + w = 20. Clearly as w gets bigger, so does w^2 + w, so there can only be one positive integer solution to this equation and the answer is C. It''s a DS question, so ...” February 7, 2013 Ian Stewart posted a reply to Mean, Standard deviation in the Problem Solving forum “There''s no need to solve a two equations/two unknowns problem here; if 58 and 98 are five standard deviations apart, the standard deviation is (98-58)/5 = 8. Thus the mean is 58 + (2)(8) = 74.” February 7, 2013 Ian Stewart posted a reply to Probability trouble! in the Data Sufficiency forum “Under any reasonable interpretation of the question, the answer should be 3/4. The answer is only equal to 3/8 if you make the ridiculous assumption that every time the man lies, he says "I rolled a six" - that is, the answer is only 3/8 if you assume the man will never lie by saying ...” February 7, 2013 Ian Stewart posted a reply to question types on the real test??? in the GMAT Math forum “I''m not sure what the reply you got above means. According to Lawrence Rudner, GMAC''s VP of research and development, "For the Quantitative section, the mix of data sufficiency, problem solving, algebra, geometry, arithmetic function, applied and formula-based questions will always be the ...” October 4, 2012 Ian Stewart posted a reply to Relation between Quant / Verbal scores and GMAT score in the GMAT Strategy forum “According to my records, a Q48/V36 is not always a 700 - it''s at least sometimes a 690 score. It would never be a score as low as 660, though. A Q46/V35 combination is usually around a 660 score, and those scores now correspond to the 73rd and 74th percentiles, so perhaps they aren''t ...” October 3, 2012 Ian Stewart posted a reply to GMAT Prep CR in the Critical Reasoning forum “C is required if the plan is to succeed. The buyers need to be aware of the new low prices to be enticed to buy the computers. If the buyers don''t even know about prices, there''s no reason to think lowering prices will change anything. So if C is true, that gives more reason to think the plan ...” October 2, 2012 Ian Stewart posted a reply to Rule in the Problem Solving forum “I think you might be asking about how we count how many divisors a number has. If you take a number like 375, and want to work out how many positive divisors 375 has, you can first prime factorize: 375 = 3*125 = (3^1)(5^3) Now to find how many positive divisors 375 has in total, we can add 1 ...” October 2, 2012 Ian Stewart posted a reply to Use of charts and tables in PS in the GMAT Math forum “Organization tends to save time, especially in complicated questions. If you have, say, an average speed problem, you have 9 numbers to keep track of (the distance, time and speed for each of the two parts of the trip, along with the total distance, time, and average speed for the two parts ...” October 1, 2012 Ian Stewart posted a reply to GMAT Prep CR in the Critical Reasoning forum “I don''t think that phrase alone lets you pick E, if I''m understanding your question correctly; each answer choice could be interpreted as a "characteristic of the marketplace".” October 1, 2012 Ian Stewart posted a reply to Neuman’s plan to increase its market share is most called in the Critical Reasoning forum “The point is that increasing production (or expanding your business) won''t help you increase market share unless you can increase sales. So E is the right answer; even with more advertising, the company hasn''t managed to increase sales, so there''s no reason to think an expanded business will have ...” October 1, 2012 Ian Stewart posted a reply to GMAT Prep CR in the Critical Reasoning forum “Normally lower prices would increase sales. If the plan is going to fail to increase sales, which is the point of the plan, there has to be some reason buyers won''t buy because of the lower prices. Answer E tells us the reason: buyers get bonuses if they can negotiate discounts. So if the prices ...” October 1, 2012 Ian Stewart posted a reply to Sets in the Data Sufficiency forum “Those grids do work if you know how to use them, but they''re never necessary. I personally really dislike them and would never choose to use them; I''d always use a Venn diagram instead. It''s much easier to tell how many unknowns you have looking at a Venn diagram, and it''s also visually much ...” September 30, 2012 Ian Stewart posted a reply to Rates and work in the Problem Solving forum “If he eats 12 each minute, then he eats 12*60 = 720 each hour, and 24*720 each day. I wouldn''t bother multiplying that out, considering how far apart the answer choices are - a very rough estimate will do just fine here. Now 20*700 is 14,000, and 24*720 won''t be too much bigger than that, so C is ...” September 30, 2012 Ian Stewart posted a reply to Slope in the Data Sufficiency forum “The slope of a line is just a number, so if we are asked to compare the slopes of two lines, we just need to know, numerically, which of the two slope values is greater. So in your example, the line with the slope of 10 would have the greater slope, since 10 is greater than -10. I think you''re ...” September 30, 2012 Ian Stewart posted a reply to Tricky DS Greenville in the Data Sufficiency forum “If you are calculating the "average home sale price", then you are naturally only considering homes that were sold; unsold homes are irrelevant here. Anup''s explanation above was perfect, and the answer should be A.” September 30, 2012 Ian Stewart posted a reply to Probability/ combination in the Problem Solving forum “Or you can just imagine lining 11 people up at random, and choosing the first 7 for the jury. The probability Tamara is in one of the first 7 spots in line is 7/11. If Tamara is in one of those spots, the probability Inga is in one of the 6 remaining spots at the front of the line is then 6/10. ...” September 29, 2012 Ian Stewart posted a reply to Slope in the Data Sufficiency forum “No, Statement 1 is not sufficient here. If, say, the x-intercept of line N is at -6, then the slope of line N is +1. Now, if the x-intercept of line M is at, say, -4, then the slope of line M is +2, which is greater than the slope of line N. But if the x-intercept of line M is at, say, 0, then the ...” September 29, 2012 Ian Stewart posted a reply to Sweet Permutation Problem. in the Problem Solving forum “My answer was the same as Brent''s, but the question is so badly worded, it''s hard to tell what it means. Incidentally, this isn''t the ''style'' of counting question the GMAT asks. I''d suggest you work with material that more closely resembles what you''ll see on the real test.” September 29, 2012 Ian Stewart posted a reply to stats in the Problem Solving forum “Everything I said above is true when your sets contain negative numbers - that actually doesn''t make any difference.” September 29, 2012 Ian Stewart posted a reply to World Time Zone difference and GMAT test taking strategy ... in the GMAT Strategy forum “When you take the GMAT, you are *not* ''competing'' with the people taking the test at the same time as you. You''re ''competing'' with everyone from around the world who has taken the GMAT in the last couple of years. Your time zone makes no difference whatsoever. If a GMAT instructor is ...” September 29, 2012 Ian Stewart posted a reply to no of positive integral solution in the Problem Solving forum “I think, if you''re asked a question like How many different solutions are there to the equation x+y=3 if x and y must be positive integers?, the most natural way to interpret the question is to find all ordered pairs (x, y) where x+y = 3. So I''d consider the answer to be two; x can be either 1 or ...” September 28, 2012 Ian Stewart posted a reply to Ans this pls? in the Critical Reasoning forum “A is not correct, because nothing in the question tells you about how profitable concert promotion is. All we know is that independent promoters offer high priced concerts and get low attendance. But if the ticket price is high enough, these concerts might still be profitable.” September 28, 2012 Ian Stewart posted a reply to stats in the Problem Solving forum “That is so, but that doesn''t mean the range determines the standard deviation. If the only fact you know about a set is that its range is 10, then all you know about the standard deviation is that it is at most 5. For example, the following two lists both have a range of 10: 0, 0, 10, 10 0, ...” September 28, 2012 Ian Stewart posted a reply to Ian...plz rply! in the Lounge forum “:embarrassed: I don''t catch every thread on BTG, unfortunately, but I just saw this, and I''ll go answer your question now. Hopefully better late than never. :)” September 28, 2012 Ian Stewart posted a reply to no of positive integral solution in the Problem Solving forum “There is a way to answer both questions without listing possibilities exhaustively, though it''s well beyond what you''d ever need to do on the GMAT. If you''re preparing for the GMAT, you don''t need to read or understand anything below. But if you''re interested in how to solve these problems: ...” September 28, 2012 Ian Stewart posted a reply to Ratio Problem in the Problem Solving forum “This is not a realistic practice question. It needs to make clear the distance traveled is the same in each direction, it needs to make clear that the speed of the cyclist (ignoring the wind) is the same in each direction, and the phrase "along the wind" does not mean what the question ...” September 28, 2012 Ian Stewart posted a reply to Percentile Discrepancies in the GMAT Strategy forum “It''s certainly true that "not all Q+V combinations are created equal", but it''s not really because of "how many questions you get right". It''s about rounding. The scaled scores that you see on your score report are not the scores the GMAT produces at the end of your test; ...” September 28, 2012 Ian Stewart posted a reply to Importance of the first 5 questions in the GMAT Strategy forum “I just wanted to highlight a couple of other things - I agree with David''s excellent points above: - first, what hurts you most on the GMAT is getting *easy* questions wrong. It really doesn''t matter when in the test those questions appear. It is true that higher level test takers are more ...” September 28, 2012 Ian Stewart posted a reply to GMAT Prep in the Data Sufficiency forum “If 2n = 7m, then 2n and 7m are the same number, so have the same divisors. So 2n is divisible by 7, and thus n is divisible by 7, and 7m is divisible by 2, which means m is divisible by 2. But it''s possible, say, that n=7 and m=2, in which case their GCD is 1, or it could be that n=700 and m=200, ...” September 28, 2012 Ian Stewart posted a reply to Points a & b in the Data Sufficiency forum “The diameter of a circle is the maximum distance between 2 points on the circle. So if the diameter is 20, any two points that are both inside the circle must be less than 20 apart. If Statement 1 is true, it is impossible for both points to be within the circle. If Statement 2 is true, B is not ...” September 27, 2012 Ian Stewart posted a reply to lines r & s in the Data Sufficiency forum “You can see the answer here just by drawing scenarios on a coordinate plane, but in words: Neither statement alone tells you anything about where the lines cross the y-axis. Together, we know they share a point with a negative x coordinate. If the slope of R is greater than the slope of S, ...” September 27, 2012 Ian Stewart posted a reply to (a, b) in the Data Sufficiency forum “I imagine where you wrote "rs 6= 0", you mean "rs is not equal to 0". If we know (-r, s) and (s, -r) are in the same quadrant, then their x-coordinates and y-coordinates have the same sign. So -r and s must have the same sign. Notice that means the points (-r, s) and (s, -r) ...” September 27, 2012 Ian Stewart posted a reply to x-intercept in the Data Sufficiency forum “These questions are a lot easier to answer just by drawing scenarios on the coordinate plane, but since we can''t do that so easily here, I''ll do my best to explain in words. We know (-4, q) is on our line. If, from Statement 1, q is negative, that means that at x = -4, the line is somewhere ...” September 27, 2012 Ian Stewart posted a reply to y-intercept in the Data Sufficiency forum “Lots of lines have an x-intercept at 3/2, so Statement 1 is not sufficient. Perpendicular lines have slopes which are negative reciprocals, so from Statement 2, we know line L has a slope of 1/2. Lots of lines have slopes of 1/2, so Statement 2 is not sufficient. Using both statements, we know ...” September 27, 2012 Ian Stewart posted a reply to Can two statements have two different answers ? in the Data Sufficiency forum “It would make no logical sense to combine the statements if they gave contradictory answers, and since it needs to be possible to look at the statements together, they can''t contradict each other. So no, you can never see a real GMAT question where the two statements are each sufficient alone and ...” September 27, 2012 Ian Stewart posted a reply to Gmat loves factors in the Problem Solving forum “If you have the prime factorization of an even number, and it looks like this: (2^k) * some odd primes then the ratio of the number of even factors to the number of odd factors is k to 1. So if you take a number like: 120 = (2^3)(3)(5) then the ratio of even to odd divisors is 3 to 1, ...” September 25, 2012 Ian Stewart posted a reply to Factor question in the Problem Solving forum “For most numbers, positive factors come in pairs. For example, for 12, we have three pairs of factors which gives us 12 as a product: 1*12 = 12 2*6 = 12 3*4 = 12 Since for most numbers, factors come in pairs, most numbers have an even number of factors. The only exception are perfect ...” September 25, 2012 Ian Stewart posted a reply to prime factors in the Data Sufficiency forum “You should take the question to mean "distinct prime factors", though a real GMAT question would include the word "distinct". If you are asked "how many prime factors does 25 have", the answer is one, not two; 25 has three factors, 1, 5 and 25, and only one of these ...” September 23, 2012 Ian Stewart posted a reply to gmat prep remainder question in the Data Sufficiency forum “Zero *is* divisible by 8. If you divide 0 by 8, you get 0, which is an integer, so by the definition of divisibility, 0 is divisible by 8. In fact, 0 is divisible by every positive integer.” September 23, 2012 Ian Stewart posted a reply to Probability Problem !!! in the Problem Solving forum “There are a few ways to break down the cases here, some a bit faster than what I''ll do below, but you can essentially just enumerate all of the possibilities to get an answer. We have 10 choices for the first card, and 10 for the second, so we have 100 choices in total - that''s our denominator. ...” September 21, 2012 Ian Stewart posted a reply to Probability Problem in the GMAT Math forum “It''s a pure ratio problem, so we can solve it just by picking a number. Imagine you have 101 people. Then 1 person has the disease, and 100 do not. If they all take this test, the test will correctly identify the 1 person who has the disease. For the 100 people who do not, the test will correctly ...” September 21, 2012 Ian Stewart posted a reply to 2 conflicting interpretations/rephasings of a Question? in the GMAT Strategy forum “This isn''t right, because you aren''t taking the square root of (x-5) here. You''re taking the square root of (x-5)^2, and that simply can never be negative. You do, however, know that √(anything) can never produce a negative result. So if √(anything) = 5 - x, then 5 - x must be greater than or ...” September 21, 2012 Ian Stewart posted a reply to sequence A, A1 = 43, A2 = 47,...., Ak = k2 + k + 41 in the Data Sufficiency forum “If k = 41, then k^2 + k + 41 = 41^2 + 41 + 41, which is a sum of multiples of 41, and is thus certainly divisible by 41 (if you factor out the 41, you can see this term is equal to 41*43). So the 41st term of the sequence will certainly not be prime. Thus Statement 2 is sufficient alone. ...” September 20, 2012 Ian Stewart posted a reply to the National Museum in the Problem Solving forum “We''re keeping the same number of artifacts on display as before, so we might as well just assume that all of the stolen artifacts were stolen from storage. We want to keep as many things in storage as possible, so we want the number of stolen artifacts to be as small as possible, and we should ...” September 20, 2012 Ian Stewart posted a reply to prime factors in the Data Sufficiency forum “The question should probably say "distinct prime factors". Using both statements, it could be that k = (2)(3)(5)(7)(11), and p = (2)(3)(5)(7)(13), in which case m would have more than 5 prime factors (it would be divisible by the six primes 2, 3, 5, 7, 11 and 13). Or it could be that ...” September 19, 2012 Ian Stewart posted a reply to Q 26 in the Problem Solving forum “The wording of the question doesn''t make sense. It asks for a probability, but if we''re finding a probability, we have to be selecting something from a clearly defined set. The question doesn''t even mention selecting anything, let alone mention how we''re making the selection. I think it should ...” September 19, 2012 Ian Stewart posted a reply to Proportions- averages in the Problem Solving forum “No, you''re not doing anything wrong. The question makes no sense. With the information given, there is not one unique answer. For example, if the proportion of students in group B is roughly 0, then (using weighted average principles), we find 1/4 of the students are in group C and 3/4 are in ...” September 18, 2012 Ian Stewart posted a reply to Elimination of radicals - Confused¿? in the GMAT Math forum “If you''re given a simple equation like x=y, that means that x and y are exactly the same number. If x and y are the same, then their squares must be the same, so x^2 = y^2 must be true. So in your equation, if √(3b-8) = √(12-b), then √(3b-8) and √(12-b) are the same number, and their ...” September 18, 2012 Ian Stewart posted a reply to OG 13 difficulty level in the GMAT Strategy forum “I agree with what Brent says above - questions which are easy for one test taker may be hard for another. But I think there are other factors at work, and I''d only take the position of questions in the OG as a kind of very rough estimate of their difficulty. I don''t think, for example, that anyone ...” September 17, 2012 Ian Stewart posted a reply to X&Y in the Data Sufficiency forum “It''s one of the harder questions in GMATPrep, so it''s a real GMAT question. It can actually be answered fairly quickly if you recognize where else you''ve seen the expressions in the question. In any right triangle with sides of length a, b and c, where c is the hypotenuse, we know that a^2 + ...” September 17, 2012 Ian Stewart posted a reply to OG 13 ,terminating decimal problem in the Data Sufficiency forum “If r and s are nonzero integers, you can tell if any fraction r/s will produce a terminating decimal by doing the following: 1. reduce your fraction 2. prime factorize the denominator s 3. if s has a prime factor different from 2 or 5, r/s will give you a non-terminating (repeating) decimal. If ...” September 17, 2012 Ian Stewart posted a reply to M/9 in the Data Sufficiency forum “If Statement 1 is true, then m is 4 greater than some multiple of 27, and thus is 4 greater than some multiple of 9, which is just another way of saying that the remainder will be 4 when m is divided by 9. So Statement 1 is sufficient. If Statement 2 is true, then m could be, for example, equal ...” September 17, 2012 Ian Stewart posted a reply to Strategy for 3-4-5 right triangles... (quant guys plz help) in the GMAT Strategy forum “Yeah, that''s definitely not true, though I have seen one GMAT company make that mistake in a prep video, and I wonder if that''s why you''re asking (if so, just ignore the video - the math in it is just wrong). As long as numbers work in the Pythagorean Theorem, they can be the sides of a right ...” September 16, 2012 Ian Stewart posted a reply to scoring 800 in the Ask the Test Maker forum “That table was first posted in this thread: www.beatthegmat.com/conversion-of-q-and-v-raw-scores-into-gmat-score-t67901.html and if you read that thread, the person who made the table concedes that it isn''t reliable for extreme scores. So one shouldn''t draw conclusions from that table about ...” September 9, 2012 Ian Stewart posted a reply to scoring 800 in the Ask the Test Maker forum “machichi, where is that table from? I ask because it does not match up well at all with data I''ve collected from real GMAT score reports. I''m almost entirely sure most of the score combinations that table suggests should give an 800 score will never produce an 800 score on the actual GMAT (I know ...” September 8, 2012 Ian Stewart posted a reply to D10 OG 12 Page 21 Geometry in the Problem Solving forum “There''s a useful GMAT-specific logical principle that can be applied here. Notice that this question has 5 exact numerical answer choices; we don''t have an answer which says ''cannot be determined''. Well, a GMAT question can''t have more than one right answer. So if one of those five answers is ...” September 3, 2012 Ian Stewart posted a reply to A certain league in the Problem Solving forum “That method doesn''t belong to any particular company. :) The first question to ask yourself when counting is whether order matters. If it does, you can just use slots. If it doesn''t, you can''t just use slots - you''ll need to account for the fact that order doesn''t matter somehow. There are ...” September 3, 2012 Ian Stewart posted a reply to DS: Primes #2 in the Data Sufficiency forum “No, that is not right; it really doesn''t matter in this question. Either way, you need to consider all of the integers *between* 11! + 2 and 11! + 12. In your solution, you seem only to have considered the smallest and largest numbers in the range, but you certainly also need to consider all of the ...” September 3, 2012 Ian Stewart posted a reply to Confused or going crazy - Cylinder Tank in the Problem Solving forum “The strange thing is, in OG12, the question is right - it says that the height of the water is 4 feet (which is probably why Anurag said that the question reads that way; it used to). But in OG13 they changed just that one number in the question to ''2'', and now the question is simply wrong. So ...” September 3, 2012 Ian Stewart posted a reply to STD Deviation in the Data Sufficiency forum “You''d never need to know this on the GMAT, but the standard deviation won''t ever be more than half the range. That''s quite easy to prove if you have a symmetric set, and not at all easy to prove if you have an asymmetric set. It''s also not a widely known or reported property of standard ...” September 1, 2012 Ian Stewart posted a reply to stats in the Problem Solving forum “Only in two cases: if the range is 0, then the standard deviation is 0. And if your set has exactly 2 elements, then you can find the standard deviation if you know the range (the standard deviation would be exactly half the range). In all other cases, absolutely not!” September 1, 2012 Ian Stewart posted a reply to diagonals question in the Problem Solving forum “Is there some reason you trust the source of this problem? Where did you find it? The answer is definitely 171, and not 170.” August 30, 2012 Ian Stewart posted a reply to Tricky Square Root Problem - Expert help please in the Problem Solving forum “While the algebraic ingredients that go into solving this question are certainly relevant on the GMAT, you won''t see a question quite like this one on the test. Almost no one would know the math required in advance of seeing this type of problem, and to work out the mathematical basis needed to ...” August 30, 2012 Ian Stewart posted a reply to diagonals question in the Problem Solving forum “The answer is 171, not 170, though I can see why the question designer got the wrong answer. It''s certainly a very difficult question, and I''m not sure my solution will be clear unless you''ve solved simpler versions of this type of problem, but in any case, you won''t need to worry about the ...” August 29, 2012 Ian Stewart posted a reply to very basic doubt in the Problem Solving forum “1/4 isn''t correct because it''s more likely you''ll have, say, 2 boys and 1 girl than it is that you''ll have 3 boys. One (long, but easily manageable in two minutes) way to do the problem is to list all of the possible sequences of boys and girls: BBB BBG BGB GBB BGG GBG GGB GGG There ...” August 29, 2012 Ian Stewart posted a reply to Probability question - Need expert help in the Problem Solving forum “I didn''t notice your ''method 1'' the first time. It''s the numerator that isn''t right; I don''t know how you arrived at "total pairs = 100", but it''s not the right number. The numerator in your ''method 2'' had the right number of pairs in the numerator. Clearly the OA is not ...” August 29, 2012 Ian Stewart posted a reply to Probability question - Need expert help in the Problem Solving forum “What you did looked fine to me. I guess from the wording of the question, it''s unclear to me whether the contestant wins by choosing 2 black marbles. That would make it very, very likely that the contestant would win, and that doesn''t sound much like a Las Vegas game of chance to me. One other way ...” August 29, 2012 Ian Stewart posted a reply to Number between 2/3 and 3/4 in the Problem Solving forum “It might be useful to understand just why this works - it''s something you''ve certainly done many times (but in a slightly different way) before learning it as a ''trick''. If you take the fractions 7/11 and 11/12, then one way to compare them is to get a common denominator. We can use 11*12. Then ...” August 29, 2012 Ian Stewart posted a reply to Basic Dice Probability Question in the Problem Solving forum “In probability (and more generally in counting problems, for the same reasons), we add when we have different cases. So if you were asked "what is the probability when you roll a die once that you get a 1, 2 or 5?" then one (long) way to answer the problem is to break it into cases. We can ...” August 29, 2012 Ian Stewart posted a reply to Average Speed in the Problem Solving forum “I have nothing to add to the solution above, which is perfect, but with those answer choices, you don''t actually need to do any work if you understand weighted averages reasonably well. Average speed is a weighted average, weighted by the time spent at each speed. If you drive equal distances ...” August 29, 2012 Ian Stewart posted a reply to DS- Parallegram, Kites, rhombus, quads etc Q1 in the Data Sufficiency forum “The word rectangle comes from the latin ''rectus'' meaning ''right'', so a rectangle is just any quadrilateral with four right angles. That includes squares - squares are a special type of rectangle in which all the sides are of equal length. So yes, the shape could be a square, but then it is also ...” August 29, 2012 Ian Stewart posted a reply to Relative Rate or Speed in the Problem Solving forum “If they are running towards each other, one at 9 meters/second, the other at 7 meters/second, then in 1 second the first runner runs 9 meters, and the second runner runs 7 meters. If they began 200 meters apart, then in 1 second they have reduced the distance between them by the total distance they ...” August 26, 2012 Ian Stewart posted a reply to Number theory in the Problem Solving forum “You can write integers as fractions if you like. The integer 2 can be written as the "irreducible fraction" 2/1, for example, or as the reducible fraction 6/3. And that''s why answer choice E here doesn''t make any mathematical sense, since no matter what x is, it can be written as a ...” August 24, 2012 Ian Stewart posted a reply to GMAT practice test problem in the Problem Solving forum “This is a tricky example of a maximization/minimization problem, a type of problem that seems to be increasingly common on the GMAT. If you haven''t solved many problems of this type before, it''s worthwhile understanding how to solve a simpler version first. Suppose you are asked: T is a data ...” August 24, 2012 Ian Stewart posted a reply to Is X even in the Data Sufficiency forum “If this were a real GMAT question (it''s clearly not) it would ask "is x an even *integer*" to make it clear that the question is not only asking if x is even, but is also asking whether x need be an integer at all. If you know in advance that x is an integer, the answer is D here. If x ...” August 24, 2012 Ian Stewart posted a reply to Relative Rate or Speed in the Problem Solving forum “I find that a slightly confusing way to think about things, and you can think about this concept differently if you like. It''s on questions where you have two things moving simultaneously where these concepts are relevant, so in a question like the following: Two runners begin running towards ...” August 24, 2012 Ian Stewart posted a reply to military taking physical conditioning test PR bin4 #3 in the Data Sufficiency forum “Finite sets cannot be normally distributed. Just quoting wikipedia, "In probability theory, the normal (or Gaussian) distribution is a continuous probability distribution". Continuous sets must be infinite sets. Finite sets with similar properties to normal distributions are normally ...” August 24, 2012 Ian Stewart posted a reply to military taking physical conditioning test PR bin4 #3 in the Data Sufficiency forum “This is a very bad practice question, and you should simply ignore it. It''s bad for several reasons: * mathematically, a finite set simply can''t be "normally distributed". Only infinite sets can be normally distributed. At best a finite set can be ''approximately normal''. So the ...” August 24, 2012 Ian Stewart posted a reply to Find x in the Data Sufficiency forum “There is no solution, unless some information is missing from the question. x can be anything here between 0 to 150 degrees - the longer you make the top line in the picture, the larger x gets (and the smaller w gets).” August 23, 2012 Ian Stewart posted a reply to Probability that 2nd ball differs by more than 2 in the Problem Solving forum “We are just choosing two different integers from 1 to 10 inclusive, and want to know the probability they aren''t consecutive. There are a few ways to do this, for example - we can choose 2 integers from 10 in 10C2 ways, so in 10*9/2 = 45 ways. That''s our denominator. Now the only pairs of integers ...” August 23, 2012 Ian Stewart posted a reply to vehicles in the Problem Solving forum “While it doesn''t turn out to affect the answer, the denominator here should be 41, and not 42. While there are indeed 42 different years from 1946 to 1987 inclusive, that isn''t quite what we want in our denominator. We want to divide by the number of times the year changed from one to the next in ...” August 23, 2012 Ian Stewart posted a reply to lawn in the Problem Solving forum “The approaches above are perfect, but it''s a pure ratio question, so you can start with a number if you prefer. The best number to work with is some multiple of your denominators, so you can start with 12 here. Then we have the following sequence of changes: 12 ----( -1/3 of 12, so -4)----> 8 ...” August 23, 2012 Ian Stewart posted a reply to Probability: 4 of a kind in the Problem Solving forum “You will *never* be asked this kind of ''poker question'' on the GMAT, though they are very popular in undergraduate combinatorics classes. For one thing, these questions are generally quite a bit too complicated for the GMAT, and for another, they rely too heavily on knowledge that not all test ...” August 22, 2012 Ian Stewart posted a reply to markup in the Problem Solving forum “This is a pure ratio/percent question, so you can feel free to invent a number for something. Markup here is 1/5 of cost, so if the cost is$5, the markup is then $1, and the selling price is$6. So the answer is 1/6 = 16 2/3 %.”
August 22, 2012
Ian Stewart posted a reply to Problem with a question from GMATPrep in the Data Sufficiency forum
“I can count only three official published problems I''ve ever seen (among many thousands) that I find mathematically questionable. There''s one problem that appeared in an older version of GMATPrep which had the wrong answer (they forgot about negative numbers!), one DS problem which can be solved ...”
August 22, 2012
Ian Stewart posted a reply to remainder in the Problem Solving forum
“I agree completely that you should just work with the remainder itself if you want to choose a number in a remainders question - that''s excellent advice. If you know that, say, "the remainder is 5 when k is divided by 23", then k can be 5 (when you divide 5 by 23, the quotient is 0 and ...”
August 21, 2012
Ian Stewart posted a reply to Inequalities ... in the Problem Solving forum
“But the question asked "which of the following must be true". Clearly from your examples, none of the three options absolutely must be true, so the answer is "none of the above". If the question asks "which of the following could be true", then the answer is I, II ...”
August 21, 2012
Ian Stewart posted a reply to face cards - P&C in the Problem Solving forum
“Face cards are J, Q and K only, but that''s not something you would ever need to know for the GMAT. The GMAT would never penalize someone for being unfamiliar with decks of cards.”
August 20, 2012
Ian Stewart posted a reply to exponents in the Data Sufficiency forum
“If k is a positive number, then √k means by definition "the positive square root of k". So √k can never be negative, because of the way the square root symbol is defined. So if you see the expression √16, that cannot be negative, and so certainly must be equal to 4 and nothing ...”
August 20, 2012
Ian Stewart posted a reply to X-Y? in the Data Sufficiency forum
“Adding the inequalities works well here. Or you can notice that Statement 1 guarantees that x - r is positive, and that y - s is negative. Positive numbers are always greater than negative ones, so x - r must be greater than y - s, and we have x - r > y - s x - y > r - s which is what ...”
August 20, 2012
Ian Stewart posted a reply to In a certain colony of cancerous cells in the Problem Solving forum
“The total number of cells doubles every hour, so if k is a positive integer, then after k hours we certainly must have an even number of cells in total, no matter how many cells we begin with. But the wording of the question itself is a bit ambiguous; it asks "how many cells will be ...”
August 20, 2012
Ian Stewart posted a reply to 0<x<1 in the Problem Solving forum
“There are quite a few ways to analyze this type of inequality. Two algebraic solutions: We can rewrite the inequality: x^2 < x. Now, this inequality can''t be true if x is negative, since if x were negative, then x^2 would be positive and would be greater than x. So we know x > 0, and that ...”
August 20, 2012
Ian Stewart posted a reply to adaptive scoring and half of questions wrong at any level? in the GMAT Strategy forum
“I also wanted to reply to at least some of what tutorphd posted above, but nothing below will be of any value to GMAT test takers, so they should feel free to ignore this post! A few points: * first, the GMAT is not a test of pure mathematical ability, and no one claims that it is. The GMAT ...”
July 17, 2012
Ian Stewart posted a reply to adaptive scoring and half of questions wrong at any level? in the GMAT Strategy forum
“To respond to thulsy''s question, the scoring algorithm is based on probabilities. For each question on the test, the algorithm knows the probability that, say, a 500-level test taker will answer correctly, and the probability that a 700-level test taker will answer correctly. A question which is a ...”
July 17, 2012
Ian Stewart posted a reply to adaptive scoring and half of questions wrong at any level? in the Ask the Test Maker forum
“You''re looking at things in the wrong way. If you get most or all of your early questions wrong, you''re answering extremely easy questions incorrectly. So ask yourself this: what is the probability that a 90th percentile test taker would answer six out of eight 300-level math questions ...”
July 11, 2012
Ian Stewart posted a reply to adaptive scoring and half of questions wrong at any level? in the Ask the Test Maker forum
“The math isn''t ''mumbo jumbo''. There are certainly assumptions that form the basis of GMAT scoring, some of which I find questionable, but if you accept them, then from the math you can prove how much information a GMAT-length test gives you about a test taker. That is, you can know statistically ...”
July 11, 2012
Ian Stewart posted a reply to adaptive scoring and half of questions wrong at any level? in the Ask the Test Maker forum
“tutorphd: look up ''Item Response Theory'' on wikipedia. The GMAT is based on what is called the ''3-parameter logistic model''. It''s definitely more complicated, mathematically, than most people would expect. GMAT test takers shouldn''t bother learning anything about it, since it won''t help ...”
July 6, 2012
Ian Stewart posted a reply to MGMAT Data Sufficiency Quesiton in the Data Sufficiency forum
“It''s not quite that straightforward, particularly the part I''ve highlighted. If we change the number ''7'' in the question to ''6'', say (or some other even number), the answer is not C. It genuinely matters here what we''re dividing by, and if you''ve just ignored the fact that we''re dividing by ...”
January 20, 2012
Ian Stewart posted a reply to MGMAT Data Sufficiency Quesiton in the Data Sufficiency forum
“The principles you''re citing are all true, but you aren''t quite using all of the information given here. In general, if the *only* thing you know about A and B is that they are not multiples of 7, then it is true that A+B will sometimes be divisible by 7, and will sometimes not be divisible by 7. ...”
January 18, 2012
Ian Stewart posted a reply to the average in the Data Sufficiency forum
“The wording of this question is terrible. The question asks about the ''newsstand price'', and Statement 2 talks about the ''cover price''. Are these the same? I don''t know how we''re supposed to guess that. I also have no idea what the ''average annual savings'' could mean. What are we supposed to ...”
January 18, 2012
Ian Stewart posted a reply to DS - Inequalities - Strategy help please in the Data Sufficiency forum
“If the question mentions √x, then x clearly cannot be negative. When we combine the two statements, then if x is 0 or 1, clearly x > y from either statement. If x is between 0 and 1, then x^3 is smaller than x, and √x is greater than x. So in this case, combining the two statements, we know ...”
January 18, 2012
Ian Stewart posted a reply to DS Question - need help in the Data Sufficiency forum
“If you know that, say, the remainder is 3 when x is divided by 10, that means that x is 3 more than some multiple of 10. In other words, x - 3 must be divisible by 10. So if the remainder is 1 when 81 is divided by a, that means that 81 is 1 more than some multiple of a, or in other words, 80 is ...”
January 18, 2012
Ian Stewart posted a reply to Data Sufficiency in the Data Sufficiency forum
“Since this is a divisibility question, we should certainly try to get factorizations. The expression y^3 - y can be factored first by factoring out one y, and then by using the difference of squares: y^3 - y = y(y^2 - 1) = (y)(y-1)(y+1) Now (y-1)(y)(y+1) is just the product of three ...”
January 18, 2012
Ian Stewart posted a reply to Properties of perfect squares in the Problem Solving forum
“You certainly need to consider 1 when you count the divisors of a positive integer, so you may have gotten bad information from what you read. Perfect squares have an odd number of divisors. It''s easy to see why this should be true. If you take a non-square, like 18, then all of the divisors are in ...”
January 16, 2012
Ian Stewart posted a reply to Number problem - prime number in the Problem Solving forum
“I frankly don''t understand most of what you''re trying to say, so it''s impossible to respond, but: This is the *only* question. If x and y can be non-prime, then III does not need to be true. Nothing else matters here.”
January 5, 2012
Ian Stewart posted a reply to Number problem - prime number in the Problem Solving forum
“This is completely backwards. The question doesn''t ask if 2x/y must be prime if III is true, which is what you''re answering. It asks if III must be true if 2x/y is prime. I don''t really understand why this question has created such controversy. There''s nothing wrong with the question, and ...”
January 5, 2012
Ian Stewart posted a reply to Remainder with 5 integers in the Data Sufficiency forum
“These principles aren''t quite right. Say you have two numbers, and the remainder is 5 when you divide the first number by 7, and the remainder is 2 when you divide the second number by 7. If you multiply these two numbers, the remainder will not be 5*2 = 10 when you divide the product by 7, since ...”
December 22, 2011
Ian Stewart posted a reply to Data sufficiency, the answer "C" in the Data Sufficiency forum
“Answer C on DS questions reads as follows: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Notice the highlighted part: you *only* consider C (and therefore *only* use both statements together) if neither statement is sufficient alone. So if you discover ...”
December 22, 2011
Ian Stewart posted a reply to A^8 x B ^4 - A^4x B^ 2= 12 in the Data Sufficiency forum
“While you don''t need to here, I''d find it easiest to factor first. We can take out the common factor of a^4 * b^2 from each expression, then use a difference of squares: (a^8)(b^4) - (a^4)(b^2) = 12 (a^4)(b^2) [ (a^4)(b^2) - 1] = 12 (a^2 * b)^2 [ (a^2)(b) + 1 ] [ (a^2)(b) - 1 ] = 12 You ...”
December 18, 2011
Ian Stewart posted a reply to Inequalities: Is pr/qs > r/q? in the Data Sufficiency forum
“We want to know if (p/s)*(r/q) > r/q. That is, we want to know whether the fraction r/q would get bigger if we multiply it by p/s. Even together the statements are not sufficient. From Statement 2 we know that r/q is positive, since r and q have the same sign. Now when we multiply r/q by p/s, ...”
December 18, 2011
Ian Stewart posted a reply to A tough function problem in the Data Sufficiency forum
“If you know exactly how the operation is defined, then you can answer any question about properties of the operation, so each Statement has to be sufficient here; you don''t actually need to do any work. But the question is badly written: it is impossible for x@y to be equal to 1/x - 1/y *and* to be ...”
December 18, 2011