# angxif

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 Stuart Kovinsky posted a reply to Probability in the Problem Solving forum “Many probability questions can be solved intuitively rather than with long calculations. Let''s try to do so with this problem! We can get off to a great start by flipping around the question: what''s the probability that Sally sits beside Andy? We know that it has to go BGBGBGBGB. We can ...” December 31, 2013 Stuart Kovinsky posted a reply to Researchers in the Sentence Correction forum “One more approach! The word "ancient" is a present use word - in other words, something is ancient from today''s perspective. Accordingly, if we''re talking about a present discovery, we don''t say "what appeared to be an ancient hunting ground"; instead, we say "what ...” December 29, 2013 Stuart Kovinsky posted a reply to MGMAT Advanced Quant- Visual Ques. in the Problem Solving forum “Hi Bharat! Let''s start by breaking down the info - there''s actually a lot more there than you may think! Possible scores are the integers 0 to 50, inclusive - that''s 51 possible scores. 100 people take the test. At most, 2 people can get the same score. Let''s assume for a moment that ...” December 29, 2013 Stuart Kovinsky posted a reply to Skeletal Heat in the Critical Reasoning forum “Hi Sid, you''ll find some decent free resources on the net, you just have to be really careful. I''d always look for reviews of the source before diving in and using its questions. For all you know, those free questions were written by some bored guy living in his mom''s basement! Depending ...” December 29, 2013 Stuart Kovinsky posted a reply to Combinatorics: Solution Explanation in the Problem Solving forum “Hi Dbloos! That answer is in fact correct. Here''s another way of looking at it: 2 out of the 14 patients will be chosen to receive P or R. Since the selection is random, each patient has a 2/14 chance of being one of the two. We can confirm this answer with common sense (a very powerful ...” December 28, 2013 Stuart Kovinsky posted a reply to Samuel's Fishing Dilemma in the Critical Reasoning forum “Hi Siddhu, a quick Google search reveals that this is yet another Platinum GMAT question, so it''s not surprising that it''s poorly constructed. The problem here is different - there are 3 valid weakeners among the choices. So, instead of no good answer (like the previous Platinum GMAT ...” December 28, 2013 Stuart Kovinsky posted a reply to E-News Ads in the Critical Reasoning forum “Hi Siddhu! This is another Platinum GMAT question - I''ve only seen 2 and I''m already super-unimpressed. There is no great weakener among the choices. For (C) to be relevant, we have to assume that "partners" means "people visiting one website will be faced with the same ...” December 28, 2013 Stuart Kovinsky posted a reply to Skeletal Heat in the Critical Reasoning forum “Hi Siddhu, please always post your sources. A quick search of the Oracle (i.e. Google) revealed that this a question from Platinum GMAT, of whom I''ve never before heard. This is a horrible question. None of the answers explain the paradox and, while a couple are classic traps, there is no ...” December 28, 2013 Stuart Kovinsky posted a reply to Dice in the Problem Solving forum “Hi Nipun! The problem with treating this like a permutations problem - which is when you''d simply do 6*5*4 - is that we don''t care about order, so you''re counting certain combinations multiple times. For example, the 3 dice could come up as a 5, a 4 and a 3. However, they could also come ...” December 28, 2013 Stuart Kovinsky posted a reply to Quicker + alternate methods in the Problem Solving forum “Hi! No such general formula exists - that pattern comes from an old GMAT question that gave you that summation as a rule to help you answer that one specific question. Whoever put it on a flashcard managed to confuse a whole bunch of people, though (which is why you should be very wary of ...” December 28, 2013 Stuart Kovinsky posted a reply to tenth digit in decimal representation in the Data Sufficiency forum “Hi! I''m assuming that this last part in quotes is your actually comment/question. It''s important to know the place names for the various digits in a numbers, so let''s do a quick review, using the example of: 12345.6789 We start numbering to the left and the right of the decimal place. ...” December 28, 2013 Stuart Kovinsky posted a reply to MGMAT CAT Esteria vs Burdistan in the Critical Reasoning forum “Hi Julls! This argument is a classic example of the most common pattern we see in critical reasoning: causation. In a causal argument, the evidence describes some phenomenon and the conclusion is the author''s explanation for that phenomenon. In every causal argument, the author makes 3 ...” December 28, 2013 Stuart Kovinsky posted a reply to In the month of August, Pentheus Corporation made$200,000 in the Problem Solving forum
“Not to derail a Magoosh post, but this one is actually solvable very quickly without backsolving or a calculator (although I''m generally a huge fan of backsolving!) as long as you know your common percent/fraction/decimal equivalences. First, we need the profit on that day: 1% of $200000 is ...” December 27, 2013 Stuart Kovinsky posted a reply to Lanuguages in the Sentence Correction forum “Hi! I''ve bolded the part of the sentence relevant to your question. Since we have "a language" in the non-underlined part, "within it" is correct. Also, it''s idiomatically correct to say "a dialect within a language", if that''s your main question. You could ...” December 26, 2013 Stuart Kovinsky posted a reply to To find the total amount of water in 3 glasses in the Problem Solving forum “Hi! Uva did a great job saying what you could do next, so I want to discuss what you could have done instead - everyone taking the GMAT should strive to follow the Lazy Test-taker Rule: Do the least amount of work possible to answer each question. On questions that ask you to find a range, ...” December 26, 2013 Stuart Kovinsky posted a reply to Integer Properties in the Data Sufficiency forum “I''m going to almost agree with Vipulgoyal, but say that the answer should be "C", together. Also, I''m assuming that the question was correctly transcribed and the "different" wasn''t omitted from "does m have more than 5 prime factors"? Since the Q stem omits ...” December 24, 2013 Stuart Kovinsky posted a reply to To find the average speed in the Data Sufficiency forum “Hi Sri! You''ve assumed that the car''s speed is constant - which is exactly what the question is designed to trick you into assuming! Remember: on the GMAT we only know what we''re explicitly told. Since we don''t know whether the car is travelling at a constant speed, there''s no way we ...” December 24, 2013 Stuart Kovinsky posted a reply to Rate Problem in the Problem Solving forum “Hi! You haven''t provided any answer choices, so I''m a bit confused - is this a problem solving or a data sufficiency question? You said that the OA is "6", but since we only have variables, how can the answer be an actual number? Your equation for time to catch up is dead on, ...” December 24, 2013 Stuart Kovinsky posted a reply to Combinatorics.Plese help. in the Problem Solving forum “All you''re really doing when you apply the "slot method" to these problem is using the combinations formula: nCk = n!/k!(n-k)! When order does NOT matter, that''s the formula we use. So, if we''re simply choosing 4 out of 7 and we don''t care about order, we get: 7C4 = 7!/4!3! ...” December 23, 2013 Stuart Kovinsky posted a reply to What is the remainder? in the Data Sufficiency forum “Hi Sri! For remainder questions, we often only need to look at the last 1 or 2 digits of the number. In this case, since we''re dividing by 5, only the last digit actually matters. So, we can recognize the pattern for powers of 2: 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = ..6 2^5 = ..2 and so ...” December 23, 2013 Stuart Kovinsky posted a reply to Need help on Percentage Question in the Problem Solving forum “Hi Scraby! First, please always post the answer choices, since they play a large role in many GMAT strategies. On this question, for example, backsolving (working backwards from the choices) is almost certainly the quickest way to get the answer. Let''s approach it via both algebra and ...” December 23, 2013 Stuart Kovinsky posted a reply to Most interns who work for pay hold positions... in the Sentence Correction forum “Hi! This sentence is all about parallelism. When we have a list, we have to make sure that all the parts are stated correctly. When each part of the list has the same modifier, you can just put that modifier at the beginning of the list. However, when different parts require different ...” December 23, 2013 Stuart Kovinsky posted a reply to What is the value of x - y ? in the Data Sufficiency forum “Hi Sri! We know that both x and y are positive and that x is greater than y. We need to find an exact value for (x-y). 1) tells us that root(x) - root(y) = 1 If we square both sides, we get: (rootx - rooty)^2 = 1 x - 2root(xy) - y = 1 well, since have no clue what x and y are, ...” December 23, 2013 Stuart Kovinsky posted a reply to Combinatorics.Plese help. in the Problem Solving forum “When we''re counting we''re always dealing with whole numbers: for example, there are never going to be 3.5 possible groups. So, as soon as you get a fraction, you know there''s a problem. The problem with the using the "slot method" is that you''ve treated 2 different selections as ...” December 23, 2013 Stuart Kovinsky posted a reply to Probabilit in the Problem Solving forum “Hi! This may look like a probability question, but it''s really all about geometry. The question is really asking "what portion of ABCD is shaded?" This question is super quick if you use your graph-lined noteboard to draw the shape to scale - you''ll quickly see that the mini ...” December 22, 2013 Stuart Kovinsky posted a reply to Probability Again in the Problem Solving forum “Hi! This question is a great illustrator of the "one minus" approach to complicated probability problems. When you see "at least" or "at most" in probability, you''re going to be solving for multiple scenarios. However, it''s often quicker to solve for what you do ...” December 22, 2013 Stuart Kovinsky posted a reply to Square Root of Variables in the Problem Solving forum “No worries! It didn''t really affect your question or my response, I was just curious. Stuart” December 22, 2013 Stuart Kovinsky posted a reply to Club members at least 35yrs old in the Data Sufficiency forum “Hi! We only care about at least 35 vs below 35, so "children" are irrelevant. Q: how many members are 35 or older? We think: value question asking us to solve for an actual number, so we need info about numbers! 1) nothing about actual numbers (i.e. just a fraction) - ...” December 22, 2013 Stuart Kovinsky posted a reply to Square Root of Variables in the Problem Solving forum “Hi! First, the problem you posted doesn''t actually include a question, so I''m not sure for what you''re solving. In other words, you posted an equation, but no question. However, I can still answer your question - the official answer you posted and your answer are actually identical. We ...” December 22, 2013 Stuart Kovinsky posted a reply to Bank fees in the Sentence Correction forum “Hi Eric! This sentence is all about proper verb tenses - one of the most commonly tested issues in sentence correction. Remember to always use the non-underlined portion of the sentence (which is, by definition, correct) to guide your selection for the underlined portion. Here, as soon as ...” December 21, 2013 Stuart Kovinsky posted a reply to Auto company profits in the Sentence Correction forum “Hi Eric! Recognizing common GMAT idioms can help you cut to the heart of a SC question and ignore all the "fluff" that the GMAT includes to distract you. There are two important idioms to recognize in this argument. First, we "attribute to". However, since every ...” December 21, 2013 Stuart Kovinsky posted a reply to Mall Occupancy in the Critical Reasoning forum “Hi Lula! Anyone who wants to be a top scorer on the GMAT needs to learn to recognize common patterns. This argument exemplifies one such pattern in critical reasoning. It''s common for authors to identify a problem and then propose a solution. It''s also common for authors to go one step ...” December 21, 2013 Stuart Kovinsky posted a reply to Number Line Data Sufficiency in the Data Sufficiency forum “Hi! In geometry, whenever two points are put together like that, they always describe the line formed by connecting them. The same rule applies to number lines, which are really just a form of linear geometry.” December 21, 2013 Stuart Kovinsky posted a reply to Please can you explain the reasoning behind this? in the Problem Solving forum “Hi! We''re told that x is positive and increasing and we''re asked to determine which of 3 expressions will increase along with x. Here''s something to remember: the GMAT is not trying to be your friend, but it is trying to see how clever you are. So, we''re always using our cleverness to ...” December 20, 2013 Stuart Kovinsky posted a reply to Pls explain the calculation in the Problem Solving forum “Hi! This question is testing your ability to find limits and estimate. We''re told that K is the sum of the reciprocals of the integers 43 through 48, inclusive. In other words: K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48 well, that''s a whole mess of ugly math, so there''s got to be a ...” December 20, 2013 Stuart Kovinsky posted a reply to Data Sufficiency Qs in the Problem Solving forum “Hi! What''s the source of this question? I''m asking because, technically, the 4 brothers could be quadruplets and all the same age. I really doubt that the question intends for that to be a possibility and the GMAT would never leave that ambiguity in place. Let''s assume that the question ...” December 20, 2013 Stuart Kovinsky posted a reply to Pls help with the solution in the Problem Solving forum “Hi! First, I''m not sure if the image I uploaded will work - for some reason the IMG uploader isn''t giving me any love! So, I''ve attached it as a document as well. In any case, let''s break the question down. We''re told that ABC are 3 points in the coordinate plane that do not form a ...” December 20, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “Hey Dan! I''m glad that the question makes sense now. Kaplan''s Premier Guide has a chapter devoted to statistics, which includes perms & combs (and of course those questions show up on our CATs). Whether that''s "enough" to get you through to test day depends on how much work ...” December 18, 2013 Stuart Kovinsky posted a reply to Im not able to undersatnd and visualise this scenario in the Problem Solving forum “Hi! Picking numbers is a great way to approach this question. However, you got a bit lost partway through your solution. Let''s go back a few steps! First, let''s state our task: We need to solve for the % greater Karen runs with gimpy John than with healthy John. In other words, percent ...” December 18, 2013 Stuart Kovinsky posted a reply to Verb Tense, Mood, & Voice - MGMT SC in the Sentence Correction forum “Hi Ian! Great job identifying that this sentence calls for the subjunctive mood. I like that term "bossy verb" - I''m going to steal that and pretend I made it up! Here''s the bare syntax for using the subjunctive: [subject 1] [bossy/question verb] that [subject 2] [infinitive ...” December 18, 2013 Stuart Kovinsky posted a reply to Median question in the Data Sufficiency forum “Hi! Here''s a thread that discusses this problem in detail: [url]http://www.beatthegmat.com/median-question-t8140.html[/url] If you still have questions about it, ask away! Stuart” December 18, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “No - the question is written in such a way that those 2 people are fixed (even if they''re not named). For the purposes of our calculation, it doesn''t matter which 2 people don''t get along. Now I feel like you''re arguing just for the sake of arguing! :D” December 17, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “Here''s the key difference: there''s only one way to choose the 2 consultants who can''t be together. There are multiple ways to choose the 8 male members of the jury. Technically, when calculating the number of disqualified teams of consultants, we''re calculating: 2C2 * 5C2 = 1*10 = 10 ...” December 17, 2013 Stuart Kovinsky posted a reply to 1000CR Test 4 Q14 in the Critical Reasoning forum “Hi Aditya! The opponents argue that people should be free to decide whether to wear seatbelts based on the rule that "you can do what you want as long as you don''t harm OTHERS". (e) doesn''t weaken because the non-seatbelt wearers are only harming themselves - something the ...” December 17, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “In this part of the solution, you''re ONLY looking at the unacceptable teams. In other words, you''re counting how many teams are disqualified due to inclusion of the 2 arch-enemies. Since we only care about disqualifying teams including the 2 troublemakers, we automatically include both of them ...” December 17, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “Your final solution for that problem was 2*3*25. So, in that problem you multiplied by 2 (possible choices for PM) and 3 (possible choices for TL) - you didn''t ignore those parts of the puzzle at all.” December 17, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “Speaking specifically to your solution, the problem in each case is when you begin with: There are 10 males total, so there are 10C8 ways to select those 8 males. You need to factor all those possibilities into your solution as well. (10C8 = 10*9/2*1 = 45) In the second case, you have to ...” December 17, 2013 Stuart Kovinsky posted a reply to 650level Combinatorics problem.Please help in the Problem Solving forum “Hi! Here''s another thread on this question in which I looked at a both algebra and strategic guessing. [url]http://www.beatthegmat.com/i-suck-at-probability-need-desperate-help-t8927.html[/url] Stuart” December 17, 2013 Stuart Kovinsky posted a reply to Functions f(x) in the Problem Solving forum “Hi! The most effective (and sometimes only) way to approach Two-part Analysis questions in IR is backsolving: using the choices to generate the matching pair of answers. There''s an infinite number of solutions for the problem, which is why you can''t "front-solve" them. Instead of ...” December 17, 2013 Stuart Kovinsky posted a reply to interesting CR in the Critical Reasoning forum “Hi again! One thing that it''s very important to remember: we accept the evidence as true. It''s not our job to discredit the evidence itself, but rather how the author uses that evidence. The vulnerable part of every argument is always the author''s assumptions: the missing but necessary ...” December 17, 2013 Stuart Kovinsky posted a reply to interesting CR in the Critical Reasoning forum “The GMAT is written according to patterns; understanding those patterns and how the test works gives you a huge advantage over your competitors. Here, we''re asked to weaken the argument. So, we need to break it down and determine what the author is assuming, then look for an answer that attacks ...” December 16, 2013 Stuart Kovinsky posted a reply to weighted averages in the Problem Solving forum “A mixture of 20 grams of lean ground beef is mixed with 50 grams of fatty ground beef to create a ground beef mix with 8% fat. How many grams of fat does the lean ground beef have? The ratio of fat content for L:F is 2:5. So, as GGNY (does he have a real name - does anyone know it?) aptly ...” December 16, 2013 Stuart Kovinsky posted a reply to Equilateral triangle inscribed in a circle in the Problem Solving forum “Hi! There''s an excellent chance that on test day you''ll see a question that involves the circle sector formula - that''s exactly what we have here. Here''s the formula: length of arc/circumference = angle of arc/360 = area of sector/area of circle In other words, every aspect of the ...” December 16, 2013 Stuart Kovinsky posted a reply to x divisible by 6? in the Data Sufficiency forum “Hi there! Not much to dissect for the q stem: we can rephrase it as "is x a multiple of 6?" No info provided, so we know nothing! (1) (x+3) is a multiple of 3, which means that x is also a multiple of 3. if x=3, then x is NOT divisible by 6. if x=6, then x IS divisible by 6. ...” December 16, 2013 Stuart Kovinsky posted a reply to line k in xy-plane in the Data Sufficiency forum “Hi there! We know that line K passes through the origin, so it must pass through exactly 2 of the 4 quadrants (ab isn''t 0, so we know that line K isn''t just one of the axes). Q: is b positive? We need info about which quadrant point a,b is in. (1) the slope is negative. If the slope ...” December 16, 2013 Stuart Kovinsky posted a reply to Square inscribed within a circle in the Data Sufficiency forum “Hi! 1. yes, they do (the diagonals of non-square rectangles also bisect each other, but not at right angles). 2. yes! The 4 angles have to add to 360 and they''re equal, so each one is 90 degrees. And, in case anyone is wondering, each statement is sufficient since each one proves that ...” December 16, 2013 Stuart Kovinsky posted a reply to Pigs or cows in the Data Sufficiency forum “Quick note: as written, (1) is both sufficient and impossible. Brent corrected the statement in his explanation. (I say (1) is impossible because it would require the farm to have (2/3)(40) = 26 2/3 cows, which is both messy and illegal in some states.)” December 16, 2013 Stuart Kovinsky posted a reply to discounted airline tickets in the Critical Reasoning forum “Hi! What''s the source of this question? The author definitely isn''t assuming (b), so if that''s the accredited answer, it''s just a bad question. The author is, on the other hand, assuming (a) - so your first instinct is correct! Breaking down the stimulus: Old plan had cheap prices ...” December 14, 2013 Stuart Kovinsky posted a reply to weighted averages in the Problem Solving forum “Sure - based on the original question, both the lean and the fatty could be 8% (or many many other combinations) and generate a different # of grams of fat. You have 2 unknowns but only 1 equation, so there''s an infinite number of solutions. Stuart” December 14, 2013 Stuart Kovinsky posted a reply to weighted averages in the Problem Solving forum “Hi! Did you omit something from the Q? Unless we know the % fat in the "fatty" ground beef, we can''t answer the Q.” December 13, 2013 Stuart Kovinsky posted a reply to proportion of women in the Critical Reasoning forum “Hi! When asked to find the answer that would most help you evaluate the argument, look for the gap - in other words, the author''s assumption. The correct answer will be directly relevant to determining whether the assumption is valid. Here, we have a classic scope shift. The author is ...” December 11, 2013 Stuart Kovinsky posted a reply to Source : GMAT PREP :New Q for old stimuli. in the Critical Reasoning forum “Certain patterns recur regularly in CR - possibly the most common argument form is causation. We can paraphrase this entire argument as "the increase in price is responsible for the decrease in sales". The most common ways to strengthen a causal argument are: 1) eliminate ...” December 11, 2013 Stuart Kovinsky posted a reply to Pls explain with a diagram-what is diametrically Opposite in the Problem Solving forum “Hi! This seems like a somewhat insanely complicated question! However, our old friend backsolving will save us from having to do crazy math. First, "diametrically opposed" means, literally, "at opposite ends of a diameter of the circle". In other words, they''re directly ...” December 11, 2013 Stuart Kovinsky posted a reply to Combinations 600 level problem..Please help in the Problem Solving forum “Hi Dan! You''re right, this question is as much about logic as it is about math. We can paraphrase the question (a great thing to do with long word problems) as: Now let''s apply some logic: x will always be either somewhere ahead of y or somewhere behind y. Is there a reason why he ...” December 10, 2013 Stuart Kovinsky posted a reply to Is 2^x greater than 100? in the Data Sufficiency forum “Hi! We have a yes/no question, so if we can get a definite YES or a definite NO, we have sufficiency. If we get a maybe/sometimes/depends, we have insufficiency. Looking at the stem, we think "we need to know about x". (1) gives us an equation to solve for x. If we can solve for ...” December 10, 2013 Stuart Kovinsky posted a reply to Female employes in X in the Data Sufficiency forum “Hi! Without any doubt, the most powerful concept for data sufficiency is "number of equations vs number of unknowns". You can use that rule (and its exceptions) to solve many DS questions without doing much, if any, math. Let''s apply it to this particular question. Step 1 of the ...” December 10, 2013 Stuart Kovinsky posted a reply to How to Buy Kaplan Premier GMAT Test Series in the Ask a Kaplan representative forum “Hi! We devote a lot of resources to "norming" our CATS to be as close to the real GMAT as possible (and we''re constantly updating them as we get new information). While no prep company has access to GMAC''s actual algorithms, I''m confident that Kaplan gets as close as possible. It ...” December 10, 2013 Stuart Kovinsky posted a reply to Usage of whom in the Sentence Correction forum “Hi! A great way to determine whether to use "whom" or "who" is to turn the sentence into a question and answer it with "he" or "him". For example, for (B) we''d ask "by whom were the mountains named?" We''d answer: "they were named by ...” July 16, 2013 Stuart Kovinsky posted a reply to Weighted Average Problem in the Problem Solving forum “Hi there! My first post on the site for a while, but I can''t resist a good PM! As Matt notes, your solution is 100% correct - a really important thing to remember about high level GMAT questions is there''s almost always an "angle" to solving them - and if you find the right one, ...” July 16, 2013 chris@veritasprep posted a reply to While airline travel can be detrimental to your health, ma in the Sentence Correction forum “As I posted earlier, I disagree on your assessment of those constructions (although I do find them unusual - which is exactly why they were chosen to create a difficult problem!). They were all three taken from meticulously edited materials so I am not the only one who disagrees with your ...” May 10, 2013 chris@veritasprep posted a reply to While airline travel can be detrimental to your health, ma in the Sentence Correction forum “I have to respectfully disagree with Ron’s previous post regarding this sentence correction problem. First, I encourage you all to VERY much trust the source of this problem. It is currently in the Veritas question bank as we collect difficulty data and establish statistical validity for ...” May 9, 2013 chris@veritasprep posted a reply to While airline travel can be detrimental to your health, ma in the Sentence Correction forum “You should be very careful on any GMAT sentence correction problem about applying rules that you believe are absolute. Sentence correction is an exercise in problem solving and leveraging differences in answer choices, not a rote regurgitation of memorized rules. In math, 2 + 2 is always 4, but ...” May 8, 2013 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
Stuart Kovinsky posted a reply to Coordinate Geometry in the Data Sufficiency forum
“We didn''t get lucky - the question was designed to reward people who saw the quick solution. Most GMAT math questions are designed with 4 levels of reward: 1) negative reward, for people who spend time on it and get it wrong; 2) 0 reward, for people who recognize that they don''t know how to ...”
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
Stuart Kovinsky posted a reply to applications in the Data Sufficiency forum
“You''re 100% correct about the interpretation, but not about the confusion. We don''t know how deposits and acceptances relate to enrolments, which is why the statements, even combined, are insufficient.”
August 20, 2012
Stuart Kovinsky posted a reply to Coordinate Geometry in the Data Sufficiency forum
“Hi! This question should take about 15 seconds if you actually draw out the x-y plane. There are no bonus points on the GMAT for super-complicated math, so avoid it whenever possible! If you plot the 2 points, you can see that, since they have the same y-coordinate (-3), one point that''s ...”
August 20, 2012
Stuart Kovinsky posted a reply to applications in the Data Sufficiency forum
“I don''t think that the problem with this question is that the language is confusing; rather, neither statement is relevant to the question, so we can very quickly say that the answer is (E). The question asks what % of students who apply actually enrol. Neither (1) nor (2) mentions enrolment, ...”
August 20, 2012
Stuart Kovinsky posted a reply to OG 13 #132 in the Data Sufficiency forum
“Hi! Normally for this type of question we can rely on our old friend, "number of equations vs number of unknowns". However, there are some cases, such as this one, in which you have more info that you originally thought and you don''t actually need as many equations as you may think. ...”
August 19, 2012
Stuart Kovinsky posted a reply to how do i solve this? in the Problem Solving forum
“Great job! Here''s a bit of clarification on solving this type of problem. There are simple rules for multiplying exponents (x^a * x^b = x^(a+b)) and raising exponents to other exponents ((x^a)^b=x^(a*b)), but there''s no simple way to add or subtract exponents. In fact, the only time you ...”
August 19, 2012
Stuart Kovinsky posted a reply to manufacturing in the Problem Solving forum
“Hi! Like many GMAT questions, this one looks much more difficult than it actually is. First, we can simplify by recognizing that the numbers on the right side are wholly irrelevant. The question would have an identical solution if the original equation were: C = rst Since that equation ...”
August 19, 2012
Stuart Kovinsky posted a reply to revolutions in the Problem Solving forum
“Hi! You can solve this doing a lot of math, but any time you have variables in the choices, you can also pick numbers to solve - and picking numbers is often much easier than algebra. Let''s try it a couple of different ways! Before we jump in, let''s make sure we identify exactly what the ...”
August 19, 2012
Stuart Kovinsky posted a reply to cabbage in the Problem Solving forum
“Hi! As always, let''s start by identifying the exact question: what''s the gross profit? Well, gross profit = total revenue - total cost. We''re given the total cost of $600, so we need to find the total revenue. We''re told that 2/3 of the heads were sold for 25% above cost/head. There ...” August 18, 2012 Stuart Kovinsky posted a reply to OG 12 DS #89 in the Data Sufficiency forum “Hi! While you certainly can solve by manipulating equations, you can also solve with common sense and logic - very powerful tools on the GMAT that people often overlook. We should be able to dismiss each statement by itself fairly quickly, since they each give us one relationship that''s not ...” August 18, 2012 Stuart Kovinsky posted a reply to Stats.. relationship among different pieces in the Problem Solving forum “1,3,5,5 is the same as 1,1,3,5 Similarly, 1,5,5,5 is the same as 1,1,1,5 The missing set is 1,1,5,5 On a side note, you will NEVER need to calculate SD on the GMAT (and, accordingly, you don''t need to know the SD formula) - you just might need to know what SD measures (how spread out are ...” August 18, 2012 Stuart Kovinsky posted a reply to median question.. in the Data Sufficiency forum “Hi! We''re told that 25% of projects have 4+ employees and 35% have 2- employees. Since the only number that doesn''t fall into "4 or more" and "2 or fewer" is 3, all of the remaining projects must have exactly 3 employees.” August 18, 2012 Stuart Kovinsky posted a reply to x/y<0? in the Data Sufficiency forum “Hi! While this question illustrates some important concepts, it is 100% NOT a real GMAT question. What''s the source? As TheCEO notes, statement (1) proves that the answer is "no" and statement (2) proves that the answer is "yes". On the GMAT, the two statements will ...” August 18, 2012 Stuart Kovinsky posted a reply to Martin's theory in the Reading Comprehension forum “Hi! Let''s look right at the beginning of the passage: Since the new research indicates that humans arrived "much earlier than 11,000 years ago", it directly attacks Martin''s theory that the arrival (i.e. not just the presence) of humans was responsible for the mass extinctions ...” August 18, 2012 Stuart Kovinsky posted a reply to Two glasses contain milk and water. In the first glass the r in the Problem Solving forum “Just a brief follow up - the problem is that we don''t know how much liquid was in each glass to start - without that info (or at least the relative volumes of the glasses), there''s no way to answer the question. The fact that there are only 4 answer choices should also raise red flags, since a ...” July 23, 2012 Stuart Kovinsky posted a reply to inequalities problem... again in the Problem Solving forum “As usual, Eagleeye provides a great explanation - using the number line is a great way to solve absolute value problems. Another way to solve, especially when you have absolute value expressions on both sides of the equal sign, is to square both sides. Doing so generally leaves you with a ...” July 22, 2012 Stuart Kovinsky posted a reply to Adam Family in the Problem Solving forum “Hi! You can solve this almost instantaneously if you understand what the question is asking. Since each brother is double the weight of the previous brother, the correct answer has to be divisible by 2 many times. The only answer that has lots of factors is 2 is 64... choose E! The ...” July 22, 2012 Stuart Kovinsky posted a reply to Problem Solving - Factorization Question?? in the Problem Solving forum “Hi! This is an old question (and actually quite poorly constructed), but it illustrates a common feature in some GMAT questions, so it''s worth reviewing. First, let''s break down the question: Whenever you see this type of question, always rewrite it as: n x 25 x 62 x 73/(5^2 * 3^3) = ...” July 22, 2012 Stuart Kovinsky posted a reply to Exponents problem in the Problem Solving forum “Let''s look at another approach we can take to the one posted by eagleeye. First, a note of caution: when dealing with inequalities, be very wary of multiplying or dividing both sides by variables. Remember, if those variables turn out to be negative you have to reverse the inequality. ...” July 22, 2012 Stuart Kovinsky posted a reply to Geometry problems: in the Problem Solving forum “Using the vertical angle rule (opposite angles of intersecting lines are equal), we know that: a=d and b=e So, since a and b are complementary, d and e must also be complementary. Further, since a=d, b and d are complementary; similarly, since b=e, a and e are complementary. We know ...” July 22, 2012 Stuart Kovinsky posted a reply to Ratios problem in the Problem Solving forum “Hi! A bit of theory before getting into the calculations. First, when converting between linear, second order and third order equations (i.e. lengths, areas and volumes), you simply apply the proper exponent to find the new ratio. For example, if comparing the areas of two squares with ...” July 22, 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 Stuart Kovinsky posted a reply to "Rounded to the nearest" - What does that term mea in the Problem Solving forum “Hi! "Rounding" means evening things off to the nearest unit mentioned. For example, "rounded to the nearest mile" means that you eliminate all decimal points. "Rounded to the nearest hour means that you ignore minutes and seconds. To properly round off, you can ...” June 17, 2012 Stuart Kovinsky posted a reply to Usage of Has-Experts please help in the Sentence Correction forum “Hello! "None of them have" and "none of them has" are both in common usage. While "none of them has" is technically "more correct", arguments can (and have!) been made for using "have" instead. I can''t recall a GMAT question that required you ...” June 12, 2012 Stuart Kovinsky posted a reply to DS: Finding percents from averages in the Data Sufficiency forum “Hi! Dimochka presents a great mathematical explanation, but let''s focus on efficiency, remembering one key rule: To get the point on a DS question, you don''t need to actually answer the question - you just need to determine whether it''s possible to do so. Keeping this rule in mind will ...” June 8, 2012 Stuart Kovinsky posted a reply to NEW ENTRY PROBLEMS in the Problem Solving forum “Hi! If it''s actually a numeric entry question, then you have to enter the answer on the computer - it''s not multiple choice. Again, these questions do NOT appear on the GMAT.” June 8, 2012 Stuart Kovinsky posted a reply to Integers x and y in the Data Sufficiency forum “Hi! If x+2 and x+4 are between x and y, won''t x+1 and x+3 be between them as well? You''re misinterpreting statement (2) as: when in fact statement (2) simply tells us that there ARE 24 integers between x and y... period. The only way this statement can be be true is if y = x + 25 ...” June 8, 2012 Stuart Kovinsky posted a reply to Primes in the Data Sufficiency forum “Hi! Like a lot of data sufficiency questions, investing a bit of time in the question stem to understand what the question is really about makes working with the statements much simpler. Let''s break down the stem: What kind of positive numbers CANNOT be expressed as the product of two ...” June 8, 2012 Stuart Kovinsky posted a reply to NEW ENTRY PROBLEMS in the Problem Solving forum “Hi! Is this a GRE question? There are no entry questions on the GMAT. The first thing to note is that, on the GRE, you actually have access to a calculator. While you don''t need to use it (in fact it''s often quicker to solve multiple choice questions without a calculator), on the numeric ...” June 8, 2012 Stuart Kovinsky posted a reply to Problem solving - Ratio / Proportion in the Problem Solving forum “Hi! As the other experts noted, this is a really tough math problem - which is why, almost certainly, the best way to approach it is strategically. If you had provided answer choices (please always provide the choices!), we could have backsolved. When you have a very complicated word problem ...” June 8, 2012 Stuart Kovinsky posted a reply to OG 10th edition CR-q174 in the Critical Reasoning forum “Hi, the question stem tells us to draw a conclusion "from the information given above". Two of those pieces of info are: So, we do definitely know that the average age will increase over that time period.” June 6, 2012 Stuart Kovinsky posted a reply to really tough CR.. in the Critical Reasoning forum “Hi! For assumption questions, start by deconstructing the argument: identify the author''s conclusion and summarize the evidence. Conclusion: the ONLY solution is to increase the number of government officials. Evidence: old folk are underrepresented in the government, which sets policy ...” June 5, 2012 Stuart Kovinsky posted a reply to BOLD in the Critical Reasoning forum “Hi! Bolded statement questions can be tricky, mostly because the answers often sound extremely similar. To avoid getting confused, rely on the most powerful tool for both RC and CR: making a prediction. The best way to make a prediction on bolded statement questions is to roadmap the ...” June 5, 2012 Stuart Kovinsky posted a reply to I didn't even understand the question! in the Problem Solving forum “Hi! A terminating decimal is one that ends, i.e. doesn''t infinitely repeat. For example, 1.4, 8, 32.888991 and 27.6 are all terminating decimals. Some fractions can be turned into terminating decimals, some can''t. For example, 1/3 is .33333 (going on forever). 1/5 is .2, which is ...” June 5, 2012 Stuart Kovinsky posted a reply to number of solutions in the Problem Solving forum “Both! 0 is an uncharged (i.e. neither positive nor negative) even integer. As an aside, all integers are rational (but not the other way around).” June 5, 2012 Stuart Kovinsky posted a reply to As part of a game, four people each must secretly in the Problem Solving forum “Here''s another way you can solve: Prob = # desired outcomes/total number of possibilities there are 4*4*4*4 = 256 total possibilities Now on to desired outcomes! The first person can pick any number, so she has 4 possibilities. We want the second to be the same as the first, so she has ...” June 5, 2012 Stuart Kovinsky posted a reply to From new GMATprep Qn - Experts help please in the Problem Solving forum “Hi! There''s a problem with the question - it doesn''t make sense as written (at least if the answer is supposed to be D). You have Betty and William earning more than 50000, but then we never hear about William again. Then the question asks whether Wilma''s annual salary is greater than ...” May 27, 2012 Stuart Kovinsky posted a reply to the long advertisement in the Critical Reasoning forum “Correct!” May 26, 2012 Stuart Kovinsky posted a reply to Inequalities DS in the Data Sufficiency forum “Sure! We want to know if the absolute value of a is greater than the absolute value of b. In other words, is the magnitude of a greater than the magnitude of b? (I.e. is a further from 0 on the number line than is b?) As always, let''s start with the simpler of the two statements (that way if ...” May 26, 2012 Stuart Kovinsky posted a reply to Inequalities DS in the Data Sufficiency forum “Hi! We want to know if the sum of x and y is positive. So, we either need the individual values of x and y or information about the expression "x+y". (1) x - y > 0 We know nothing about x and y individually, so (1) is insufficient. If the concepts don''t jump out at you, ...” May 26, 2012 Stuart Kovinsky posted a reply to Probability problem in the Problem Solving forum “That''s the exact rule! If you just care about which objects to select, then you use the combinations formula. If you care not only about which objects to select, but also the order of selection (or arrangement), then you use the permutations formula. Here are two examples to illustrate the ...” May 26, 2012 Stuart Kovinsky posted a reply to the long advertisement in the Critical Reasoning forum “Hi! Just a reminder, please post the source of your questions (always a good habit). Whenever you have an assumption family question (assumption/strengthen/weaken/flaw), start by deconstructing the argument: find the conclusion, summarize the evidence and identify the assumption. Here, we ...” May 26, 2012 Stuart Kovinsky posted a reply to Probability problem in the Problem Solving forum “Just to elaborate a bit more, here''s the probability formula: probability = (# of desired outcomes)/(total # of possibilities) and, as Anurag noted, 36 was the total number of possible choices. Whenever you''re doing a probability problem, starting out by writing that equation on your ...” May 26, 2012 Stuart Kovinsky posted a reply to Coordinate plane in the Problem Solving forum “Hi! Let''s start with what''s probably the quickest approach: actually graphing the line. The notepad that you get on the GMAT is graph-lined, so it''s pretty easy to accurately draw out coordinate geometry questions. Accordingly, one option for solving this problem is to plot the two points, ...” May 26, 2012 Stuart Kovinsky posted a reply to Quadrilateral in the Data Sufficiency forum “Hi! It''s been a long time since I read this thread, but happy to reiterate a couple of key points. First, and I can''t stress this enough: a square IS by definition a rectangle, since it has all the properties of a rectangle. The opposite is not true (i.e. a rectangle is not by definition a ...” May 26, 2012 Stuart Kovinsky posted a reply to Manhattan - weaken in the Critical Reasoning forum “Hello! We''re asked to find the answer that would be cited by a SUPPORTER of the argument; in other words, we want to find the answer that, if true, would most STRENGTHEN the conclusion. First, of course, we need to identify the conclusion. There are a number of tools we can use to do so: ...” May 24, 2012 Stuart Kovinsky posted a reply to Strengthen in the Critical Reasoning forum “Hi! For strengthening questions, start by deconstructing the argument: find the conclusion, summarize the evidence and identify the author''s assumption. Next, make your prediction: the correct answer will support the assumption. Let''s break down this argument: Conclusion - TV ...” May 23, 2012 Stuart Kovinsky posted a reply to Assumption question quiet confusing... in the Critical Reasoning forum “Hi! What''s the source of this question? It sounds a LOT more like an LSAT question than a GMAT one. If it''s from an LSAT source, then I''d advise that you completely ignore it, since the difference between sufficiency and necessity is rarely tested on the GMAT. **FEEL FREE TO STOP READING ...” May 23, 2012 Stuart Kovinsky posted a reply to Explain the Discrepancy CR Question - MGMAT CAT in the Critical Reasoning forum “Hi! (C) is outside the scope because of two key factors: 1) the stimulus tells us that the ATMs are "on the driver''s side of a lane accessible only to automobiles" and "Clearly, blind people do not drive automobiles"; and 2) (C) says that "all ATMs accessible to the ...” May 23, 2012 Stuart Kovinsky posted a reply to Something Wrong with the question??? in the Data Sufficiency forum “Hi! Remember - when inequalities and variables are involved, you have to be very careful with your manipulations! You cannot simply cross-multiply by a-b, since it''s possible that a-b is negative. If a-b IS negative, then when you cross multiply you get: Is 1/(a-b)<(b-a)? Is 1 > ...” May 23, 2012 Stuart Kovinsky posted a reply to stocks in the Problem Solving forum “Hi! At first glance this may look like a permutations question, but it''s actually an exponent question with a tiny bit of permutations thrown in. Since there''s no restriction on how many times we use each letter in each code, the number of possible 5 letter codes is simply 26^5 and the ...” May 23, 2012 Stuart Kovinsky posted a reply to households in the Problem Solving forum “Hi! I played with the numbers a bit to maximize the duplicates, keeping in mind that I wanted to use as many of the DVDs, cell phones and MP3 players as possible twice. I started with the MP3s, since that was the smallest group. Then I noted that there were 5 more Cell phones than DVDs, so I ...” May 22, 2012 Stuart Kovinsky posted a reply to three and four digit numbers in the Problem Solving forum “Hi! Is there a reason why we couldn''t have x=170 and y=850? In order for x+y to be a 4 digit number, at least one of the two must be greater than 500 (and the hundreds digits must sum to at least 9), but both don''t need to be greater than 500. Fortunately, that issue doesn''t cause any ...” May 22, 2012 Stuart Kovinsky posted a reply to Counting Numbers -1 in the Problem Solving forum “Hi! Because you''re multiplying by a smaller number, you''ve actually removed those duplicates. Here''s another way you could write the product: (number of digits that could go in the first spot) * (number of digits that could go in the second spot that you haven''t used yet) * (number of ...” May 22, 2012 Stuart Kovinsky posted a reply to advanced gmat guide- inequality in the Data Sufficiency forum “Hi! The two statements aren''t identical, since for (2) a could be the negative root of a^2 and for (1) a is definitely non-negative. For example, for statement (1) we could pick a=4 and b=2 (since 4 = 2^2). For statement (2) we could pick those same numbers (since 4^2 = 2^4), but we could ...” May 21, 2012 Stuart Kovinsky posted a reply to Consulting in the Data Sufficiency forum “Hi! From the stem, we know that the fee is$x/hour for the first 100 hours and $y/hour for extra hours. We also know that Acme was charged a total of$14000. So, we can create the following formula: 100*$x + (n-100)*$y = $14000 (n = total number of hours charged) and the question is ...” May 21, 2012 Stuart Kovinsky posted a reply to Probability | Playing Cards in the Problem Solving forum “Hi! We want the probability of getting at least one matching pair. So, the only thing we don''t want to happen is 0 matching pairs. Accordingly, this is a great question on which to apply the "one minus" approach. Remember this key formula for complex probability problems: ...” May 21, 2012 Stuart Kovinsky posted a reply to households in the Problem Solving forum “Hello! First, a key strategy on min/max questions: whenever a question asks you to minimize one thing, maximize others; whenever a question asks you to maximize one thing, minimize others. Next, let''s break this question down into two parts. First, the max number of households that has all ...” May 21, 2012 Stuart Kovinsky posted a reply to Sum of numbers in the Problem Solving forum “Hello! On this type of question you always want to look for a pattern. In this case, let''s separate the units and tens digits. Overall, we have 10 sets of numbers here: 0-9, 10-19, 20-29, ..., 90-99. In each set of 10, we have 1 of each units digit, so that''s 10 of each. For each set ...” May 21, 2012 Stuart Kovinsky posted a reply to prime in the Problem Solving forum “Hi! The wording of this question is a bit too ambiguous for the GMAT. Even though we can reason out what the question is supposed to say, you''ll never be put in that position on test day. What''s the source? Better wording would have been: Like many number property questions, we can ...” May 21, 2012 Stuart Kovinsky posted a reply to Coin flip questions made easy in the GMAT Math forum “Hi! The formula is more complicated for die rolls because there are more than 2 possible outcomes, so "what you want" doesn''t equal "what you don''t want". If you''re looking for one specific result, there''s a 1/6 chance of what you want and a 5/6 chance of what you ...” May 20, 2012 Stuart Kovinsky posted a reply to Problem Solving in the Problem Solving forum “Hi! We see a fraction question with unknown values. Perfect time to pick numbers! First, let''s identify the exact question: what fraction of UNSOLD cars were HYBRIDS. In other words, we want to solve for: (# of unsold hybrids)/(total # of unsold cars) To make the math work out, ...” May 19, 2012 Stuart Kovinsky posted a reply to 3 categories of workers in the Problem Solving forum “Hi again! I strongly disagree - you will never have to make assumptions of this nature on the actual GMAT and doing so in practice will lead to habits on test day that could lead to fatal errors. For example, one of the most common DS mistakes is to assume facts that aren''t actually in ...” May 19, 2012 Stuart Kovinsky posted a reply to 3 categories of workers in the Problem Solving forum “Where do you see that information in the question stem? Also, does a higher number in the ratio mean that a worker is more efficient or less efficient? For example, if you measure efficiency in tasks per hour, then higher is better; but if you measure efficiency in hours per task, then lower is ...” May 19, 2012 Stuart Kovinsky posted a reply to If 0<x<y, is y-x < 0.00005 in the Data Sufficiency forum “Sometimes brute force is the key to happiness on the GMAT. (1) doesn''t give us any information about the upper boundary of y, so there''s no way it''s sufficient by itself: eliminate A and D. (2) gives us an upper boundary on y AND we already know that x > 0, so it''s actually possible ...” May 19, 2012 Stuart Kovinsky posted a reply to 3 categories of workers in the Problem Solving forum “Hi! This is a very poorly worded question and makes little sense. What does "the efficiency of the 3 categories of workers" mean? How is it related to wage? Nowhere does it say that different workers get different hourly rates (e.g. that hourly wages are proportional to efficiency, ...” May 19, 2012 Stuart Kovinsky posted a reply to Maths Problem in the Problem Solving forum “Hi! Since p is a positive integer, p^3 is a perfect cube. Here''s an important rule about prime factoring of perfect squares, cubes, etc...: perfect squares contain prime factors in pairs; perfect cubes contain prime factors in triplets; and so on... For example: 36 is a perfect square; ...” May 19, 2012 Stuart Kovinsky posted a reply to Sets in the Data Sufficiency forum “Hi! I can''t speak for all the experts here, but when I see a question linked in an image instead of typed in, I usually skip over replying (unless the image contains a diagram, which is a good excuse for attaching one). The reason why I skip over these posts is because 90% of the time I''m ...” May 19, 2012 Stuart Kovinsky posted a reply to board of directors in the Problem Solving forum “A great opportunity to use logic instead of math! There are 5 different people with whom Michael can be matched. There are 2 spots available on Michael''s team. Therefore, any one of the other 5 people will appear on 2/5 = 40% of Michael''s teams. Pick C!” May 19, 2012 Stuart Kovinsky posted a reply to Can someone please explain? in the Problem Solving forum “Hi! We can set up a couple of simple equations to solve this relatively painlessly. Let''s call his one way walking time "W" and his one way cycling time "C". We want to know the time for walking both ways, so we''re solving for 2W. We know that: W+C = 2h40min ...” May 18, 2012 Stuart Kovinsky posted a reply to perpendicular in the Problem Solving forum “Hi! Although it may be somewhat time-consuming, your best bet is to rewrite the equation in the stem and in each choice into standard y=mx+b form - that way you''ll be able to quickly compare the slopes. Original: 3x + 4y = 8 4y = -3x - 8 y = -3/4(x) - 8 Slope = -3/4 Since ...” May 18, 2012 Stuart Kovinsky posted a reply to Probabilities in the Problem Solving forum “*TANGENT ALERT* No math here, if you''re looking for math, move along! There''s no need to put it directly before that (in fact, I challenge you to rewrite the sentence to put that where you want without causing a modification error in the remainder of the sentence) - the verb makes it clear ...” May 18, 2012 Stuart Kovinsky posted a reply to prime number in the Data Sufficiency forum “Hi! Very open question, but we see it''s about primes. Whenever you see a DS question about primes, always think about 2, the only even prime! Pretty straightforward question, so let''s dive right into the statements. (2) seems simpler, so let''s start there. The only way that (2) could ...” May 18, 2012 Stuart Kovinsky posted a reply to Probabilities in the Problem Solving forum “Hi! Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can''t be the referent of that.” May 18, 2012 Stuart Kovinsky posted a reply to Are x and y both positive? in the Data Sufficiency forum “Hi! (2) says that x/y > 1 If you plug in x = -3/2 and y = -2, you get: x/y = -(3/2)/-2 = -(3/2)*-(1/2) = 3/4 which is NOT greater than 1. Since your numbers don''t satisfy the statement, they''re impermissible and must be discarded. As Aneesh aptly notes, you have to be VERY careful ...” May 18, 2012 Stuart Kovinsky posted a reply to Overlapping sets - OG12 in the Problem Solving forum “Hi! Yes - if you want to solve with a Venn diagram, that''s exactly where you''d put the 60. Stuart” May 17, 2012 Stuart Kovinsky posted a reply to If a, b, and c in the Data Sufficiency forum “Hi! Picking numbers is a great way to solve this (and many other) DS questions. We quickly decide that (1) is insufficient, since it gives us no info about c. So, let''s eliminate A and D and jump to (2). (2) a-b>c We can see that b is to the right of a on the number line, so let''s ...” May 17, 2012 Stuart Kovinsky posted a reply to Are x and y both positive? in the Data Sufficiency forum “Eagleeye gives a good math explanation; let''s look at the question purely using number properties concepts. Q: are x and y BOTH positive. (1) 2x-2y=1 or x - y = 1/2 Let''s think about what this means: on the number line, x is 1/2 to the right of y. Does that tell us anything about ...” May 17, 2012 Stuart Kovinsky posted a reply to Overlapping sets - OG12 in the Problem Solving forum “Hi! You''ve put 60 in the Brand A "total" column, which includes "brand A/brand B" and "brand A/not brand B". People in the "brand A/brand B" column are NOT "brand A ONLY" - they''re using both. The 60 should go in the "brand a/not brand ...” May 17, 2012 Stuart Kovinsky posted a reply to Percentages in the Problem Solving forum “Hi! I''m not sure where you''re getting these questions, but they, for the most part, suck. Each one only has 4 choices, they often have awkward or ambiguous language and test concepts far beyond (and irrelevant to) the GMAT. If you''re actually studying for the GMAT, I''d avoid this source ...” May 17, 2012 Stuart Kovinsky posted a reply to Six digit numbers in the Problem Solving forum “Only 4 answer choices, so clearly this isn''t a real GMAT question - please always post your source we know if it''s relevant to the GMAT! This question is a far more complicated version of a question that may appear on the GMAT, so it''s worth discussing. Once you understand how one of these ...” May 17, 2012 Stuart Kovinsky posted a reply to Another good evaluate question... in the Critical Reasoning forum “But what does "coming second" mean? If the Bible got 999 votes and 1984 got 1 vote, then 1984 came second; if the Bible got 501 votes and 1984 got 499 votes, then 1984 came second. Do both scenarios make us think that 1984 actually affected a lot of people''s lives?” May 16, 2012 Stuart Kovinsky posted a reply to jury in the Problem Solving forum “Hi! I gave a detailed explanation to this question here: http://www.beatthegmat.com/i-suck-at-probability-need-desperate-help-t8927.html” May 15, 2012 Stuart Kovinsky posted a reply to Inequalities OG12 #38 in the Problem Solving forum “Hi! When you''re not sure what to do with the algebra, don''t waste your valuable test time trying to figure it out. Instead, dive right in and pick numbers. As you noted, each statement must be insufficient alone, since each one only provides 1/2 the picture. So, let''s jump right to ...” May 15, 2012 Stuart Kovinsky posted a reply to Another good evaluate question... in the Critical Reasoning forum “Hi! Relevant information questions are really scope questions - we want the answer that''s most inside the scope of the issue. These questions belong to the assumption family. A great approach is to break down the argument just as you would for any assumption/str/wkn question: find the ...” May 14, 2012 Stuart Kovinsky posted a reply to Couldn't get the problem in the Problem Solving forum “Hi! Wacky symbol questions appear from time to time on the GMAT; these questions almost always resolve to simple substitution. Of course, before you can substitute you have to understand the question. So, the key to solving these problems is to take the time you need to break down the question ...” May 14, 2012 Stuart Kovinsky posted a reply to Confusing Probability in the Problem Solving forum “Hi! Part of you''re analysis is 100% correct: for any given string of 7 coin flips, there''s a (1/2)^7 chance of it happening. For example, there''s a (1/2)^7 probability of getting: HHHHHHH; or HHHHHHT; or HHHHHTT; and so on... However, here''s the problem: to satisfy what the ...” May 14, 2012 Stuart Kovinsky posted a reply to weighted averages in the GMAT Math forum “Here''s a very useful rule to remember for data sufficiency: In order to find the actual value of a quantity, you need at least one actual quantity somewhere in the information. For example, if all you''re given is a ratio, there''s no way to determine the actual quantities involved; ...” May 12, 2012 Stuart Kovinsky posted a reply to Confusing Probability in the Problem Solving forum “Hi! We can definitely solve using the coin flip formula and adding up the probability of each scenario that we want. However, we can solve MUCH quicker using logic. We want all the cases with an even number of heads. So, we want: 0H 2H 4H 6h We DON''T want all the cases with an odd ...” May 11, 2012 Stuart Kovinsky posted a reply to MGMAT Geo series - Need expert help with my calculation in the Problem Solving forum “I have to admit that I''m not an expert on geometric series - I''d always attack this kind of question by picking numbers, which to me is much simpler. However, I think the problem is that you''re using "y" to mean different things in different places. You say that: In that ...” May 11, 2012 Stuart Kovinsky posted a reply to How to plug in for this? Official GMAC Hard in the Problem Solving forum “Hi! First, let''s make sure we understand the essence of the question - since we''re increasing by a set percent each year, what we really have here is a compound interest problem. The problem basically boils down to: Principle investment on Jan 1, 1992:$k interest rate per year: c% total ...”
May 11, 2012
Stuart Kovinsky posted a reply to Question pack 1 DS (hard section) in the Data Sufficiency forum
“Hi! Please check out: [url]http://www.beatthegmat.com/x-the-12th-power-of-an-integer-t110825.html[/url] for some expert explanations!”
May 11, 2012
Stuart Kovinsky posted a reply to remainder problem in the Problem Solving forum
“Hi! Picking numbers is a great approach to solving many number property questions. Here, our constraints are that n/9 must have a remainder of 8 and n must be even. What''s the smallest number that satisfies these constraints? n=8 (8/9 has a quotient of 0 and a remainder of 8). Now let''s ...”
May 11, 2012
Stuart Kovinsky posted a reply to abc in the Problem Solving forum
“Hi, those will indeed have different results, but since 6/2 doesn''t satisfy the condition that ab^2/c is even, we can ignore that possibility. Remember, we take the equation in the question stem as a given; accepting that the equation is true, we now check to see which statement MUST also be ...”
May 11, 2012
Stuart Kovinsky posted a reply to Single eqn solving?? in the Problem Solving forum
“Hi! We can solve this question super-duper quickly via backsolving. Since we want the minimum number of copper coins, let''s start with the smallest answer, (E). (E) 0 copper means $2.80 from brass - since 280 is not a multiple of 25, wrong! (D) 1 copper means$2.60 from brass - since 260 ...”
May 11, 2012
Stuart Kovinsky posted a reply to usage of will and would in the Sentence Correction forum
“It''s not wrong, it''s just overly wordy - and the GMAT doesn''t like overly wordy sentences.”
May 11, 2012
Stuart Kovinsky posted a reply to Remainder R in the Data Sufficiency forum
“Picking numbers is a very efficient way to solve number property DS questions. From the question stem, we know that (4+7n)/3 has a remainder of r; we want to know that value. What do we need? Information about n. 1) n+1 is a multiple of 3. If n=2 (we''re allowed to pick 2 since 2+1 is a ...”
May 9, 2012
Stuart Kovinsky posted a reply to Sets problem in the Data Sufficiency forum
“Let''s solve using the most powerful rule for data sufficiency: number of equations vs number of unknowns. First, picture (sorry, I''m not good at computer diagrams!) a Venn diagram with 3 circles. There are 7 different sections: Only R, only S, only T, RS overlap, RT overlap, ST overlap, RST ...”
May 9, 2012
Stuart Kovinsky posted a reply to usage of will and would in the Sentence Correction forum
“For the first one I''d say "there is hope that the economy will grow". You would only use "would grow" if you''re adding a "but" to the end. For example, "I had hoped that the economy would grow, but it shrunk." (Or "I hoped that the economy would grow, ...”
May 9, 2012
Stuart Kovinsky posted a reply to Confused - Any Ideas in the Problem Solving forum
“From the question stem, we know that n is an integer. Accordingly, we know that sqrt(3+x) is an integer. What numbers have roots that are integers? Perfect squares. Consequently, (3+x) must be a perfect square, i.e. 1, 4, 9, 16, 25, 36, ... Now we just need to plug in each answer to see ...”
May 8, 2012
Stuart Kovinsky posted a reply to usage of will and would in the Sentence Correction forum
“Hi, would is NOT the past tense of will. Would is used in conditionals, e.g. "I would go to Harvard if I were to get an 800 on my GMAT". Would can be used in different tenses. For example: I would have gone to Harvard if I had gotten an 800 on my GMAT. "Will" ...”
May 8, 2012
Stuart Kovinsky posted a reply to function h(n) number properties in the Problem Solving forum
“Here''s the takeaway: if h(100) is divisible by every prime from 1 to 50, then h(100)+1 CANNOT be a multiple of any of those numbers. What Bill was saying is that the greatest common factor of any TWO consecutive integers is 1. Since h(100) and h(100)+1 are consecutive integers, then any prime ...”
May 7, 2012
Stuart Kovinsky posted a reply to Airline Fleet - GMAT Prep in the Problem Solving forum
“You can think of it that way, but you have to count the actual number of years starting from the beginning of 1980. I guess technically you''d hit your target 8 years and 364 days after you start, but that''s still 9 years, not 8. (If you start on Jan 1st 1980, you have your 9th change on Dec 31st ...”
May 4, 2012
Stuart Kovinsky posted a reply to numbers 2 in the Problem Solving forum
“Hi, I''m happy to explain the concepts, but first it''s important to note that the wording of both questions is definitely NOT what you''d see on the GMAT. Also, there are only 4 answer choices and, of course, on the real GMAT there will be 5. Please always post the source of your questions so ...”
May 4, 2012
Stuart Kovinsky posted a reply to Airline Fleet - GMAT Prep in the Problem Solving forum
“Hi! You could solve this question very quickly by brute force - just make a chart and keep track of what happens each year. Remember, on the GMAT you get points for picking the right answer, not for HOW you arrive at that answer. Sometimes brute force is quicker than algebra. Year A planes ...”
May 3, 2012
Stuart Kovinsky posted a reply to OG 13 #229 How many of the integers... in the Problem Solving forum
“Here''s the #1 thing to remember when using the OG: it''s a great source of questions, but a horrible source of explanations. Especially for math, OG explanations are rarely the most efficient way to solve problems. Since the biggest answer given is 5, plug ''n play is a great alternative way ...”
May 3, 2012
Stuart Kovinsky posted a reply to if b < 1 and 2x - b = 0 in the Problem Solving forum
“Hi! Like many GMAT questions, we should start by simplifying the question itself. We know that b < 1 and that 2x-b=0. We can rewrite the equation as: 2x = b Putting the two statements together: 2x = b < 1 2x < 1 x < 1/2 Now we need to find the answer that MUST be true, ...”
May 3, 2012
Stuart Kovinsky posted a reply to Probability of cars in the Problem Solving forum
“Hi! Lots of good solutions already posted, so I''m just going to focus on your actual question. When we made the calculation to get 192, we were working on the basis that order DID matter. If you think about those possibilities, you''ll see that we''ve over counted. For example, if the ...”
May 3, 2012
Stuart Kovinsky posted a reply to Thought process on remainders in the Problem Solving forum
“Hi, for the GMAT, your goal is to be as efficient as possible. While you could certainly derive a fancy formula to solve this type of problem, brute force is almost certainly quicker. Since we want all the numbers that leave a remainder of 1 when divided into 16, what we really want is the ...”
May 3, 2012
Stuart Kovinsky posted a reply to Quadratic Equation in the Data Sufficiency forum
“Hi! There are two problems with your analysis, one of which may just have been a typo. First, the minor issue: (C) is correct if you require both statements in combination; based on the rest of your post, I''m going to assume that you meant that you thought the correct answer should be (D), ...”
May 3, 2012
Stuart Kovinsky posted a reply to Challenge-statistics in the Data Sufficiency forum
“Hi! You seem to have misinterpreted the question as "what is the smallest possible number in the set?", when in fact it''s simply "what is the smallest number in the set?" With (1) alone, there''s no way to determine the actual value of x, y or z, so (1) is insufficient. ...”
May 1, 2012
Stuart Kovinsky posted a reply to Angles in the Problem Solving forum
“Hi! You''d definitely benefit from drawing out a clock on this question (as you would on pretty much any geometry question). Sadly, computer-generating diagrams is not one of my strengths, so we''ll just visualize. Let''s think about where the hands are at 4:20: the little hand is on the 4 ...”
May 1, 2012
Stuart Kovinsky posted a reply to Does this ques represent Complex or Normal GMAT standard? in the Problem Solving forum
“One other thing that''s important to note... while the OG is a good source of questions, it''s generally a horrible source of explanations (especially in math). The OG math explanations tend to be the "how to get 10/10 on your grade 10 math test" solution, rather than the "how to ...”
May 1, 2012
Stuart Kovinsky posted a reply to Confusion with wording of option (2) ? in the Data Sufficiency forum
“Hi, the key word is "any". (2) says that the difference between ANY two factors of n is odd; read ANY as EVERY (they mean the same thing). So, if n=12, then we have lots of pairs of factors that do NOT have an odd difference, e.g.: 3-1=2 4-2=2 6-2=4 and so on... The ...”
May 1, 2012
Stuart Kovinsky posted a reply to Confusion with wording of option (2) ? in the Data Sufficiency forum
“Hi Ronnie, what, exactly, is ambiguous? I''d argue that there''s only one way that it can be properly interpreted (the word "any" is the key to proper interpretation).”
April 30, 2012
Stuart Kovinsky posted a reply to Combinations Problem in the Problem Solving forum
“Hi! You''ve ignored the "of the same size" requirement for each possible package type, which is why you ended up with twice the possibilities.”
April 30, 2012
Stuart Kovinsky posted a reply to Combinations Problem in the Problem Solving forum
“Hi! Let''s start with Step 1 of the Kaplan Method for PS: analyzing the question stem. We''re told that there are 2 different sizes of pad - let''s call them small and large ("s" and "l"). There are also 4 different colours, b, g, y and p. We''re allowed to make 2 ...”
April 30, 2012