









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 ...”












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 ...”



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 ...”



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 seeminglyvertical 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.
...”



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 ...”






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, ...”






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 ...”



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 ...”












Ian Stewart
posted a reply to If \(n\) is a positive integer and \(r\) is the remainder
in the Data Sufficiency forum
“n1, n and n+1 are three consecutive integers. If, as Statement 1 tells us, n is odd, then n1 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 (n1)(n+1) is ...”















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 ...”

































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 * ...”









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 ...”



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. ...”



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 ...”









Ian Stewart
posted a reply to If N is a positive twodigit 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 ...”
















































Ian Stewart
posted a reply to If y is a positive integer, is y prime?
in the Data Sufficiency forum
“This is a nearexact 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 ...”


















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 690710 range on several GMATPrep tests, your level essentially has to be in the 690710 range right now.
It''s very unlikely, though not impossible, ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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, ...”



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 ...”



Ian Stewart
posted a reply to If the yintercept of a line is greater than 2
in the Data Sufficiency forum
“The line meets the yaxis above the origin. Using Statement 1, we know (2, 3) is on the line. Here it''s best to draw different diagrams, placing the yintercept above and below y=3, to see where the xintercept will be in different cases. If the yintercept is only very slightly greater than 2, ( ...”



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 xcoordinate. 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 ...”



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 ...”






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 ...”



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 ...”



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 ...”



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 ...”



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 ...”






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. ...”






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 nonterminating 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 ...”



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 ...”



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 ...”



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 ...”



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 ...”






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 ...”



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.”



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 ...”






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 nonsquare.
So the area of ...”






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 ...”



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 sixweek timeframe is perfectly ...”



Ian Stewart
posted a reply to HighLevel 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 ...”



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 ...”



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/thegmatbloghub/theofficialgmatblog/2013/sep/studysmartforyourbestgmat.aspx
Notice from the tables that median study time (which is the relevant number if we''re ...”



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 ...”



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 ...”



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
...”



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 ...”



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 ...”



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
...”



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 yintercept (where the line meets the yaxis). So if we rewrite the equation above in that form, we ...”



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 ...”



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 ...”



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 5,00010,000 official Quant questions I''ve seen. I''ve seen exactly two real questions where a test taker might ...”



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 ...”



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(b1)
So we know that a and b1 are integers which multiply together to give 1. That can only ...”



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 ...”



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.”



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 ...”



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 ...”



Ian Stewart
posted a reply to weight problem
in the Problem Solving forum
“Mitch''s solution is obviously fastest, but there is a novariable 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 ...”



Ian Stewart
posted a reply to PSOG#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 ...”



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 ...”






Ian Stewart
posted a reply to 5160 math
in the GMAT Math forum
“The highest Quant score you can get is 51. The "060" range was used a very long, long time ago, but now the range in Quant and in Verbal is 651 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 ...”



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 ...”



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, ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”






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 ...”






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, ...”



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 ...”



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 VO2max than B after moderate activity
• So A will have better VO2max than B after intensive activity
We''re comparing two different situations  moderate activity and intensive activity. We''re assuming the comparison in the first ...”



Ian Stewart
posted a reply to T1 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 ...”






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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



Ian Stewart
posted a reply to What is the number of 7element 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 7element subset which must sum to a multiple of 3.
So we really just ...”



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 ...”



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.”



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 ...”



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 ...”



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 ...”






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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 620630 range. Assuming you perform to your abilities on test day, and don''t improve between now and then, that would be your expected score. ...”



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 ...”



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 ...”



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 ...”



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".”



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 306090 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 ...”



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 ...”



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 testtaking ''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 ...”



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 ...”



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 ...”









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 ...”



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 ...”



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, ...”



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 ...”



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 ...”



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 ...”



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 ...”



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.
...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 yintercepts of the line are not both at (0,0). So the question is not wellwritten. I think it means to ask for the ratio between the ...”



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.”



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 LR.
So here, we want to know if gr > h  s, or rewriting this, if g+s > h + r. Neither statement is sufficient alone, but if you line up the two inequalities ...”



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 ...”



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 ...”



Ian Stewart
posted a reply to yintercept of line l?
in the Problem Solving forum
“If you haven''t memorized formulas for xintercepts (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 yintercept. We need to find the value of b.
Neither statement is sufficient alone. From Statement 2, we know ...”



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.”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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.”



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:
...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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) ...”



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 ...”



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 (9858)/5 = 8. Thus the mean is 58 + (2)(8) = 74.”



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 ...”



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 formulabased questions will always be the ...”



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 ...”



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 ...”



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 ...”



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 ...”



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".”






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 ...”



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 ...”



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 ...”



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 ...”



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.”



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. ...”



Ian Stewart
posted a reply to Slope
in the Data Sufficiency forum
“No, Statement 1 is not sufficient here. If, say, the xintercept of line N is at 6, then the slope of line N is +1. Now, if the xintercept 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 xintercept of line M is at, say, 0, then the ...”



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.”



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.”






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 ...”



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.”



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, ...”



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. :)”



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:
...”



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 ...”



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; ...”



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 ...”



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, ...”



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 ...”



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 yaxis.
Together, we know they share a point with a negative x coordinate. If the slope of R is greater than the slope of S, ...”



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 xcoordinates and ycoordinates have the same sign. So r and s must have the same sign. Notice that means the points (r, s) and (s, r) ...”



Ian Stewart
posted a reply to xintercept
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 ...”



Ian Stewart
posted a reply to yintercept
in the Data Sufficiency forum
“Lots of lines have an xintercept 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 ...”



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 ...”



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, ...”



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 ...”



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 ...”



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.”



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. ...”



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 ...”



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 (x5) here. You''re taking the square root of (x5)^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 ...”



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.
...”



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 ...”



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 ...”



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 ...”



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 ...”



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 √(3b8) = √(12b), then √(3b8) and √(12b) are the same number, and their ...”



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 ...”



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 + ...”



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 nonterminating (repeating) decimal. If ...”



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 ...”



Ian Stewart
posted a reply to Strategy for 345 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 ...”



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/conversionofqandvrawscoresintogmatscoret67901.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 ...”



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 ...”



Ian Stewart
posted a reply to D10 OG 12 Page 21 Geometry
in the Problem Solving forum
“There''s a useful GMATspecific 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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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!”






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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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 ...”



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).”



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 ...”



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 ...”



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 ...”



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 ...”



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 %.”



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 ...”



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 ...”



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 ...”



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.”



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 ...”



Ian Stewart
posted a reply to XY?
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 ...”



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 ...”



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 ...”



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 ...”



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 500level test taker will answer correctly, and the probability that a 700level test taker will answer correctly. A question which is a ...”












Ian Stewart
posted a reply to MGMAT Data Sufficiency Quesiton
in the Data Sufficiency forum
“It''s not quite that straightforward, particularly the part I''ve highlighted. If we change the number ''7'' in the question to ''6'', say (or some other even number), the answer is not C. It genuinely matters here what we''re dividing by, and if you''ve just ignored the fact that we''re dividing by ...”



Ian Stewart
posted a reply to MGMAT Data Sufficiency Quesiton
in the Data Sufficiency forum
“The principles you''re citing are all true, but you aren''t quite using all of the information given here. In general, if the *only* thing you know about A and B is that they are not multiples of 7, then it is true that A+B will sometimes be divisible by 7, and will sometimes not be divisible by 7. ...”



Ian Stewart
posted a reply to the average
in the Data Sufficiency forum
“The wording of this question is terrible. The question asks about the ''newsstand price'', and Statement 2 talks about the ''cover price''. Are these the same? I don''t know how we''re supposed to guess that. I also have no idea what the ''average annual savings'' could mean. What are we supposed to ...”



Ian Stewart
posted a reply to DS  Inequalities  Strategy help please
in the Data Sufficiency forum
“If the question mentions √x, then x clearly cannot be negative. When we combine the two statements, then if x is 0 or 1, clearly x > y from either statement. If x is between 0 and 1, then x^3 is smaller than x, and √x is greater than x. So in this case, combining the two statements, we know ...”



Ian Stewart
posted a reply to DS Question  need help
in the Data Sufficiency forum
“If you know that, say, the remainder is 3 when x is divided by 10, that means that x is 3 more than some multiple of 10. In other words, x  3 must be divisible by 10. So if the remainder is 1 when 81 is divided by a, that means that 81 is 1 more than some multiple of a, or in other words, 80 is ...”



Ian Stewart
posted a reply to Data Sufficiency
in the Data Sufficiency forum
“Since this is a divisibility question, we should certainly try to get factorizations. The expression y^3  y can be factored first by factoring out one y, and then by using the difference of squares:
y^3  y = y(y^2  1) = (y)(y1)(y+1)
Now (y1)(y)(y+1) is just the product of three ...”



Ian Stewart
posted a reply to Properties of perfect squares
in the Problem Solving forum
“You certainly need to consider 1 when you count the divisors of a positive integer, so you may have gotten bad information from what you read. Perfect squares have an odd number of divisors. It''s easy to see why this should be true. If you take a nonsquare, like 18, then all of the divisors are in ...”



Ian Stewart
posted a reply to Number problem  prime number
in the Problem Solving forum
“I frankly don''t understand most of what you''re trying to say, so it''s impossible to respond, but:
This is the *only* question. If x and y can be nonprime, then III does not need to be true. Nothing else matters here.”



Ian Stewart
posted a reply to Number problem  prime number
in the Problem Solving forum
“This is completely backwards. The question doesn''t ask if 2x/y must be prime if III is true, which is what you''re answering. It asks if III must be true if 2x/y is prime.
I don''t really understand why this question has created such controversy. There''s nothing wrong with the question, and ...”



Ian Stewart
posted a reply to Remainder with 5 integers
in the Data Sufficiency forum
“These principles aren''t quite right. Say you have two numbers, and the remainder is 5 when you divide the first number by 7, and the remainder is 2 when you divide the second number by 7. If you multiply these two numbers, the remainder will not be 5*2 = 10 when you divide the product by 7, since ...”



Ian Stewart
posted a reply to Data sufficiency, the answer "C"
in the Data Sufficiency forum
“Answer C on DS questions reads as follows:
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Notice the highlighted part: you *only* consider C (and therefore *only* use both statements together) if neither statement is sufficient alone. So if you discover ...”



Ian Stewart
posted a reply to A^8 x B ^4  A^4x B^ 2= 12
in the Data Sufficiency forum
“While you don''t need to here, I''d find it easiest to factor first. We can take out the common factor of a^4 * b^2 from each expression, then use a difference of squares:
(a^8)(b^4)  (a^4)(b^2) = 12
(a^4)(b^2) [ (a^4)(b^2)  1] = 12
(a^2 * b)^2 [ (a^2)(b) + 1 ] [ (a^2)(b)  1 ] = 12
You ...”



Ian Stewart
posted a reply to Inequalities: Is pr/qs > r/q?
in the Data Sufficiency forum
“We want to know if (p/s)*(r/q) > r/q. That is, we want to know whether the fraction r/q would get bigger if we multiply it by p/s.
Even together the statements are not sufficient. From Statement 2 we know that r/q is positive, since r and q have the same sign. Now when we multiply r/q by p/s, ...”



Ian Stewart
posted a reply to A tough function problem
in the Data Sufficiency forum
“If you know exactly how the operation is defined, then you can answer any question about properties of the operation, so each Statement has to be sufficient here; you don''t actually need to do any work. But the question is badly written: it is impossible for x@y to be equal to 1/x  1/y *and* to be ...”



Ian Stewart
posted a reply to Integer S
in the Data Sufficiency forum
“I don''t really have anything to add to the comments Ron made above, but I don''t find the question at all ambiguous. I do, however, think these questions can seem abstract if you haven''t seen a similar question before. As for this:
there are two very similar questions to this one in the ...”



Ian Stewart
posted a reply to Power question
in the Data Sufficiency forum
“This question doesn''t really make any sense. When they define a function f(x) in the question, that makes it seem as though x is a variable. But it isn''t a variable here; it''s a constant. There''s no reason to introduce a function, and it''s completely illogical to do so  I don''t understand why ...”



Ian Stewart
posted a reply to Focus on specific Quant topics to reach minimum goal?
in the GMAT Strategy forum
“This isn''t true, though I''ve seen it repeated it many times. You don''t see more counting/probability questions at the high level of the test; you see harder counting/probability questions at the high level of the test. I had (only) one question in counting/probability the last time I took the ...”



Ian Stewart
posted a reply to 700 level questions in the GMAT REVIEW book
in the GMAT Strategy forum
“There aren''t all that many really highlevel questions in the Official Guides, unfortunately, though as IJR says the questions generally get harder near the end of each section. Most of the questions in the OG are quite old now, and were written by a different company than the one currently ...”



Ian Stewart
posted a reply to coordinate slopeintercept problem
in the Data Sufficiency forum
“The question asks if the slope of the line is negative. A line has a negative slope if it is falling as it moves to the right.
From Statement 1, we learn that (ac) and (bd) have opposite signs. Now the slope of the line is (bd)/(a  c) (using the standard slope formula); if (ac) and (bd) ...”



Ian Stewart
posted a reply to value of AB(A+2B)?
in the Data Sufficiency forum
“There''s something wrong with the question; if AB = 40, as we learn in the stem, then certainly AB cannot be equal to 18, as we''re told in Statement 2.”



Ian Stewart
posted a reply to Doubt in Inequality
in the Problem Solving forum
“There is no need to ''complete the square'' here, or to calculate discriminants  neither of those techniques are ever required in real GMAT questions. When x < 1/2, then 2x  1 is equal to 1  2x. So our inequality becomes
x^2  (1  2x) > 3x  5
x^2 + 2x  1 > 3x  5
x^2 > x ...”






Ian Stewart
posted a reply to GMAT Prep 1  GMAT Prep 2 Overlap
in the GMAT Strategy forum
“There should be no overlap between the two GMATPrep tests. Last I checked, there were four different questions that could appear at the beginning of test 1, so if you take that test five times, your first question is certain to be a repeat. I think after four attempts you''ll find you''ve more or ...”



Ian Stewart
posted a reply to GMAT Scoring Algorithm
in the GMAT Strategy forum
“Almost everyone who takes the GMAT gets about one third of his or her questions wrong in Quant. Even people who get a Q50 score usually have 1013 mistakes. I''ve often seen people draw an analogy between the GMAT scoring algorithm and athletic competitions like the high jump or the pole vault. I ...”



Ian Stewart
posted a reply to GMAT Scoring Algorithm
in the GMAT Strategy forum
“I''m not precisely sure what it is about the numbers that you find unusual, but if you let me know, I can try to answer in more detail  is it that your scaled score is higher, but percentile rank is lower, in Quant than in Verbal? The Quant and Verbal scaled scores are not directly comparable. They ...”



Ian Stewart
posted a reply to DS Mathematics OG #166
in the Data Sufficiency forum
“I don''t recommend learning rules for inequalities and reciprocals, because they aren''t entirely straightforward. You can always just multiply and divide on both sides of your inequality to get the same result, so you don''t need to learn any rules for reciprocation. It is true that you need to ...”



Ian Stewart
posted a reply to Cost of item
in the Problem Solving forum
“There''s an important distinction here  important because it''s tested on the GMAT all the time. If you decrease something by 15%, then increase it by 15%, you don''t get back to where you started. The reason is that the 15% increase is being applied to a smaller value than the 15% decrease, so ...”



Ian Stewart
posted a reply to An infinite sequence of positive integers is called an "
in the Data Sufficiency forum
“A sequence is just a list of numbers in order. We can create two sequences which satisfy both statements here, one of which will have an infinite number of even values, and one of which will have a finite number of even values. We can just make the first ten values of our sequence all equal to 8, ...”



Ian Stewart
posted a reply to Question from the 'GMAT Review 12th ed'
in the Problem Solving forum
“That last line should read:
=0.40+0.85  (0.40)(0.85) = 0.91
If A and C were mutually exclusive, then P(A or C) would be equal to P(A) + P(C), so would be equal to 0.23 + 0.85 = 1.08. But that''s greater than 1, and probabilities can never be greater than 1. So, since we get a nonsensical ...”



Ian Stewart
posted a reply to Divisors question !
in the Problem Solving forum
“I don''t know quite what it is about the wording of this question that you find ambiguous, but the words ''divisor'' and ''factor'' mean the same thing in Number Theory. The integer b is a divisor (or factor) of the integer a if a/b is also an integer.”



Ian Stewart
posted a reply to Is X^3Y^2Z^3 >0
in the Data Sufficiency forum
“I think you meant to say the answer is B (since you said Statement 2 was sufficient alone), but that''s not quite right. With Statement 2 alone, there is still the possibility that y=0, in which case the answer to the question would be ''no''. That is, with Statement 2 alone, all we can be sure of ...”



Ian Stewart
posted a reply to is linear eqn with 2 variables sufficient
in the Data Sufficiency forum
“The fact that the statements need to be consistent means that, when using Statement 2 alone, there must be at least one solution for which Marta buys exactly 6 pencils. But that doesn''t tell you anything useful: what you need to be sure of is that there is not some other solution where Marta buys 5 ...”



Ian Stewart
posted a reply to Equation Qs
in the Data Sufficiency forum
“You''re using the question here as though it were a fact. The question *asks* if xy = 1. We don''t know if that''s true, so we can''t use it to draw any conclusions. Of course, if we assume that xy = 1 is true, then obviously we''ll find out that xy = 1 is true  that''s the "begging the ...”



Ian Stewart
posted a reply to How do you quickly find prime factors of a large number
in the Problem Solving forum
“This isn''t true in my experience. I''ve seen many thousand official GMAT questions, and I''m almost certain the largest actual number I''ve ever needed to prime factorize was 441 (in a PS question in OG11).
What you do often need to do is prime factorize expressions which represent large ...”



Ian Stewart
posted a reply to How do you quickly find prime factors of a large number
in the Problem Solving forum
“You really can''t be asked to find prime factors of ''awkward'' large numbers on the GMAT, because it just takes far too long. The only large numbers that can be prime factorized in any reasonable amount of time are numbers which are divisible by 2, 3 and/or 5, since we have quick tests that let us ...”



Ian Stewart
posted a reply to is 1/k > 0?
in the Data Sufficiency forum
“"1/k > 0" means exactly the same thing as "k > 0". Similarly, 1/(k+1) > 0 just means that k + 1 > 0, or that k > 1. So Statement 1 is not sufficient. Since 1/(k1) > 0 just means that k  1 > 0, or that k > 1, Statement 2 is sufficient.”



Ian Stewart
posted a reply to Soccer league participation
in the Problem Solving forum
“That''s not quite right, and if the source says that''s the right answer (where is it from?) then there''s a problem with their solution. The question asks for the proportion of participants who are women *now* in the league. In the solution above, m and w represent the number of men and women *last ...”



Ian Stewart
posted a reply to Selecting a committee of n people
in the Problem Solving forum
“You''re right  that solution is completely wrong, since it ignores the fact that we must choose one person from each office. Where is it from?
To pick a committee consisting of n/2 men and n/2 women, we just need to choose which half of the offices will contribute a woman to the committee; then ...”



Ian Stewart
posted a reply to Inequality with Multiple Variables and Fractions
in the Data Sufficiency forum
“That is *only* true if your numerator and denominator do not become negative after you subtract. If you start, say, with the fraction 5/9, and you subtract 4 from the numerator and denominator, then our numerator and denominator will still be positive, and the value of the fraction will certainly go ...”



Ian Stewart
posted a reply to Inequality  Concept
in the Problem Solving forum
“Most of the time they will alternate, but not always. For example, if you have this inequality, which I''ll borrow from a highlevel official question found in gmatfocus (so it''s not some entirely irrelevant example) :
(x/3) + (3/x) > 2
There are two important things to notice here if you ...”



Ian Stewart
posted a reply to Number of triangles
in the Problem Solving forum
“If no three of the points are collinear, the answer would be 8C3 = 56. Since we don''t want to count the 1 trio of points which lie in a straight line, the answer must be 8C3  1, which is equal to 55.
Your approach is a perfectly good alternative method, and also gives the answer of 55. Is ...”



Ian Stewart
posted a reply to Mean = median > evenly spaced question
in the Data Sufficiency forum
“No, that''s backwards. When a set is equally spaced, then yes, the mean and median are always equal. But the reverse is not necessarily true. For example, in the set below, the mean and median are equal:
0, 1, 50, 99, 100
but the set is certainly not equally spaced.”



Ian Stewart
posted a reply to Positive Negtive
in the Data Sufficiency forum
“If all four of the quantities a, b, c and d, are negative, then ab is positive and so is cd, so ab/cd is certainly positive. So yes, the example given satisfies the condition in the question.”



Ian Stewart
posted a reply to Expert names
in the GMAT Strategy forum
“I think the forum names you''re looking for are:
Stuart Kovinsky
Ian Stewart
Ron Purewal
Stacey Koprince
Testluv
Brent Hanneson
There are many other experts who post on this forum. I think if you spend a bit of time on the site, you''ll quickly discover whose explanations resonate most ...”



Ian Stewart
posted a reply to GCF and LCM of multiple numbers  Data Sufficiency
in the Data Sufficiency forum
“Where is this question from? There are a dozen things wrong with it. First, a real GMAT DS question will never ask for the value of two different quantities; it would ask for the GCD or for the LCM, but not for both. Second, the question should tell you that x is a positive integer. Third, if a DS ...”



Ian Stewart
posted a reply to Different ways in which donuts can be distributed
in the Problem Solving forum
“I discussed a related problem here:
http://www.beatthegmat.com/combinationt41362.html
That said, I have *never* seen a ''partition problem'' on the actual GMAT, or in any published source of official questions. While I think there is some nonzero chance the GMAT could ask such a question, ...”



Ian Stewart
posted a reply to Is x > 0?
in the Data Sufficiency forum
“That''s the fast way to do the problem, and it''s perfectly correct.
Your analysis of these cases isn''t quite right. x+3 is equal to x+3 when *what''s inside the absolute value* is positive. So x+3 = x+3 when x > 3, not when x > 0. You then find, solving, the perfectly good ...”



Ian Stewart
posted a reply to Inequalities  Wierd doubt
in the Data Sufficiency forum
“I''ve highlighted your mistake. You absolutely can NOT divide one inequality by another. You can see why this is not correct just using numerical examples. The following inequalities are both true:
4 > 2
3 > 1
but if we divide the first inequality by the second, the result is not true. ...”



Ian Stewart
posted a reply to Prime numbers
in the Data Sufficiency forum
“Let''s, for convenience, use the symbol "29$" to mean "the product of the primes up to 29". The question asks about the divisors of 29$ + 1.
First, 29$ + 1 is some large positive integer. Every positive integer greater than 1 is divisible by at least one prime, so I must be ...”



Ian Stewart
posted a reply to Prime numbers
in the Data Sufficiency forum
“If you take a positive integer x which is not a perfect square, then if x is *not* prime, it must be possible to write x as a product of two smaller integers:
x = a*b
If x is not a perfect square, then a and b must be *different* (and if a and b are both less than 24, neither of them is equal ...”



Ian Stewart
posted a reply to Positive Negtive
in the Data Sufficiency forum
“Yes, the answer is E, not B. We could have, using both statements, either of the following scenarios:
a = 4, b = 3, c = 2, d = 1
or
a = 1, b = 3, c = 2, d = 4
In the first case bc is greater than cd, and in the second bc is less than cd.”



Ian Stewart
posted a reply to Inequalities
in the Data Sufficiency forum
“Statement 1 is not sufficient here. You might, just looking at the inequality in the question, quickly ask when 3x would be greater than 7y. Since 3 is smaller than 7, that won''t be true unless x is quite a bit bigger than y. Using Statement 1, we know that x is more than 4 greater than y. If y is ...”



Ian Stewart
posted a reply to a data from gmat forum
in the Data Sufficiency forum
“No, when you square, say, 1/100, you will get 1/10,000. That hasn''t decreased by all that much  the decrease is only 1/100  1/10,000 = 99/10,000 = 0.0099. When you square 1/2, the decrease is much larger  the decrease is 0.25.
The standard way to prove that x  x^2 is greatest when x = 1/2 is ...”



Ian Stewart
posted a reply to Ratios
in the Problem Solving forum
“If, say, the ratio of boys to girls is 10 to 11, that means you can divide up all of the people into groups of 21, where each group contains 10 boys and 11 girls. So the ratio of boys to girls can only be 10 to 11 if the number of boys is a multiple of 10, the number of girls is a multiple of 11, ...”



Ian Stewart
posted a reply to probability safe code
in the Problem Solving forum
“There are 8 digits to choose from (0, 2, 3, 5, 6, 7, 8 and 9), 4 of which are odd. Assuming we pick our codes randomly, and that we can use repeated digits, the probability any individual digit is odd is 4/8 = 1/2. The probability all are odd is thus just (1/2)(1/2)(1/2)(1/2) = 1/16, and the ...”



Ian Stewart
posted a reply to Which way to go?
in the GMAT Strategy forum
“That''s wrong. I''ve looked at the answer choices to almost 1000 official questions, and each answer choice is correct equally often. A GMAC research report also says very clearly that they control for ''answer position'' to ensure that a test taker using a ''always guess D'' strategy will have no ...”



Ian Stewart
posted a reply to OG Vs Gmat
in the GMAT Strategy forum
“The real GMAT is adaptive  as you proceed through the test, the algorithm will discover your ability level and keep giving you questions that are challenging for you. The OG is not adaptive; it covers the entire difficulty spectrum, which means if you''re well above average in ability, most of the ...”



Ian Stewart
posted a reply to a data from gmat forum
in the Data Sufficiency forum
“The answer ought to be B  who is saying that it''s E?
If the range of X is 2, then one value in the set must be greater than 2, since all the values are positive. If you square that value, it must increase by more than 2. Then the only way for the set of squares (set Y) to have a lower sum than ...”



Ian Stewart
posted a reply to numbers
in the Problem Solving forum
“edit: didn''t see the posts above before writing this, but another approach:
First, if we are writing this number as a product (a+b)(ab), then we''re writing it as a product of two factors which differ by 2b. For example, if b were 5, then our product would be (a+5)(a5), so we''re just writing ...”



Ian Stewart
posted a reply to DS. TRIANLGE
in the Data Sufficiency forum
“Where is this question from? You don''t need any information to answer it. If you inscribe a triangle in a circle, the circumference of the circle is always greater than the perimeter of the triangle. You can see this easily enough: if we draw 3 points A, B and C, on the circumference of the circle, ...”



Ian Stewart
posted a reply to Combinations
in the Problem Solving forum
“The above solutions are perfect. You could also look at the problem as follows: when entering a code, for each button we have 2 choices (we push the button or we don''t). So we have 2*2*2*2*2 = 2^5 = 32 choices in total. This count is too high by 1, because it includes the possibility of not ...”



Ian Stewart
posted a reply to Ambiguous question
in the Data Sufficiency forum
“I guess I don''t understand what it is about the wording that so many people find ambiguous. The use of language here is entirely standard on the GMAT, and in mathematics in general, and you''re quite likely to encounter similarly worded questions in the future, so it would be worth taking some time ...”



Ian Stewart
posted a reply to DS. VARIANCE
in the Data Sufficiency forum
“Where is this question from? It is not mathematically possible for a set to have a variance of 5 and a range of 1, so the two statements are completely incompatible. That can never happen on a real GMAT question.
In any case, variance is just the square of standard deviation, so Statement 1 is ...”



Ian Stewart
posted a reply to twice as close idiom!!
in the Problem Solving forum
“They should bother you  they make no sense. "Twice" means "two times", in the sense of multiplication, so one thing cannot be "twice as small" as another. We say ''half as big'' in English, not ''twice as small''. So they aren''t ''idioms'' at all. I have seen them ...”



Ian Stewart
posted a reply to My First GMATPrep Test...
in the GMAT Strategy forum
“Not sure which expert this is from, but this is very far from being true. If you make even one mistake in Verbal, you''ll get a 49 or 50 on GMATPrep, and with two mistakes you''ll get a 47 or 48. Those scores are still in the 99th percentile, so while it looks like you''re losing a lot of points per ...”



Ian Stewart
posted a reply to To cancel out common terms & not cancel?
in the Data Sufficiency forum
“When you see the equation (x^2  1)/(x+1) = 1, you can be certain that x+1 is not zero, so you can cancel it freely. However, when you see the equation
(a+b)(ab) = (ab)^2
then it is certainly possible, absent any other information, that ab = 0. We can only divide both sides of an equation ...”



Ian Stewart
posted a reply to Probability
in the Problem Solving forum
“The answer is 1/11 only if you make a pretty ridiculous assumption  that when he lies, he always says "I rolled a 3". If that''s the case, then there''s a 1/6 chance he will roll a 3, and a 1/3 chance he will tell the truth about it, so a (1/3)(1/6) = 1/18 chance he both rolls a 3 and ...”



Ian Stewart
posted a reply to DS: S . D
in the Data Sufficiency forum
“Yes, that is true. It is not something you will *ever* need to use on the GMAT (if you think that fact is needed on a GMAT question, you''ve misunderstood something). That relationship is also irrelevant for the question above  I don''t see why you think it makes statement 1 sufficient, so I can''t ...”



Ian Stewart
posted a reply to Probability spades, kings, queens
in the Problem Solving forum
“You don''t need to know anything about cards for the GMAT, but there are 13 spades in a deck, including the K and Q of spades. There are 3 other (nonspade) Queens and 3 other Kings, for a total of 19 cards which are spades, kings or queens. So the answer is 19/52 (you need to be careful here not to ...”



Ian Stewart
posted a reply to DS: S . D
in the Data Sufficiency forum
“We want to know which set has the greater standard deviation  that is, we want to know in which set the elements tend to be further from the mean. We don''t care at all how big the mean is; we only care how far away elements are from the mean. So Statement 2 here is completely useless.
Statement ...”



Ian Stewart
posted a reply to Integers
in the Problem Solving forum
“The minimum amount he could have spent on $12 tickets is $0. He could have bought 27 balcony tickets.
If we are to assume he actually bought *some* $12 tickets, then if f represents the number of field tickets, and b the number of balcony tickets, we know:
12f + 5b = 135
12f = 135  5b
5 ...”



Ian Stewart
posted a reply to inequality
in the Data Sufficiency forum
“I''ve highlighted the mistake in your solution above. You''ve divided by XY on both sides of the equation, but you can only do that if you''re sure that XY is not equal to zero (you can never divide by zero). Since, before reading the statements, it''s certainly possible that X=Y, you do need ...”



Ian Stewart
posted a reply to quadratic equation
in the Problem Solving forum
“I imagine many people reading this forum won''t even know what ''H.P'' or ''A.G.P.'' even stand for. If you''re preparing for the GMAT, you don''t need to know; these are most definitely not GMAT questions.”



Ian Stewart
posted a reply to Mean and Standard Deviation
in the Problem Solving forum
“Yes, that is exactly what I think. And, as I''ve posted many times, several of their questions about those rules are mathematically nonsensical.
If you disagree with me, feel free to point me to even one official question which would require you to know the 689599 "rule".”






Ian Stewart
posted a reply to Mean and Standard Deviation
in the Problem Solving forum
“No, this is definitely not a ''valid'' GMAT question. Normal distributions are never tested on the GMAT. I''ve seen quite a few prep company questions about normal distributions and the 689599 rule, and they are all completely irrelevant questions for GMAT test takers to study.”



Ian Stewart
posted a reply to A complicated math, pls help to explain
in the Data Sufficiency forum
“Because the Gross Domestic Product may have changed from 1985 to 1994. If, say, the GDP in 1985 was $100, and in 1994 it was $1,000,000, then the percent increase in US trade would be enormous (it would have increased from $17 to $230,000). If instead, the GDP was $100 in both 1985 and 1994, then ...”



Ian Stewart
posted a reply to Accuracy of GMATPrep score?
in the GMAT Strategy forum
“Your GMATPrep scores sound entirely normal. When comparing Quant and Verbal scores, you should be comparing percentiles (which essentially are what are used to generate your score out of 800), and not the raw scores out of 51. The raw scores were comparable when the GMAT was first developed (long ...”



Ian Stewart
posted a reply to Median
in the Data Sufficiency forum
“Negative numbers are never considered prime. The smallest prime number is 2. If a number is both even and prime, that number must be equal to 2, which makes Statement 1 sufficient.
While the reasoning in your solution is correct, you''ve made one mistake (a few times). If N < 8, the ...”



Ian Stewart
posted a reply to (3^2)^0.5 = ...
in the Problem Solving forum
“I don''t think I have ever seen a decimal exponent in an official GMAT question (though I have seen fractional exponents), but yes, if you see 4^0.5, or 4^(1/2), that is equal to 2, and not to 2. You can interpret the power of 1/2 to be the equivalent of a radical sign; that is, it gives you the ...”



Ian Stewart
posted a reply to Fairly Simple One
in the Data Sufficiency forum
“Where is the question from? It''s not clear what the question even means. If I can work out that x and y are 2 and 3, in some order, is that sufficient? Or do I need to know which of my values is equal to x, and which is equal to y? Since the question is open to two different legitimate ...”



Ian Stewart
posted a reply to Scaled Score
in the GMAT Strategy forum
“Scaled scores ranged from 0 to 60 in the early days of the GMAT. Now scaled scores range from 6 to 51; it is impossible to get a score higher than 51. To get a 51 in either section you need to be essentially perfect on the questions which count (of course, if you answer experimental questions ...”



Ian Stewart
posted a reply to Is 0 a multiple of all numbers?
in the Problem Solving forum
“I''m sure you got a longer discussion than you needed :)
Technically, the answer is yes, but this is precisely the kind of issue about 0 that you will never need to be concerned about on the GMAT. If a GMAT asks about the factors of some number, the test will always make clear that the number ...”



Ian Stewart
posted a reply to a data from gmat club
in the Data Sufficiency forum
“Good point  I''ve seen so many questions like this one before, I just glossed over the word ''right'' in the question. If the question asks about an ''isosceles right triangle'', the question doesn''t make any sense, since it''s impossible to construct an isosceles right triangle with the ...”



Ian Stewart
posted a reply to Please help: Prime #'s and odd?
in the Data Sufficiency forum
“Yes, your logic for Statement 2 here is perfect, and Statement 2 is certainly sufficient, since if y=2, we know that y(x3) is even.
The answer is not B here, however, because Statement 1 alone is also sufficient. If x > 10 and x is prime, then x must be odd, so x3 must be even. Thus with ...”



Ian Stewart
posted a reply to TRUE OR FALSE?
in the GMAT Strategy forum
“I don''t think that anyone can properly answer your question here without more information about the program to which you''re applying. Different schools use GMAT scores in different ways; for some, the Quant section is especially important, while for others, it''s the score out of 800 which matters ...”



Ian Stewart
posted a reply to a data from gmat club
in the Data Sufficiency forum
“If the sides of a triangle are a, b and c, it is always true that the sum of any two sides of the triangle must exceed the third side  that is, that
a + b > c
a + c > b
b + c > a
So with both statements together, it''s certainly possible for the three sides to be 9, 9 and 4. It ...”



Ian Stewart
posted a reply to Is 0 a multiple of all numbers?
in the Problem Solving forum
“First, I wasn''t discussing any particular company when I mentioned prep company questions; I was just describing a general impression I''ve gained from questions posted on forums. You seem to have interpreted my comments as an indictment of one particular company, and I meant no such implication.
...”



Ian Stewart
posted a reply to Is 0 a multiple of all numbers?
in the Problem Solving forum
“I think that''s overstating things. In practice, I find official GMAT questions almost never test exceptional properties of zero, and in cases where zero might act as some kind of exception, official questions usually go to great lengths to rule zero out from consideration. Prep company questions, ...”






Ian Stewart
posted a reply to Divisibility Problem
in the Data Sufficiency forum
“That''s not quite right. If x + y is greater than x^2 + y^2, then it''s certainly true that *one of* x or y is between 0 and 1. They do not both need to be between 0 and 1; it might be that x = 1/2, and y = 11/10, for example.
Still, as long as we know that one of our two letters is between 0 ...”



Ian Stewart
posted a reply to gmat club DS
in the Data Sufficiency forum
“If you read the instructions given for DS on the GMAT, you''ll see:
NOTE: In data sufficiency problems that ask for the value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for the quantity.
So if a DS question ...”



Ian Stewart
posted a reply to Divisibility Problem
in the Data Sufficiency forum
“If these properties are unfamiliar, it''s best to explore them first using specific numerical examples, since the ''proofs'' are a bit abstract. But we can see why all of the above facts are true algebraically. First, if you add or subtract two multiples of, say, 7, you must get a multiple of 7. ...”



Ian Stewart
posted a reply to X, Y positive??
in the Data Sufficiency forum
“From Statement 1, x = y + 1/2, which tells us nothing about the signs of x and y. We do, however, learn that x > y.
From Statement 2, we know that x and y share the same sign, but both could be negative or both could be positive.
With both statements, we know from Statement 1 that x > y. ...”



Ian Stewart
posted a reply to How many odd threedigit integers....
in the Problem Solving forum
“If our number is between 800 and 899, we have 5 choices for the units digit, since it must be odd. Now, the tens digit cannot be the same as the units digit and also cannot be the same as the hundreds digit, so there are 8 remaining choices for the tens digit. There are thus 5*8 = 40 odd numbers ...”



Ian Stewart
posted a reply to odds and evens  WOW.
in the Problem Solving forum
“a  c + b is even, and d + b  a is odd, so if we subtract the first expression from the second expression, the result must be odd:
d + b  a  (a  c + b) = d + b  a  a + c  b = c + d  2a
So c + d  2a is odd. Since 2a is even, c + d must therefore be odd.”






Ian Stewart
posted a reply to Option B or Option D?
in the GMAT Strategy forum
“I checked a set of about 600 official GMAT Quant questions, and statistically no answer choice is correct more often than another; each is correct 20% of the time. There''s also an official GMAC report that says that they control for answer position. So to answer your question, no, B and D are no ...”



Ian Stewart
posted a reply to Reply, with as many solutions as possible!
in the Problem Solving forum
“Again, since you want additional approaches (the ones Ashley suggests are perfectly good, and are most likely what I''d use), you can also estimate here easily enough. We''re adding roughly half of the numbers from 100 to 300, so we''re adding roughly 100 numbers with an average of 200, so the sum ...”






Ian Stewart
posted a reply to I need many ways for this one too!
in the Problem Solving forum
“I''d probably just solve this algebraically, but since you asked for alternative approaches:
* when you plug in x=0, the answer needs to be 60
* when you plug in x=100, the answer needs to be 40
* now, that gets you down to C or E. Average speed is a weighted average, but it''s weighted by ...”



Ian Stewart
posted a reply to Veritas Prep Challenge Question
in the Critical Reasoning forum
“A and D are not the same, I don''t agree with the interpretations above about the usefulness of D. D certainly is useful, because it is possible that some people are not able to swim, run or cycle (perhaps because of some medical issue), but are still able to use the Fitness game. Thus, the answer ...”



Ian Stewart
posted a reply to Need expert help :( (I am a bit confused)
in the Critical Reasoning forum
“Cause/Effect statements can be rephrased as conditional statements. When I say that "X (always) causes Y", I''m saying that "if X happens, Y happens", or "if X is true, then Y will be true".
Voodoo, I think part of the issue here is that you need to distinguish ...”



Ian Stewart
posted a reply to Need expert help :( (I am a bit confused)
in the Critical Reasoning forum
“I find the discussion you''re quoting pretty misleading. Modifying the example you quote above, imagine the following dialogue: "If I turn my cell phone on during a flight, that will cause the plane to crash." "How do you know that?" "Because I kept my cell phone off the ...”



Ian Stewart
posted a reply to Need expert help :( (I am a bit confused)
in the Critical Reasoning forum
“A few things here:
I don''t recommend learning formal logic for the GMAT. It is not explicitly tested, and it can lead to a lot of confusions. Some of the ideas we express in words, like ''smoking causes cancer'', need to be rephrased more precisely if you want to express them in formal logic. ...”






Ian Stewart
posted a reply to Tough Kaplan DS
in the Data Sufficiency forum
“They are very clearly *supposed* to be exponents. The question is pretty much pointless unless the letters are exponents, since if they are not exponents, the answer obviously has to be E. There would also be no reason at all to intermingle letters and numbers as written (no mathematician would ever ...”






Ian Stewart
posted a reply to Is the positive integer z a prime number
in the Data Sufficiency forum
“Statement 1 is not sufficient; if y is 9, then z could be 3 or 9, so z could be prime or not.
Does Statement 2 say ''unique factors'', or ''unique prime factors''? If the question only says ''unique factors'' in Statement 2, then Statement 2 is sufficient alone. Perfect squares must have an odd ...”



Ian Stewart
posted a reply to Chris tosses all his spare change
in the Data Sufficiency forum
“You know the ratio of coins of each type, so if you know the total number of coins, you can then find the number of coins of each type, so statement 1 has to be sufficient. If you actually needed to find the answer (it''s DS, so you don''t, but if it were PS), if the ratio of pennies to nickels to ...”



Ian Stewart
posted a reply to Remainder when x cube divided by 3
in the Data Sufficiency forum
“I assume the question should read: What is the remainder when x^3 is divided by 10?
When you divide a positive integer by 10, the remainder is just the number''s units digit. So the question is just asking for the units digit of x^3.
Even using both statements, x could be 15, and x^3 will ...”



Ian Stewart
posted a reply to What's the best score possible after being penalized?
in the GMAT Strategy forum
“The only specific comment I''ve seen from official reports about the penalty for leaving questions unanswered is that the penalty is ''proportional''. But I haven''t read anywhere just how that ''proportional'' penalty is applied. If it''s applied to the scaled score, then if you had answered 21 out ...”



Ian Stewart
posted a reply to Standard Dev
in the Problem Solving forum
“I think I''ve asked you this a few times in other threads, but where are these questions from?
The wording here is pretty bad. What they mean to say is that, for each value y_k in the second set, b*y_k = a*x_k  c, so y_k = (a/b)*x_k  c. That is, to get the values in the second set, we take ...”



Ian Stewart
posted a reply to Combo/Perm PS and veritas teacher response
in the Problem Solving forum
“If, on a GMAT counting problem, you''re just plugging the numbers in the question into some formula, you''re going to get almost every question wrong.
Here, the test taker makes a sequence of choices. When you want to count how many different sequences of choices are possible, you multiply the ...”



Ian Stewart
posted a reply to Coordinate Geometry Data Sufficiency Problem
in the Data Sufficiency forum
“That solution relies on a knowledge of coordinate geometry far beyond what you need on the GMAT.
In this question, we are asked about yintercepts. To find yintercepts, we plug in x=0. So we want to know if there are any solutions to
(0  a)^2 + (y  b)^2 = 16
a^2 + (y  b)^2 = 16
...”



Ian Stewart
posted a reply to Teacher
in the Critical Reasoning forum
“While I agree with the expert assessments above, I don''t care for the question. What is the source? The fact that "the evidence shows that more than 92% of the female students" should have passed *does* give reason to believe the female students were graded too harshly. But that alone is ...”



Ian Stewart
posted a reply to Simple Strategy Question
in the Problem Solving forum
“If you need to do any arithmetic (especially any division or multiplication), you''d always want to use the expression ''16/3'', and not ''5 1/3'', unless you''re only concerned with getting an estimate. I can''t see how you''d easily go about dividing, say, 5 1/3 by 7 1/5, but if you write those ...”



Ian Stewart
posted a reply to Absolute Question
in the Data Sufficiency forum
“Statement 1 is almost sufficient, but not quite: M can be negative (as explained in the post above), as required, or M can be 0. We need Statement 2 to ensure that M is not zero, so the answer is C.”



Ian Stewart
posted a reply to frequency distribution
in the Data Sufficiency forum
“I''ve never seen a real GMAT question which abstractly discussed a ''random variable'', or which provided a frequency table that didn''t include whole numbers, so this probably isn''t an important example to study. The table above is just another way of saying that 18% of the values in your set are ...”



Ian Stewart
posted a reply to Divisibility Problem
in the Data Sufficiency forum
“If you add or subtract two integers a and b, and the result is divisible by 3, there are two possibilities: either a and b are *both* divisible by 3, or a and b are *both* not divisible by 3. If one of a or b is divisible by 3, and the other is not, you will never get a multiple of 3 when you add or ...”



Ian Stewart
posted a reply to Necklace
in the Problem Solving forum
“I have an issue with the wording of the question. Necklaces are circular; how can you identify where the pattern of beads begins, if there is no ''first bead'' in a circular pattern? The question designer ought to have found a different setup in which the pattern is in a line or a row, rather than ...”



Ian Stewart
posted a reply to Starting out on a 1 month prep for the GMAT. Target: 750
in the GMAT Strategy forum
“A few points here:
* The fact that someone has plagiarized official questions and distributed an illegal document over the web containing those questions is hardly grounds for complaint against GMAC. Nor is it reason to object to anything David has said;
* I cannot find any claim from GMAC ...”



Ian Stewart
posted a reply to Remainders
in the Problem Solving forum
“These questions test principles of modular arithmetic, which is beyond the scope of the GMAT, so test takers reading this  you can move on.
The solutions above are perfect, except for the last step in the first problem:
Since the pattern repeats in ''blocks of 3'', 4444^3, 4444^6, ...”



Ian Stewart
posted a reply to Prime Factor
in the Problem Solving forum
“There''s no way to factor that expression (beyond applying a Difference of Squares once), so there is no way to answer the question without a computer, unless you can somehow use process of elimination with the answer choices. Where is the question from, and what answer choices are given?
There ...”






Ian Stewart
posted a reply to square roots, etc: how many are essential to know?
in the GMAT Math forum
“The GMAT is not a test of whether you are a human calculator, so the answer is ''not many''. Most prep books recommend memorizing far more than is actually ever useful. You certainly want to know your multiplication table up to 12x12, perfect squares up to 15^2, perfect cubes up to 6^3, and the ...”



Ian Stewart
posted a reply to Word prob
in the Data Sufficiency forum
“You need to understand perfectly just what you''re doing when you plug numbers into a DS question. If you plug in numbers, of course you are going to get *some* answer to the question. If, when evaluating Statement 1, you plug in x=60 and y=40 here, you find that the rent is lower in 1999. *All* you ...”



Ian Stewart
posted a reply to Number of subway riders
in the Critical Reasoning forum
“I posted a reply about this question on gmatclub, so I''ll just copy an edited version here:
_______
I don''t think this is a good question at all; I can justify almost all of the answer choices by making appropriate assumptions, yet can justify none of them without making assumptions.
...”



Ian Stewart
posted a reply to Conflicting DS statements  Quant Edition 2 Q92
in the Data Sufficiency forum
“Oh I see now what you were doing. It''s this assumption which is wrong. Some employees might never have gone to college, some employees might have only an undergraduate degree, and some employees may have a Master''s degree. The 50% who are college graduates *includes* the people who have Master''s ...”



Ian Stewart
posted a reply to Are there not enough difficult CR questions in OG?
in the GMAT Strategy forum
“I only teach high level Quant these days, so I''m not the best person to ask about Verbal resources. I''ve generally disliked the approach to CR taken by every book I''ve read (I particularly dislike the distinction books draw among Assumption, Strengthen and Weaken questions, since in each case ...”



Ian Stewart
posted a reply to Conflicting DS statements  Quant Edition 2 Q92
in the Data Sufficiency forum
“I''ve highlighted the two parts of your reasoning that I don''t follow. In the red portion, you say that ''42% of employees are over 40 and do not have Master''s degrees'' and from that conclude that "8 percent are over 40 and DO NOT have master degree." We''ve just established that 42% ...”



Ian Stewart
posted a reply to Conflicting DS statements  Quant Edition 2 Q92
in the Data Sufficiency forum
“You won''t find a single example of a question with conflicting statements in either Official Guide; if you think you''ve found such a question, you''ve made some kind of mistake. I don''t know how you arrived at the ''32%'' figure, but it is not right; there is nothing in the stem alone that lets ...”



Ian Stewart
posted a reply to Equality/Nonequality
in the Data Sufficiency forum
“The question doesn''t really make sense (the ''if'' clauses in each statement are something you would never see on the GMAT), but regardless the answer certainly is not C.
From Statement 1, we know that if p=2, the answer to the question is ''no. But we don''t know that p equals 2 at all; ...”



Ian Stewart
posted a reply to How to tell if a number is divisible by 7?
in the GMAT Math forum
“There are divisibility ''tricks'' for all kinds of numbers, but many of them are awkward to apply. The only ones I''ve ever found useful on GMAT questions are the ''tricks'' for 2, 3, 5 and multiples of those primes (4, 9, 10, etc).
While there is certainly no harm in knowing a ''trick'' for ...”



Ian Stewart
posted a reply to Are there not enough difficult CR questions in OG?
in the GMAT Strategy forum
“I don''t think CR is any different from any other question type in the OG; the questions in the book span all difficulty levels, so the vast majority are below the 800level. That said, if you answered 120 correctly out of 124, that''s certainly an outstanding result.
In general, I find GMATPrep ...”



Ian Stewart
posted a reply to Master Gmat  Allincluded tour package brochure
in the Critical Reasoning forum
“You could make Sentence Correction questions out of most of the sentences above. For example:
"A marketing investigation shows that while more costly, tourists electing the "inexpensive" option ... "
Clearly the tourists are not ''more costly'' than something else, which ...”



Ian Stewart
posted a reply to ogds 125
in the Data Sufficiency forum
“That question doesn''t make sense as a DS question. Clearly n^2 is not equal to n "for all values of n", so you wouldn''t need any statements to answer the question. Statement 1 then tells us we''re not concerned with "all values of n", but rather only with integer values of n, ...”



Ian Stewart
posted a reply to GMAT scoring change?
in the I just Beat The GMAT! forum
“First, don''t trust any ''online scoring calculators''; none of them are right. They will give decent estimates, but will often be wrong by 1020 points.
Second, I''ve seen several cases where two test takers have the same scaled scores, but have a 10point difference in their /800 score, and ...”



Ian Stewart
posted a reply to DS
in the Data Sufficiency forum
“This is the kind of prep company question I hate, because it misleads test takers about what is tested on the GMAT. On the GMAT, ratios always only involve positive quantities. If the question designer wanted to allow for negative values of x and y, he or she should not have used the word ''ratio'' ...”



Ian Stewart
posted a reply to CAT question  Why is Verbal so Low?
in the GMAT Strategy forum
“I won''t give any specific advice, since without knowing your strengths and weaknesses, I wouldn''t be sure the advice would be suitable. But speaking generally about the test:
* when comparing Verbal and Quant scores, as David stressed, look at your percentiles, not the raw scores. Raw scores ...”



Ian Stewart
posted a reply to Leaving questions unanswered..
in the GMAT Strategy forum
“The only official data I''ve seen about the number of experimental questions on the test said that there will be between 7 and 14 experimental questions in each section. I''m guessing the number is higher in the Verbal section than in the Quant, if only because that section is longer, but I don''t ...”



Ian Stewart
posted a reply to deck of cards
in the Problem Solving forum
“The issue is that you''re not counting all of the ways you might get exactly one pair, or two pairs. When you calculate:
you are assuming that the 1st and 2nd cards are pairs, and that the 3rd and 4th cards are paired. There are other possibilities  it might be that the 1st and 3rd cards are ...”



Ian Stewart
posted a reply to CAT question  Why is Verbal so Low?
in the GMAT Strategy forum
“Don''t compare Verbal and Quant scaled scores directly. Verbal scores are *much* lower than Quant scores, generally. To know how good you are in each section, convert your scores to percentiles using the tables at the back of OG12. A 41 Verbal score is outstanding. A 44 Quant is certainly good, but ...”



Ian Stewart
posted a reply to Median
in the Problem Solving forum
“You can''t answer the question. If in the first set of numbers, everything is equal to 88, and in the second set everything is equal to 92, then our median will be 92 when we combine the two sets. If, on the other hand, in the first set everything is equal to 88 and in the second set half our values ...”






Ian Stewart
posted a reply to Is p divisible by 168?
in the Data Sufficiency forum
“You''ll probably find, after doing a lot of practice in this area (which you should do  it''s crucially important on the GMAT) that this becomes almost instinctual. For now, I can suggest you try two things:
* If you can rephrase what you want to find as "something per something ...”



Ian Stewart
posted a reply to Absolute
in the Problem Solving forum
“I don''t understand the question. What is the point of mentioning x at all here if x isn''t part of the expression we need to evaluate?
In any case the absolute value of 2.4 is equal to 2.4, so
2.4 + 4.4 = 2.4 + 4.4 = 6.8
edit: I think, in the first part of the question, they are ...”



Ian Stewart
posted a reply to Combi
in the Problem Solving forum
“I discussed this question on another forum recently in a thread with a few questions from the same source, so I''ll cut and paste the relevant portions. Apparently the source thinks the answer ought to be 12 to this question, which they arrive at by adding the number of choices from each university ...”



Ian Stewart
posted a reply to Is p divisible by 168?
in the Data Sufficiency forum
“You''re answering the opposite question to what''s being asked. You''re (correctly) answering the question:
Is positive integer x a divisor of 24?
1. x is a divisor of 4
2. x is a divisor of 6
In this case, each Statement is sufficient  from Statement 1, x can only be 1, 2 or 4, and from ...”



Ian Stewart
posted a reply to Challenging CR
in the Critical Reasoning forum
“"Weaken" does *not* mean the same thing as "disprove". That''s crucially important in GMAT CR. Here we need an answer which suggests that the conclusion might not be true. We do *not* need an answer which *proves* the conclusion is false.
A is not correct, since it''s talking ...”



Ian Stewart
posted a reply to Tough algebra Equation
in the Problem Solving forum
“[quote="wieke13"][
Ian,
Can I ask you, how do I get from 0 < 20  k < k  10 to 15 < k < 20?
Sorry, I don''t get it..
/quote]
You can see this by separating the threepart inequality 0 < 20  k < k  10 into two inequalities:
0 < 20  k, and adding k to ...”



Ian Stewart
posted a reply to Check this one out
in the Data Sufficiency forum
“Sure, it''s ''very hard'', because it''s impossible to tell what it means. It''s easy to invent ''very hard'' problems  for example, I could ask "What prime number am I thinking of?" That''s a hard problem for anyone (but me) to get right, but it''s certainly not a good practice problem. ...”



Ian Stewart
posted a reply to Educated Guess
in the GMAT Strategy forum
“I think this is the conclusion we all agree on: if you''re guessing, guess *quickly*. That said, if by spending 15 seconds you can eliminate 2 or 3 wrong answer choices, that is surely time well spent. If you''d need to spend 2 minutes to do that, that''s a huge waste of time, since 2 minutes spent ...”



Ian Stewart
posted a reply to Confusing Strengthen Question
in the Critical Reasoning forum
“This is a question about cause and effect. The stem suggests that smoking leads to depression. Isn''t the reverse equally possible  that depression leads people to start smoking? We need to eliminate that second possibility to strengthen the argument, which is what A does.”



Ian Stewart
posted a reply to 0^0
in the Problem Solving forum
“If you read that text, it makes clear there no universally agreed view on the value of 0^0. If 0^0 were defined to have a value, then the value 1 makes the most sense, but there are equally good reasons for declaring 0^0 to be an undefined quantity. Regardless, on the GMAT it doesn''t matter  ...”



Ian Stewart
posted a reply to Educated Guess
in the GMAT Strategy forum
“You''ll read a lot about guessing strategies in various prep books  some prep companies seem to focus more on guessing strategies than on actual content. I''ve done a lot of research into the effectiveness of some of the guessing strategies I''ve seen in print, and I''ve come to the conclusion that ...”



Ian Stewart
posted a reply to Accuracy of Knewton CATs
in the GMAT Strategy forum
“I wouldn''t want to comment on the integrity of any individual company''s scoring algorithm, so I''m just speaking generally about GMATstyle scoring algorithms. If a test is full of hard questions, you can make several mistakes and still get a good score. If, on the other hand, a test is full of ...”



Ian Stewart
posted a reply to GMATPrep  please advise
in the GMAT Strategy forum
“Brent''s post above is (as always) very good advice. To the reasons he outlines for taking a prep test early on, I''d add that you want to know the balance of your Quant and Verbal skills to apportion your study time most effectively. Verbal scores are much lower, on average, than Quant scores, so ...”



Ian Stewart
posted a reply to Leaving questions unanswered..
in the GMAT Strategy forum
“As best as I could determine from the GMAC reports on scoring, the penalty for unanswered questions is proportional  that is, for each unanswered question your score estimate is reduced by a factor of 1/37. However, their reports aren''t completely clear on just how this proportional penalty works, ...”



Ian Stewart
posted a reply to 0^0
in the Problem Solving forum
“0^0 is not defined, for the reason you point out: for positive values of x, x^0 is always equal to 1, but 0^x is always equal to 0, so there''s no way to define a value of 0^0 that will make sense. On official questions, you''ll never need to consider what 0^0 is; the question will always give ...”






Ian Stewart
posted a reply to GMAT Prep  Factors
in the Problem Solving forum
“I don''t think there is any quicker way than testing values here, but fortunately 75 is small enough that we can arrive at an answer within two minutes. I''d start by looking at the squares closest to 75, since that will narrow down our possibilities most quickly. We know a^2 + b^2 + c^2 = 75. First ...”



Ian Stewart
posted a reply to Check this one out
in the Data Sufficiency forum
“This question makes no logical sense. From Statement 1, we learn that there are some restrictions on what n can be, but we have no idea if these are the *only* restrictions on the value of n. If they are, of course you can count how many n there are. If they are not, then of course you can''t ...”



Ian Stewart
posted a reply to DSsequence and series
in the Data Sufficiency forum
“All Statement 1 tells you is that the first four terms are 4, 9, 16 and 25. Statement 1 tells you nothing about how the sequence continues beyond the fourth term. The sequence might, for example, be a ''looping'' sequence like the following:
4, 9, 16, 25, 4, 9, 16, 25, 4, 9, 16, 25, ...
or of ...”



Ian Stewart
posted a reply to Factor
in the Problem Solving forum
“Where is the question from? First, you wouldn''t need to prime factorize a number as awkward as 7056 on the GMAT. Second, while we can prime factorize to get:
7056 = (2^4)(3^2)(7^2)
and then adding 1 to each power and multiplying, determine that 7056 has (5)(3)(3) = 45 distinct positive ...”



Ian Stewart
posted a reply to Some clarification
in the GMAT Math forum
“I answered this question here:
www.beatthegmat.com/dsquestionsonprobabilityt85649.html
The answer would be 1, or 100%  with more students than numbers to pick, two students simply must pick the same number.”



Ian Stewart
posted a reply to Concern with this problem
in the Data Sufficiency forum
“As the question is worded, the answer is definitely E. While we know the elements in the set A are divisible by 2, that does *not* mean that every multiple of 2 is in set A. The set might be {2}, or it might be {2, 10}, or it might be {2, 10, 14}, among many other possibilities. If the question ...”






Ian Stewart
posted a reply to combinatorics and probability
in the GMAT Math forum
“I had exactly one question on probability and counting on my last real GMAT, and it was a completely standard question. There is a myth that probability and counting is somehow more heavily tested at the higher level of the GMAT. It''s not; probability and counting questions can be easy, or they can ...”



Ian Stewart
posted a reply to Is it good to purposely answer incorrectly at the beginning?
in the GMAT Math forum
“If you''re well above average in Quant, then the questions early in your test are much more likely to be easy/medium than the questions later in your test, assuming you proceed normally through the test. The key point about GMAT scoring, which David mentioned above, is this:
* it hurts you *a ...”



Ian Stewart
posted a reply to Series
in the Problem Solving forum
“Yes, Frankenstein is right  you have *no* information in the question about how the sequence progresses beyond the first four terms, so it is absolutely impossible to answer the question. I suspect that Frankenstein is right, and the question means to ask about a Fibonacci type sequence  something ...”






Ian Stewart
posted a reply to DS Questions on probability
in the Data Sufficiency forum
“First, if P(Alex) is 0.7, then P(Alex)*P(Arif) is less than or equal to 0.7, since P(Arif) is at most 1. So we don''t need both statements here.
Second, it''s not at all clear that our events are independent, so it is not clear that we can even multiply our probabilities here. Maybe Arif and Alex ...”



Ian Stewart
posted a reply to DS Questions on probability
in the Data Sufficiency forum
“You can''t dismiss Statement 2 so quickly here. If 7 of the balls are blue, then we have at most 5 red balls. If we have 5 red balls, the maximum we could have, the probability we pick 4 red balls in 4 selections is:
(5/12)(4/11)(3/10)(2/9) = 1/99
That''s clearly less than 1/33, so we have ...”



Ian Stewart
posted a reply to DS Questions on probability
in the Data Sufficiency forum
“If the probability that Alex is present is 0.7, then the probability Alex and someone else are both present can''t be more than 0.7, so Statement 1 is sufficient. Statement 2 is not, since it may be that the probability is 1 that Alex is present (in which case the probability would be 0.8 both are ...”



Ian Stewart
posted a reply to DS Questions on probability
in the Data Sufficiency forum
“If there are more than 20 students, then two students must have picked the same number (since even if the first 20 students all pick a different number, the 21st student will have to pick a number which is the same as one that''s already been chosen). So if there are more than 20 students, the ...”



Ian Stewart
posted a reply to Cricketers
in the Critical Reasoning forum
“This question isn''t even in English. The sentence "The presenter of this argument has raised a justifiable objection for all possible reasons" is completely meaningless. The word "70s" should have ''the'' in front of it; "it''s" should not have an apostrophe; etc, etc, ...”



Ian Stewart
posted a reply to OG10 inference  expert comment please
in the Critical Reasoning forum
“Answer D doesn''t even talk about the *proportion* of collisions in each country  it talks about the absolute *number* of collisions in each country. Surely there are all kinds of factors besides headlight laws that determine the *number* of collisions each year in a country  the number of cars ...”



Ian Stewart
posted a reply to CR Music Industry
in the Critical Reasoning forum
“I just replied to this very question at gmatclub, so I might as well paste my reply here:
This is a very subtle question  if you don''t read the wording extremely carefully, it''s easy to be tempted by a few of the answer choices. The key point to notice here is that we are concerned with ...”



Ian Stewart
posted a reply to Best "plugins" for inequality questions?
in the Problem Solving forum
“It really depends on the type of question you''re looking at. A lot of different situations can crop up in GMAT inequality questions, so it''s impossible to list any numberpicking rules that will be applicable to every question. In general, most inequality questions hinge on negatives and ...”



Ian Stewart
posted a reply to Function
in the Problem Solving forum
“This is miles away from being a realistic GMAT question. You will *never* be tested on sums of infinite series on the GMAT, nor do you need to know what it means for a series to be ''convergent''. If the author of your prep material thinks this is a realistic practice question, he or she doesn''t ...”






Ian Stewart
posted a reply to Cricket tournament
in the Problem Solving forum
“No, you''d never see such a question on the GMAT. The test is very carefully edited to ensure it is fair to all test takers. When they include a question as an experimental question on the GMAT, one of the things they are looking at is whether the question is ''biased''. If a question is, say, very ...”



Ian Stewart
posted a reply to remainder
in the Problem Solving forum
“As Frankenstein pointed out above, if you''re dividing some integer n by an even number like 18 and your remainder is odd, then n must be odd. So 3013 is the only possible answer choice. There''s really no reason to do any work here.
There is a lot of very bad GMAT material on the internet. ...”



Ian Stewart
posted a reply to Are Variance questions tested on the GMAT ?
in the Problem Solving forum
“I have seen one, and only one, official question which mentions variance (and I''ve probably seen somewhere between 5000 and 10,000 official questions by now). That question is in the diagnostic test at the start of OG12. For that question, you only need to know that you can find the standard ...”



Ian Stewart
posted a reply to Is Y odd?
in the Data Sufficiency forum
“Whenever one statement is sufficient alone, it will, of course, *always* be possible to answer the question using both statements; after all, you''re then using the statement that was sufficient on its own in addition to the information in the other statement. It is crucially important to understand ...”



Ian Stewart
posted a reply to Remainder when dividing negative numbers
in the Problem Solving forum
“Remainders, by definition, are *never* negative. If you are dividing by 6, for example, there are only six possible remainders: 0, 1, 2, 3, 4 or 5.
If you want to understand what the remainder would be when you divide, say, 7 by 6, we can first see how we find remainders with positive numbers. ...”



Ian Stewart
posted a reply to Cards
in the Problem Solving forum
“Yes, four Aces, four Kings, four Queens and four Jacks, so the answer would be 16/52 = 4/13. Fortunately you don''t need to know anything at all about standard decks of cards for the GMAT.”



Ian Stewart
posted a reply to Probability.
in the Problem Solving forum
“The probability that we don''t get a 3 on the die is 5/6, and the probability we don''t get Heads is 1/2, so the probability neither event happens is (1/2)(5/6) = 5/12. Thus the probability one or both events happen is 1  5/12 = 7/12.”



Ian Stewart
posted a reply to MGMAT Problem (Advanced Quant)
in the Data Sufficiency forum
“I wasn''t giving every solution to the equation; I was only proving the statement is not sufficient. To do that, we just need one example which gives a ''yes'' answer to the question, and one which gives a ''no'' answer. There are lots of other examples I could have chosen, but 1 and 1 seemed the ...”



Ian Stewart
posted a reply to Probability
in the Problem Solving forum
“It''s not clear what the question means. When we get the ''same thing'' each time, is that the thing with the probability of 0.4? Then we just have a sequence of events where we want a certain result each time, so we multiply the probability for each event: the answer would be (0.4)(0.4)(0.4)(0.4) = ...”



Ian Stewart
posted a reply to Know the answer?
in the Problem Solving forum
“First it''s not a clearly worded question. If the apples are all identical and the oranges are all identical, the answer is just 2  the ordering either starts with an apple or starts with an orange, and the rest of the slots are then determined.
If the apples and oranges are all different, we ...”

