
Ian Stewart
posted a reply to If the positive integer x divisible by 200?
in the Data Sufficiency forum
“If we prime factorize everything:
The question asks if x is divisible by 2^3 * 5^2
From S1: x^2 is divisible by 2^3 * 5^4. For x^2 to be divisible by 2^3, it will need to be true that x itself is divisible by at least 2^2, since if x were only divisible by 2^1, then x^2 would only be divisible ...”



Ian Stewart
posted a reply to A number when divided successively by 4 and 5 leaves
in the Problem Solving forum
“The question means something different from what it actually says, but I can guess what it''s trying to say.
When we take our number, "n", and divide it by 4, we get a remainder of 1. So n is exactly 1 greater than some multiple of 4, and we have:
n = 4q + 1
It''s here where the ...”


















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 ...”



Stuart Kovinsky
posted a reply to Probability
in the Problem Solving forum
“Many probability questions can be solved intuitively rather than with long calculations. Let''s try to do so with this problem!
We can get off to a great start by flipping around the question: what''s the probability that Sally sits beside Andy?
We know that it has to go BGBGBGBGB. We can ...”



Stuart Kovinsky
posted a reply to Researchers
in the Sentence Correction forum
“One more approach!
The word "ancient" is a present use word  in other words, something is ancient from today''s perspective.
Accordingly, if we''re talking about a present discovery, we don''t say "what appeared to be an ancient hunting ground"; instead, we say "what ...”



Stuart Kovinsky
posted a reply to MGMAT Advanced Quant Visual Ques.
in the Problem Solving forum
“Hi Bharat!
Let''s start by breaking down the info  there''s actually a lot more there than you may think!
Possible scores are the integers 0 to 50, inclusive  that''s 51 possible scores.
100 people take the test.
At most, 2 people can get the same score.
Let''s assume for a moment that ...”



Stuart Kovinsky
posted a reply to Skeletal Heat
in the Critical Reasoning forum
“Hi Sid,
you''ll find some decent free resources on the net, you just have to be really careful. I''d always look for reviews of the source before diving in and using its questions. For all you know, those free questions were written by some bored guy living in his mom''s basement!
Depending ...”



Stuart Kovinsky
posted a reply to Combinatorics: Solution Explanation
in the Problem Solving forum
“Hi Dbloos!
That answer is in fact correct.
Here''s another way of looking at it: 2 out of the 14 patients will be chosen to receive P or R. Since the selection is random, each patient has a 2/14 chance of being one of the two.
We can confirm this answer with common sense (a very powerful ...”



Stuart Kovinsky
posted a reply to Samuel's Fishing Dilemma
in the Critical Reasoning forum
“Hi Siddhu,
a quick Google search reveals that this is yet another Platinum GMAT question, so it''s not surprising that it''s poorly constructed.
The problem here is different  there are 3 valid weakeners among the choices. So, instead of no good answer (like the previous Platinum GMAT ...”



Stuart Kovinsky
posted a reply to ENews Ads
in the Critical Reasoning forum
“Hi Siddhu!
This is another Platinum GMAT question  I''ve only seen 2 and I''m already superunimpressed.
There is no great weakener among the choices. For (C) to be relevant, we have to assume that "partners" means "people visiting one website will be faced with the same ...”



Stuart Kovinsky
posted a reply to Skeletal Heat
in the Critical Reasoning forum
“Hi Siddhu,
please always post your sources. A quick search of the Oracle (i.e. Google) revealed that this a question from Platinum GMAT, of whom I''ve never before heard.
This is a horrible question. None of the answers explain the paradox and, while a couple are classic traps, there is no ...”



Stuart Kovinsky
posted a reply to Dice
in the Problem Solving forum
“Hi Nipun!
The problem with treating this like a permutations problem  which is when you''d simply do 6*5*4  is that we don''t care about order, so you''re counting certain combinations multiple times.
For example, the 3 dice could come up as a 5, a 4 and a 3. However, they could also come ...”



Stuart Kovinsky
posted a reply to Quicker + alternate methods
in the Problem Solving forum
“Hi!
No such general formula exists  that pattern comes from an old GMAT question that gave you that summation as a rule to help you answer that one specific question. Whoever put it on a flashcard managed to confuse a whole bunch of people, though (which is why you should be very wary of ...”



Stuart Kovinsky
posted a reply to tenth digit in decimal representation
in the Data Sufficiency forum
“Hi! I''m assuming that this last part in quotes is your actually comment/question.
It''s important to know the place names for the various digits in a numbers, so let''s do a quick review, using the example of:
12345.6789
We start numbering to the left and the right of the decimal place. ...”



Stuart Kovinsky
posted a reply to MGMAT CAT Esteria vs Burdistan
in the Critical Reasoning forum
“Hi Julls!
This argument is a classic example of the most common pattern we see in critical reasoning: causation.
In a causal argument, the evidence describes some phenomenon and the conclusion is the author''s explanation for that phenomenon. In every causal argument, the author makes 3 ...”






Stuart Kovinsky
posted a reply to Lanuguages
in the Sentence Correction forum
“Hi!
I''ve bolded the part of the sentence relevant to your question.
Since we have "a language" in the nonunderlined part, "within it" is correct.
Also, it''s idiomatically correct to say "a dialect within a language", if that''s your main question. You could ...”



Stuart Kovinsky
posted a reply to To find the total amount of water in 3 glasses
in the Problem Solving forum
“Hi!
Uva did a great job saying what you could do next, so I want to discuss what you could have done instead  everyone taking the GMAT should strive to follow the Lazy Testtaker Rule: Do the least amount of work possible to answer each question.
On questions that ask you to find a range, ...”



Stuart Kovinsky
posted a reply to Integer Properties
in the Data Sufficiency forum
“I''m going to almost agree with Vipulgoyal, but say that the answer should be "C", together.
Also, I''m assuming that the question was correctly transcribed and the "different" wasn''t omitted from "does m have more than 5 prime factors"?
Since the Q stem omits ...”



Stuart Kovinsky
posted a reply to To find the average speed
in the Data Sufficiency forum
“Hi Sri!
You''ve assumed that the car''s speed is constant  which is exactly what the question is designed to trick you into assuming!
Remember: on the GMAT we only know what we''re explicitly told. Since we don''t know whether the car is travelling at a constant speed, there''s no way we ...”



Stuart Kovinsky
posted a reply to Rate Problem
in the Problem Solving forum
“Hi!
You haven''t provided any answer choices, so I''m a bit confused  is this a problem solving or a data sufficiency question?
You said that the OA is "6", but since we only have variables, how can the answer be an actual number?
Your equation for time to catch up is dead on, ...”



Stuart Kovinsky
posted a reply to Combinatorics.Plese help.
in the Problem Solving forum
“All you''re really doing when you apply the "slot method" to these problem is using the combinations formula:
nCk = n!/k!(nk)!
When order does NOT matter, that''s the formula we use.
So, if we''re simply choosing 4 out of 7 and we don''t care about order, we get:
7C4 = 7!/4!3! ...”



Stuart Kovinsky
posted a reply to What is the remainder?
in the Data Sufficiency forum
“Hi Sri!
For remainder questions, we often only need to look at the last 1 or 2 digits of the number. In this case, since we''re dividing by 5, only the last digit actually matters.
So, we can recognize the pattern for powers of 2:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = ..6
2^5 = ..2
and so ...”



Stuart Kovinsky
posted a reply to Need help on Percentage Question
in the Problem Solving forum
“Hi Scraby!
First, please always post the answer choices, since they play a large role in many GMAT strategies. On this question, for example, backsolving (working backwards from the choices) is almost certainly the quickest way to get the answer.
Let''s approach it via both algebra and ...”



Stuart Kovinsky
posted a reply to Most interns who work for pay hold positions...
in the Sentence Correction forum
“Hi!
This sentence is all about parallelism.
When we have a list, we have to make sure that all the parts are stated correctly. When each part of the list has the same modifier, you can just put that modifier at the beginning of the list. However, when different parts require different ...”



Stuart Kovinsky
posted a reply to What is the value of x  y ?
in the Data Sufficiency forum
“Hi Sri!
We know that both x and y are positive and that x is greater than y. We need to find an exact value for (xy).
1) tells us that root(x)  root(y) = 1
If we square both sides, we get:
(rootx  rooty)^2 = 1
x  2root(xy)  y = 1
well, since have no clue what x and y are, ...”



Stuart Kovinsky
posted a reply to Combinatorics.Plese help.
in the Problem Solving forum
“When we''re counting we''re always dealing with whole numbers: for example, there are never going to be 3.5 possible groups. So, as soon as you get a fraction, you know there''s a problem.
The problem with the using the "slot method" is that you''ve treated 2 different selections as ...”



Stuart Kovinsky
posted a reply to Probabilit
in the Problem Solving forum
“Hi!
This may look like a probability question, but it''s really all about geometry. The question is really asking "what portion of ABCD is shaded?"
This question is super quick if you use your graphlined noteboard to draw the shape to scale  you''ll quickly see that the mini ...”



Stuart Kovinsky
posted a reply to Probability Again
in the Problem Solving forum
“Hi! This question is a great illustrator of the "one minus" approach to complicated probability problems.
When you see "at least" or "at most" in probability, you''re going to be solving for multiple scenarios. However, it''s often quicker to solve for what you do ...”






Stuart Kovinsky
posted a reply to Club members at least 35yrs old
in the Data Sufficiency forum
“Hi! We only care about at least 35 vs below 35, so "children" are irrelevant.
Q: how many members are 35 or older?
We think: value question asking us to solve for an actual number, so we need info about numbers!
1) nothing about actual numbers (i.e. just a fraction)  ...”



Stuart Kovinsky
posted a reply to Square Root of Variables
in the Problem Solving forum
“Hi!
First, the problem you posted doesn''t actually include a question, so I''m not sure for what you''re solving. In other words, you posted an equation, but no question.
However, I can still answer your question  the official answer you posted and your answer are actually identical.
We ...”



Stuart Kovinsky
posted a reply to Bank fees
in the Sentence Correction forum
“Hi Eric!
This sentence is all about proper verb tenses  one of the most commonly tested issues in sentence correction.
Remember to always use the nonunderlined portion of the sentence (which is, by definition, correct) to guide your selection for the underlined portion.
Here, as soon as ...”



Stuart Kovinsky
posted a reply to Auto company profits
in the Sentence Correction forum
“Hi Eric!
Recognizing common GMAT idioms can help you cut to the heart of a SC question and ignore all the "fluff" that the GMAT includes to distract you.
There are two important idioms to recognize in this argument.
First, we "attribute to". However, since every ...”



Stuart Kovinsky
posted a reply to Mall Occupancy
in the Critical Reasoning forum
“Hi Lula!
Anyone who wants to be a top scorer on the GMAT needs to learn to recognize common patterns. This argument exemplifies one such pattern in critical reasoning.
It''s common for authors to identify a problem and then propose a solution. It''s also common for authors to go one step ...”



Stuart Kovinsky
posted a reply to Number Line Data Sufficiency
in the Data Sufficiency forum
“Hi!
In geometry, whenever two points are put together like that, they always describe the line formed by connecting them. The same rule applies to number lines, which are really just a form of linear geometry.”



Stuart Kovinsky
posted a reply to Please can you explain the reasoning behind this?
in the Problem Solving forum
“Hi!
We''re told that x is positive and increasing and we''re asked to determine which of 3 expressions will increase along with x.
Here''s something to remember: the GMAT is not trying to be your friend, but it is trying to see how clever you are. So, we''re always using our cleverness to ...”



Stuart Kovinsky
posted a reply to Pls explain the calculation
in the Problem Solving forum
“Hi!
This question is testing your ability to find limits and estimate.
We''re told that K is the sum of the reciprocals of the integers 43 through 48, inclusive. In other words:
K = 1/43 + 1/44 + 1/45 + 1/46 + 1/47 + 1/48
well, that''s a whole mess of ugly math, so there''s got to be a ...”



Stuart Kovinsky
posted a reply to Data Sufficiency Qs
in the Problem Solving forum
“Hi!
What''s the source of this question? I''m asking because, technically, the 4 brothers could be quadruplets and all the same age. I really doubt that the question intends for that to be a possibility and the GMAT would never leave that ambiguity in place. Let''s assume that the question ...”



Stuart Kovinsky
posted a reply to Pls help with the solution
in the Problem Solving forum
“Hi!
First, I''m not sure if the image I uploaded will work  for some reason the IMG uploader isn''t giving me any love! So, I''ve attached it as a document as well.
In any case, let''s break the question down.
We''re told that ABC are 3 points in the coordinate plane that do not form a ...”



Stuart Kovinsky
posted a reply to 650level Combinatorics problem.Please help
in the Problem Solving forum
“Hey Dan!
I''m glad that the question makes sense now.
Kaplan''s Premier Guide has a chapter devoted to statistics, which includes perms & combs (and of course those questions show up on our CATs). Whether that''s "enough" to get you through to test day depends on how much work ...”






Stuart Kovinsky
posted a reply to Verb Tense, Mood, & Voice  MGMT SC
in the Sentence Correction forum
“Hi Ian!
Great job identifying that this sentence calls for the subjunctive mood. I like that term "bossy verb"  I''m going to steal that and pretend I made it up!
Here''s the bare syntax for using the subjunctive:
[subject 1] [bossy/question verb] that [subject 2] [infinitive ...”



Stuart Kovinsky
posted a reply to Median question
in the Data Sufficiency forum
“Hi!
Here''s a thread that discusses this problem in detail:
[url]http://www.beatthegmat.com/medianquestiont8140.html[/url]
If you still have questions about it, ask away!
Stuart”



Stuart Kovinsky
posted a reply to 650level Combinatorics problem.Please help
in the Problem Solving forum
“No  the question is written in such a way that those 2 people are fixed (even if they''re not named). For the purposes of our calculation, it doesn''t matter which 2 people don''t get along.
Now I feel like you''re arguing just for the sake of arguing!
:D”



Stuart Kovinsky
posted a reply to 650level Combinatorics problem.Please help
in the Problem Solving forum
“Here''s the key difference: there''s only one way to choose the 2 consultants who can''t be together. There are multiple ways to choose the 8 male members of the jury.
Technically, when calculating the number of disqualified teams of consultants, we''re calculating:
2C2 * 5C2 = 1*10 = 10
...”



Stuart Kovinsky
posted a reply to 1000CR Test 4 Q14
in the Critical Reasoning forum
“Hi Aditya!
The opponents argue that people should be free to decide whether to wear seatbelts based on the rule that "you can do what you want as long as you don''t harm OTHERS".
(e) doesn''t weaken because the nonseatbelt wearers are only harming themselves  something the ...”



Stuart Kovinsky
posted a reply to 650level Combinatorics problem.Please help
in the Problem Solving forum
“In this part of the solution, you''re ONLY looking at the unacceptable teams. In other words, you''re counting how many teams are disqualified due to inclusion of the 2 archenemies.
Since we only care about disqualifying teams including the 2 troublemakers, we automatically include both of them ...”






Stuart Kovinsky
posted a reply to 650level Combinatorics problem.Please help
in the Problem Solving forum
“Speaking specifically to your solution, the problem in each case is when you begin with:
There are 10 males total, so there are 10C8 ways to select those 8 males. You need to factor all those possibilities into your solution as well. (10C8 = 10*9/2*1 = 45)
In the second case, you have to ...”






Stuart Kovinsky
posted a reply to Functions f(x)
in the Problem Solving forum
“Hi!
The most effective (and sometimes only) way to approach Twopart Analysis questions in IR is backsolving: using the choices to generate the matching pair of answers.
There''s an infinite number of solutions for the problem, which is why you can''t "frontsolve" them. Instead of ...”



Stuart Kovinsky
posted a reply to interesting CR
in the Critical Reasoning forum
“Hi again!
One thing that it''s very important to remember: we accept the evidence as true. It''s not our job to discredit the evidence itself, but rather how the author uses that evidence. The vulnerable part of every argument is always the author''s assumptions: the missing but necessary ...”



Stuart Kovinsky
posted a reply to interesting CR
in the Critical Reasoning forum
“The GMAT is written according to patterns; understanding those patterns and how the test works gives you a huge advantage over your competitors.
Here, we''re asked to weaken the argument. So, we need to break it down and determine what the author is assuming, then look for an answer that attacks ...”



Stuart Kovinsky
posted a reply to weighted averages
in the Problem Solving forum
“A mixture of 20 grams of lean ground beef is mixed with 50 grams of fatty ground beef to create a ground beef mix with 8% fat. How many grams of fat does the lean ground beef have?
The ratio of fat content for L:F is 2:5. So, as GGNY (does he have a real name  does anyone know it?) aptly ...”



Stuart Kovinsky
posted a reply to Equilateral triangle inscribed in a circle
in the Problem Solving forum
“Hi!
There''s an excellent chance that on test day you''ll see a question that involves the circle sector formula  that''s exactly what we have here.
Here''s the formula:
length of arc/circumference = angle of arc/360 = area of sector/area of circle
In other words, every aspect of the ...”



Stuart Kovinsky
posted a reply to x divisible by 6?
in the Data Sufficiency forum
“Hi there!
Not much to dissect for the q stem: we can rephrase it as "is x a multiple of 6?" No info provided, so we know nothing!
(1) (x+3) is a multiple of 3, which means that x is also a multiple of 3.
if x=3, then x is NOT divisible by 6.
if x=6, then x IS divisible by 6.
...”



Stuart Kovinsky
posted a reply to line k in xyplane
in the Data Sufficiency forum
“Hi there!
We know that line K passes through the origin, so it must pass through exactly 2 of the 4 quadrants (ab isn''t 0, so we know that line K isn''t just one of the axes).
Q: is b positive? We need info about which quadrant point a,b is in.
(1) the slope is negative.
If the slope ...”



Stuart Kovinsky
posted a reply to Square inscribed within a circle
in the Data Sufficiency forum
“Hi!
1. yes, they do (the diagonals of nonsquare rectangles also bisect each other, but not at right angles).
2. yes! The 4 angles have to add to 360 and they''re equal, so each one is 90 degrees.
And, in case anyone is wondering, each statement is sufficient since each one proves that ...”



Stuart Kovinsky
posted a reply to Pigs or cows
in the Data Sufficiency forum
“Quick note: as written, (1) is both sufficient and impossible. Brent corrected the statement in his explanation.
(I say (1) is impossible because it would require the farm to have (2/3)(40) = 26 2/3 cows, which is both messy and illegal in some states.)”



Stuart Kovinsky
posted a reply to discounted airline tickets
in the Critical Reasoning forum
“Hi!
What''s the source of this question? The author definitely isn''t assuming (b), so if that''s the accredited answer, it''s just a bad question.
The author is, on the other hand, assuming (a)  so your first instinct is correct!
Breaking down the stimulus:
Old plan had cheap prices ...”



Stuart Kovinsky
posted a reply to weighted averages
in the Problem Solving forum
“Sure  based on the original question, both the lean and the fatty could be 8% (or many many other combinations) and generate a different # of grams of fat. You have 2 unknowns but only 1 equation, so there''s an infinite number of solutions.
Stuart”






Stuart Kovinsky
posted a reply to proportion of women
in the Critical Reasoning forum
“Hi!
When asked to find the answer that would most help you evaluate the argument, look for the gap  in other words, the author''s assumption. The correct answer will be directly relevant to determining whether the assumption is valid.
Here, we have a classic scope shift. The author is ...”



Stuart Kovinsky
posted a reply to Source : GMAT PREP :New Q for old stimuli.
in the Critical Reasoning forum
“Certain patterns recur regularly in CR  possibly the most common argument form is causation.
We can paraphrase this entire argument as "the increase in price is responsible for the decrease in sales".
The most common ways to strengthen a causal argument are:
1) eliminate ...”






Stuart Kovinsky
posted a reply to Combinations 600 level problem..Please help
in the Problem Solving forum
“Hi Dan!
You''re right, this question is as much about logic as it is about math.
We can paraphrase the question (a great thing to do with long word problems) as:
Now let''s apply some logic: x will always be either somewhere ahead of y or somewhere behind y. Is there a reason why he ...”



Stuart Kovinsky
posted a reply to Is 2^x greater than 100?
in the Data Sufficiency forum
“Hi!
We have a yes/no question, so if we can get a definite YES or a definite NO, we have sufficiency. If we get a maybe/sometimes/depends, we have insufficiency.
Looking at the stem, we think "we need to know about x".
(1) gives us an equation to solve for x. If we can solve for ...”



Stuart Kovinsky
posted a reply to Female employes in X
in the Data Sufficiency forum
“Hi!
Without any doubt, the most powerful concept for data sufficiency is "number of equations vs number of unknowns". You can use that rule (and its exceptions) to solve many DS questions without doing much, if any, math.
Let''s apply it to this particular question.
Step 1 of the ...”






Stuart Kovinsky
posted a reply to Usage of whom
in the Sentence Correction forum
“Hi!
A great way to determine whether to use "whom" or "who" is to turn the sentence into a question and answer it with "he" or "him".
For example, for (B) we''d ask "by whom were the mountains named?" We''d answer: "they were named by ...”



Stuart Kovinsky
posted a reply to Weighted Average Problem
in the Problem Solving forum
“Hi there!
My first post on the site for a while, but I can''t resist a good PM!
As Matt notes, your solution is 100% correct  a really important thing to remember about high level GMAT questions is there''s almost always an "angle" to solving them  and if you find the right one, ...”












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 ...”



Stuart Kovinsky
posted a reply to Coordinate Geometry
in the Data Sufficiency forum
“We didn''t get lucky  the question was designed to reward people who saw the quick solution.
Most GMAT math questions are designed with 4 levels of reward:
1) negative reward, for people who spend time on it and get it wrong;
2) 0 reward, for people who recognize that they don''t know how to ...”



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 ...”



Stuart Kovinsky
posted a reply to applications
in the Data Sufficiency forum
“You''re 100% correct about the interpretation, but not about the confusion. We don''t know how deposits and acceptances relate to enrolments, which is why the statements, even combined, are insufficient.”



Stuart Kovinsky
posted a reply to Coordinate Geometry
in the Data Sufficiency forum
“Hi!
This question should take about 15 seconds if you actually draw out the xy plane. There are no bonus points on the GMAT for supercomplicated math, so avoid it whenever possible!
If you plot the 2 points, you can see that, since they have the same ycoordinate (3), one point that''s ...”



Stuart Kovinsky
posted a reply to applications
in the Data Sufficiency forum
“I don''t think that the problem with this question is that the language is confusing; rather, neither statement is relevant to the question, so we can very quickly say that the answer is (E).
The question asks what % of students who apply actually enrol. Neither (1) nor (2) mentions enrolment, ...”



Stuart Kovinsky
posted a reply to OG 13 #132
in the Data Sufficiency forum
“Hi!
Normally for this type of question we can rely on our old friend, "number of equations vs number of unknowns". However, there are some cases, such as this one, in which you have more info that you originally thought and you don''t actually need as many equations as you may think.
...”



Stuart Kovinsky
posted a reply to how do i solve this?
in the Problem Solving forum
“Great job!
Here''s a bit of clarification on solving this type of problem.
There are simple rules for multiplying exponents (x^a * x^b = x^(a+b)) and raising exponents to other exponents ((x^a)^b=x^(a*b)), but there''s no simple way to add or subtract exponents.
In fact, the only time you ...”



Stuart Kovinsky
posted a reply to manufacturing
in the Problem Solving forum
“Hi!
Like many GMAT questions, this one looks much more difficult than it actually is.
First, we can simplify by recognizing that the numbers on the right side are wholly irrelevant. The question would have an identical solution if the original equation were:
C = rst
Since that equation ...”



Stuart Kovinsky
posted a reply to revolutions
in the Problem Solving forum
“Hi!
You can solve this doing a lot of math, but any time you have variables in the choices, you can also pick numbers to solve  and picking numbers is often much easier than algebra. Let''s try it a couple of different ways!
Before we jump in, let''s make sure we identify exactly what the ...”



Stuart Kovinsky
posted a reply to cabbage
in the Problem Solving forum
“Hi!
As always, let''s start by identifying the exact question: what''s the gross profit?
Well, gross profit = total revenue  total cost. We''re given the total cost of $600, so we need to find the total revenue.
We''re told that 2/3 of the heads were sold for 25% above cost/head. There ...”



Stuart Kovinsky
posted a reply to OG 12 DS #89
in the Data Sufficiency forum
“Hi!
While you certainly can solve by manipulating equations, you can also solve with common sense and logic  very powerful tools on the GMAT that people often overlook.
We should be able to dismiss each statement by itself fairly quickly, since they each give us one relationship that''s not ...”



Stuart Kovinsky
posted a reply to Stats.. relationship among different pieces
in the Problem Solving forum
“1,3,5,5 is the same as 1,1,3,5
Similarly, 1,5,5,5 is the same as 1,1,1,5
The missing set is 1,1,5,5
On a side note, you will NEVER need to calculate SD on the GMAT (and, accordingly, you don''t need to know the SD formula)  you just might need to know what SD measures (how spread out are ...”



Stuart Kovinsky
posted a reply to median question..
in the Data Sufficiency forum
“Hi!
We''re told that 25% of projects have 4+ employees and 35% have 2 employees. Since the only number that doesn''t fall into "4 or more" and "2 or fewer" is 3, all of the remaining projects must have exactly 3 employees.”



Stuart Kovinsky
posted a reply to x/y<0?
in the Data Sufficiency forum
“Hi!
While this question illustrates some important concepts, it is 100% NOT a real GMAT question. What''s the source?
As TheCEO notes, statement (1) proves that the answer is "no" and statement (2) proves that the answer is "yes". On the GMAT, the two statements will ...”



Stuart Kovinsky
posted a reply to Martin's theory
in the Reading Comprehension forum
“Hi!
Let''s look right at the beginning of the passage:
Since the new research indicates that humans arrived "much earlier than 11,000 years ago", it directly attacks Martin''s theory that the arrival (i.e. not just the presence) of humans was responsible for the mass extinctions ...”






Stuart Kovinsky
posted a reply to inequalities problem... again
in the Problem Solving forum
“As usual, Eagleeye provides a great explanation  using the number line is a great way to solve absolute value problems.
Another way to solve, especially when you have absolute value expressions on both sides of the equal sign, is to square both sides. Doing so generally leaves you with a ...”



Stuart Kovinsky
posted a reply to Adam Family
in the Problem Solving forum
“Hi!
You can solve this almost instantaneously if you understand what the question is asking.
Since each brother is double the weight of the previous brother, the correct answer has to be divisible by 2 many times. The only answer that has lots of factors is 2 is 64... choose E!
The ...”



Stuart Kovinsky
posted a reply to Problem Solving  Factorization Question??
in the Problem Solving forum
“Hi! This is an old question (and actually quite poorly constructed), but it illustrates a common feature in some GMAT questions, so it''s worth reviewing.
First, let''s break down the question:
Whenever you see this type of question, always rewrite it as:
n x 25 x 62 x 73/(5^2 * 3^3) = ...”



Stuart Kovinsky
posted a reply to Exponents problem
in the Problem Solving forum
“Let''s look at another approach we can take to the one posted by eagleeye.
First, a note of caution: when dealing with inequalities, be very wary of multiplying or dividing both sides by variables. Remember, if those variables turn out to be negative you have to reverse the inequality.
...”



Stuart Kovinsky
posted a reply to Geometry problems:
in the Problem Solving forum
“Using the vertical angle rule (opposite angles of intersecting lines are equal), we know that:
a=d
and
b=e
So, since a and b are complementary, d and e must also be complementary.
Further, since a=d, b and d are complementary; similarly, since b=e, a and e are complementary.
We know ...”



Stuart Kovinsky
posted a reply to Ratios problem
in the Problem Solving forum
“Hi!
A bit of theory before getting into the calculations.
First, when converting between linear, second order and third order equations (i.e. lengths, areas and volumes), you simply apply the proper exponent to find the new ratio.
For example, if comparing the areas of two squares with ...”



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 ...”















Stuart Kovinsky
posted a reply to Usage of HasExperts please help
in the Sentence Correction forum
“Hello!
"None of them have" and "none of them has" are both in common usage. While "none of them has" is technically "more correct", arguments can (and have!) been made for using "have" instead.
I can''t recall a GMAT question that required you ...”



Stuart Kovinsky
posted a reply to DS: Finding percents from averages
in the Data Sufficiency forum
“Hi!
Dimochka presents a great mathematical explanation, but let''s focus on efficiency, remembering one key rule:
To get the point on a DS question, you don''t need to actually answer the question  you just need to determine whether it''s possible to do so.
Keeping this rule in mind will ...”



Stuart Kovinsky
posted a reply to NEW ENTRY PROBLEMS
in the Problem Solving forum
“Hi!
If it''s actually a numeric entry question, then you have to enter the answer on the computer  it''s not multiple choice.
Again, these questions do NOT appear on the GMAT.”



Stuart Kovinsky
posted a reply to Integers x and y
in the Data Sufficiency forum
“Hi!
If x+2 and x+4 are between x and y, won''t x+1 and x+3 be between them as well?
You''re misinterpreting statement (2) as:
when in fact statement (2) simply tells us that there ARE 24 integers between x and y... period.
The only way this statement can be be true is if y = x + 25 ...”



Stuart Kovinsky
posted a reply to Primes
in the Data Sufficiency forum
“Hi!
Like a lot of data sufficiency questions, investing a bit of time in the question stem to understand what the question is really about makes working with the statements much simpler.
Let''s break down the stem:
What kind of positive numbers CANNOT be expressed as the product of two ...”



Stuart Kovinsky
posted a reply to NEW ENTRY PROBLEMS
in the Problem Solving forum
“Hi!
Is this a GRE question? There are no entry questions on the GMAT.
The first thing to note is that, on the GRE, you actually have access to a calculator. While you don''t need to use it (in fact it''s often quicker to solve multiple choice questions without a calculator), on the numeric ...”



Stuart Kovinsky
posted a reply to Problem solving  Ratio / Proportion
in the Problem Solving forum
“Hi!
As the other experts noted, this is a really tough math problem  which is why, almost certainly, the best way to approach it is strategically.
If you had provided answer choices (please always provide the choices!), we could have backsolved. When you have a very complicated word problem ...”



Stuart Kovinsky
posted a reply to OG 10th edition CRq174
in the Critical Reasoning forum
“Hi,
the question stem tells us to draw a conclusion "from the information given above". Two of those pieces of info are:
So, we do definitely know that the average age will increase over that time period.”



Stuart Kovinsky
posted a reply to really tough CR..
in the Critical Reasoning forum
“Hi!
For assumption questions, start by deconstructing the argument: identify the author''s conclusion and summarize the evidence.
Conclusion: the ONLY solution is to increase the number of government officials.
Evidence: old folk are underrepresented in the government, which sets policy ...”



Stuart Kovinsky
posted a reply to BOLD
in the Critical Reasoning forum
“Hi!
Bolded statement questions can be tricky, mostly because the answers often sound extremely similar. To avoid getting confused, rely on the most powerful tool for both RC and CR: making a prediction.
The best way to make a prediction on bolded statement questions is to roadmap the ...”



Stuart Kovinsky
posted a reply to I didn't even understand the question!
in the Problem Solving forum
“Hi!
A terminating decimal is one that ends, i.e. doesn''t infinitely repeat.
For example, 1.4, 8, 32.888991 and 27.6 are all terminating decimals.
Some fractions can be turned into terminating decimals, some can''t. For example, 1/3 is .33333 (going on forever). 1/5 is .2, which is ...”






Stuart Kovinsky
posted a reply to As part of a game, four people each must secretly
in the Problem Solving forum
“Here''s another way you can solve:
Prob = # desired outcomes/total number of possibilities
there are 4*4*4*4 = 256 total possibilities
Now on to desired outcomes!
The first person can pick any number, so she has 4 possibilities.
We want the second to be the same as the first, so she has ...”



Stuart Kovinsky
posted a reply to From new GMATprep Qn  Experts help please
in the Problem Solving forum
“Hi!
There''s a problem with the question  it doesn''t make sense as written (at least if the answer is supposed to be D).
You have Betty and William earning more than 50000, but then we never hear about William again. Then the question asks whether Wilma''s annual salary is greater than ...”






Stuart Kovinsky
posted a reply to Inequalities DS
in the Data Sufficiency forum
“Sure!
We want to know if the absolute value of a is greater than the absolute value of b. In other words, is the magnitude of a greater than the magnitude of b? (I.e. is a further from 0 on the number line than is b?)
As always, let''s start with the simpler of the two statements (that way if ...”



Stuart Kovinsky
posted a reply to Inequalities DS
in the Data Sufficiency forum
“Hi!
We want to know if the sum of x and y is positive. So, we either need the individual values of x and y or information about the expression "x+y".
(1) x  y > 0
We know nothing about x and y individually, so (1) is insufficient.
If the concepts don''t jump out at you, ...”



Stuart Kovinsky
posted a reply to Probability problem
in the Problem Solving forum
“That''s the exact rule!
If you just care about which objects to select, then you use the combinations formula.
If you care not only about which objects to select, but also the order of selection (or arrangement), then you use the permutations formula.
Here are two examples to illustrate the ...”



Stuart Kovinsky
posted a reply to the long advertisement
in the Critical Reasoning forum
“Hi! Just a reminder, please post the source of your questions (always a good habit).
Whenever you have an assumption family question (assumption/strengthen/weaken/flaw), start by deconstructing the argument: find the conclusion, summarize the evidence and identify the assumption.
Here, we ...”



Stuart Kovinsky
posted a reply to Probability problem
in the Problem Solving forum
“Just to elaborate a bit more, here''s the probability formula:
probability = (# of desired outcomes)/(total # of possibilities)
and, as Anurag noted, 36 was the total number of possible choices.
Whenever you''re doing a probability problem, starting out by writing that equation on your ...”



Stuart Kovinsky
posted a reply to Coordinate plane
in the Problem Solving forum
“Hi!
Let''s start with what''s probably the quickest approach: actually graphing the line.
The notepad that you get on the GMAT is graphlined, so it''s pretty easy to accurately draw out coordinate geometry questions. Accordingly, one option for solving this problem is to plot the two points, ...”



Stuart Kovinsky
posted a reply to Quadrilateral
in the Data Sufficiency forum
“Hi! It''s been a long time since I read this thread, but happy to reiterate a couple of key points.
First, and I can''t stress this enough: a square IS by definition a rectangle, since it has all the properties of a rectangle. The opposite is not true (i.e. a rectangle is not by definition a ...”



Stuart Kovinsky
posted a reply to Manhattan  weaken
in the Critical Reasoning forum
“Hello!
We''re asked to find the answer that would be cited by a SUPPORTER of the argument; in other words, we want to find the answer that, if true, would most STRENGTHEN the conclusion.
First, of course, we need to identify the conclusion. There are a number of tools we can use to do so: ...”



Stuart Kovinsky
posted a reply to Strengthen
in the Critical Reasoning forum
“Hi!
For strengthening questions, start by deconstructing the argument: find the conclusion, summarize the evidence and identify the author''s assumption. Next, make your prediction: the correct answer will support the assumption.
Let''s break down this argument:
Conclusion  TV ...”



Stuart Kovinsky
posted a reply to Assumption question quiet confusing...
in the Critical Reasoning forum
“Hi!
What''s the source of this question? It sounds a LOT more like an LSAT question than a GMAT one. If it''s from an LSAT source, then I''d advise that you completely ignore it, since the difference between sufficiency and necessity is rarely tested on the GMAT.
**FEEL FREE TO STOP READING ...”






Stuart Kovinsky
posted a reply to Something Wrong with the question???
in the Data Sufficiency forum
“Hi!
Remember  when inequalities and variables are involved, you have to be very careful with your manipulations!
You cannot simply crossmultiply by ab, since it''s possible that ab is negative. If ab IS negative, then when you cross multiply you get:
Is 1/(ab)<(ba)?
Is 1 > ...”



Stuart Kovinsky
posted a reply to stocks
in the Problem Solving forum
“Hi!
At first glance this may look like a permutations question, but it''s actually an exponent question with a tiny bit of permutations thrown in.
Since there''s no restriction on how many times we use each letter in each code, the number of possible 5 letter codes is simply 26^5 and the ...”



Stuart Kovinsky
posted a reply to households
in the Problem Solving forum
“Hi!
I played with the numbers a bit to maximize the duplicates, keeping in mind that I wanted to use as many of the DVDs, cell phones and MP3 players as possible twice.
I started with the MP3s, since that was the smallest group. Then I noted that there were 5 more Cell phones than DVDs, so I ...”



Stuart Kovinsky
posted a reply to three and four digit numbers
in the Problem Solving forum
“Hi!
Is there a reason why we couldn''t have x=170 and y=850?
In order for x+y to be a 4 digit number, at least one of the two must be greater than 500 (and the hundreds digits must sum to at least 9), but both don''t need to be greater than 500.
Fortunately, that issue doesn''t cause any ...”



Stuart Kovinsky
posted a reply to Counting Numbers 1
in the Problem Solving forum
“Hi!
Because you''re multiplying by a smaller number, you''ve actually removed those duplicates.
Here''s another way you could write the product:
(number of digits that could go in the first spot) * (number of digits that could go in the second spot that you haven''t used yet) * (number of ...”



Stuart Kovinsky
posted a reply to advanced gmat guide inequality
in the Data Sufficiency forum
“Hi!
The two statements aren''t identical, since for (2) a could be the negative root of a^2 and for (1) a is definitely nonnegative.
For example, for statement (1) we could pick a=4 and b=2 (since 4 = 2^2).
For statement (2) we could pick those same numbers (since 4^2 = 2^4), but we could ...”



Stuart Kovinsky
posted a reply to Consulting
in the Data Sufficiency forum
“Hi!
From the stem, we know that the fee is $x/hour for the first 100 hours and $y/hour for extra hours. We also know that Acme was charged a total of $14000. So, we can create the following formula:
100*$x + (n100)*$y = $14000
(n = total number of hours charged)
and the question is ...”



Stuart Kovinsky
posted a reply to Probability  Playing Cards
in the Problem Solving forum
“Hi! We want the probability of getting at least one matching pair. So, the only thing we don''t want to happen is 0 matching pairs. Accordingly, this is a great question on which to apply the "one minus" approach.
Remember this key formula for complex probability problems:
...”



Stuart Kovinsky
posted a reply to households
in the Problem Solving forum
“Hello!
First, a key strategy on min/max questions: whenever a question asks you to minimize one thing, maximize others; whenever a question asks you to maximize one thing, minimize others.
Next, let''s break this question down into two parts. First, the max number of households that has all ...”



Stuart Kovinsky
posted a reply to Sum of numbers
in the Problem Solving forum
“Hello!
On this type of question you always want to look for a pattern. In this case, let''s separate the units and tens digits.
Overall, we have 10 sets of numbers here: 09, 1019, 2029, ..., 9099.
In each set of 10, we have 1 of each units digit, so that''s 10 of each.
For each set ...”



Stuart Kovinsky
posted a reply to prime
in the Problem Solving forum
“Hi!
The wording of this question is a bit too ambiguous for the GMAT. Even though we can reason out what the question is supposed to say, you''ll never be put in that position on test day. What''s the source?
Better wording would have been:
Like many number property questions, we can ...”



Stuart Kovinsky
posted a reply to Coin flip questions made easy
in the GMAT Math forum
“Hi!
The formula is more complicated for die rolls because there are more than 2 possible outcomes, so "what you want" doesn''t equal "what you don''t want".
If you''re looking for one specific result, there''s a 1/6 chance of what you want and a 5/6 chance of what you ...”



Stuart Kovinsky
posted a reply to Problem Solving
in the Problem Solving forum
“Hi!
We see a fraction question with unknown values. Perfect time to pick numbers!
First, let''s identify the exact question: what fraction of UNSOLD cars were HYBRIDS. In other words, we want to solve for:
(# of unsold hybrids)/(total # of unsold cars)
To make the math work out, ...”



Stuart Kovinsky
posted a reply to 3 categories of workers
in the Problem Solving forum
“Hi again!
I strongly disagree  you will never have to make assumptions of this nature on the actual GMAT and doing so in practice will lead to habits on test day that could lead to fatal errors. For example, one of the most common DS mistakes is to assume facts that aren''t actually in ...”



Stuart Kovinsky
posted a reply to 3 categories of workers
in the Problem Solving forum
“Where do you see that information in the question stem?
Also, does a higher number in the ratio mean that a worker is more efficient or less efficient? For example, if you measure efficiency in tasks per hour, then higher is better; but if you measure efficiency in hours per task, then lower is ...”



Stuart Kovinsky
posted a reply to If 0<x<y, is yx < 0.00005
in the Data Sufficiency forum
“Sometimes brute force is the key to happiness on the GMAT.
(1) doesn''t give us any information about the upper boundary of y, so there''s no way it''s sufficient by itself: eliminate A and D.
(2) gives us an upper boundary on y AND we already know that x > 0, so it''s actually possible ...”



Stuart Kovinsky
posted a reply to 3 categories of workers
in the Problem Solving forum
“Hi!
This is a very poorly worded question and makes little sense. What does "the efficiency of the 3 categories of workers" mean? How is it related to wage? Nowhere does it say that different workers get different hourly rates (e.g. that hourly wages are proportional to efficiency, ...”



Stuart Kovinsky
posted a reply to Maths Problem
in the Problem Solving forum
“Hi!
Since p is a positive integer, p^3 is a perfect cube. Here''s an important rule about prime factoring of perfect squares, cubes, etc...:
perfect squares contain prime factors in pairs;
perfect cubes contain prime factors in triplets;
and so on...
For example:
36 is a perfect square; ...”



Stuart Kovinsky
posted a reply to Sets
in the Data Sufficiency forum
“Hi!
I can''t speak for all the experts here, but when I see a question linked in an image instead of typed in, I usually skip over replying (unless the image contains a diagram, which is a good excuse for attaching one).
The reason why I skip over these posts is because 90% of the time I''m ...”



Stuart Kovinsky
posted a reply to board of directors
in the Problem Solving forum
“A great opportunity to use logic instead of math!
There are 5 different people with whom Michael can be matched. There are 2 spots available on Michael''s team. Therefore, any one of the other 5 people will appear on 2/5 = 40% of Michael''s teams. Pick C!”



Stuart Kovinsky
posted a reply to Can someone please explain?
in the Problem Solving forum
“Hi!
We can set up a couple of simple equations to solve this relatively painlessly.
Let''s call his one way walking time "W" and his one way cycling time "C". We want to know the time for walking both ways, so we''re solving for 2W.
We know that:
W+C = 2h40min
...”



Stuart Kovinsky
posted a reply to perpendicular
in the Problem Solving forum
“Hi!
Although it may be somewhat timeconsuming, your best bet is to rewrite the equation in the stem and in each choice into standard y=mx+b form  that way you''ll be able to quickly compare the slopes.
Original:
3x + 4y = 8
4y = 3x  8
y = 3/4(x)  8
Slope = 3/4
Since ...”



Stuart Kovinsky
posted a reply to Probabilities
in the Problem Solving forum
“*TANGENT ALERT*
No math here, if you''re looking for math, move along!
There''s no need to put it directly before that (in fact, I challenge you to rewrite the sentence to put that where you want without causing a modification error in the remainder of the sentence)  the verb makes it clear ...”



Stuart Kovinsky
posted a reply to prime number
in the Data Sufficiency forum
“Hi!
Very open question, but we see it''s about primes. Whenever you see a DS question about primes, always think about 2, the only even prime!
Pretty straightforward question, so let''s dive right into the statements. (2) seems simpler, so let''s start there.
The only way that (2) could ...”



Stuart Kovinsky
posted a reply to Probabilities
in the Problem Solving forum
“Hi!
Because the sentence reads "that are", that must be referring to a plural subject; since "warehouse" is singular, it can''t be the referent of that.”



Stuart Kovinsky
posted a reply to Are x and y both positive?
in the Data Sufficiency forum
“Hi!
(2) says that x/y > 1
If you plug in x = 3/2 and y = 2, you get:
x/y = (3/2)/2 = (3/2)*(1/2) = 3/4 which is NOT greater than 1. Since your numbers don''t satisfy the statement, they''re impermissible and must be discarded.
As Aneesh aptly notes, you have to be VERY careful ...”






Stuart Kovinsky
posted a reply to If a, b, and c
in the Data Sufficiency forum
“Hi! Picking numbers is a great way to solve this (and many other) DS questions.
We quickly decide that (1) is insufficient, since it gives us no info about c. So, let''s eliminate A and D and jump to (2).
(2) ab>c
We can see that b is to the right of a on the number line, so let''s ...”



Stuart Kovinsky
posted a reply to Are x and y both positive?
in the Data Sufficiency forum
“Eagleeye gives a good math explanation; let''s look at the question purely using number properties concepts.
Q: are x and y BOTH positive.
(1) 2x2y=1
or
x  y = 1/2
Let''s think about what this means: on the number line, x is 1/2 to the right of y. Does that tell us anything about ...”



Stuart Kovinsky
posted a reply to Overlapping sets  OG12
in the Problem Solving forum
“Hi!
You''ve put 60 in the Brand A "total" column, which includes "brand A/brand B" and "brand A/not brand B". People in the "brand A/brand B" column are NOT "brand A ONLY"  they''re using both.
The 60 should go in the "brand a/not brand ...”



Stuart Kovinsky
posted a reply to Percentages
in the Problem Solving forum
“Hi!
I''m not sure where you''re getting these questions, but they, for the most part, suck. Each one only has 4 choices, they often have awkward or ambiguous language and test concepts far beyond (and irrelevant to) the GMAT.
If you''re actually studying for the GMAT, I''d avoid this source ...”



Stuart Kovinsky
posted a reply to Six digit numbers
in the Problem Solving forum
“Only 4 answer choices, so clearly this isn''t a real GMAT question  please always post your source we know if it''s relevant to the GMAT!
This question is a far more complicated version of a question that may appear on the GMAT, so it''s worth discussing. Once you understand how one of these ...”



Stuart Kovinsky
posted a reply to Another good evaluate question...
in the Critical Reasoning forum
“But what does "coming second" mean?
If the Bible got 999 votes and 1984 got 1 vote, then 1984 came second; if the Bible got 501 votes and 1984 got 499 votes, then 1984 came second. Do both scenarios make us think that 1984 actually affected a lot of people''s lives?”



Stuart Kovinsky
posted a reply to jury
in the Problem Solving forum
“Hi!
I gave a detailed explanation to this question here:
http://www.beatthegmat.com/isuckatprobabilityneeddesperatehelpt8927.html”



Stuart Kovinsky
posted a reply to Inequalities OG12 #38
in the Problem Solving forum
“Hi!
When you''re not sure what to do with the algebra, don''t waste your valuable test time trying to figure it out. Instead, dive right in and pick numbers.
As you noted, each statement must be insufficient alone, since each one only provides 1/2 the picture. So, let''s jump right to ...”



Stuart Kovinsky
posted a reply to Another good evaluate question...
in the Critical Reasoning forum
“Hi!
Relevant information questions are really scope questions  we want the answer that''s most inside the scope of the issue. These questions belong to the assumption family.
A great approach is to break down the argument just as you would for any assumption/str/wkn question: find the ...”



Stuart Kovinsky
posted a reply to Couldn't get the problem
in the Problem Solving forum
“Hi! Wacky symbol questions appear from time to time on the GMAT; these questions almost always resolve to simple substitution.
Of course, before you can substitute you have to understand the question. So, the key to solving these problems is to take the time you need to break down the question ...”



Stuart Kovinsky
posted a reply to Confusing Probability
in the Problem Solving forum
“Hi!
Part of you''re analysis is 100% correct: for any given string of 7 coin flips, there''s a (1/2)^7 chance of it happening.
For example, there''s a (1/2)^7 probability of getting:
HHHHHHH; or
HHHHHHT; or
HHHHHTT; and so on...
However, here''s the problem: to satisfy what the ...”



Stuart Kovinsky
posted a reply to weighted averages
in the GMAT Math forum
“Here''s a very useful rule to remember for data sufficiency:
In order to find the actual value of a quantity, you need at least one actual quantity somewhere in the information.
For example, if all you''re given is a ratio, there''s no way to determine the actual quantities involved; ...”



Stuart Kovinsky
posted a reply to Confusing Probability
in the Problem Solving forum
“Hi!
We can definitely solve using the coin flip formula and adding up the probability of each scenario that we want. However, we can solve MUCH quicker using logic.
We want all the cases with an even number of heads. So, we want:
0H
2H
4H
6h
We DON''T want all the cases with an odd ...”






Stuart Kovinsky
posted a reply to How to plug in for this? Official GMAC Hard
in the Problem Solving forum
“Hi! First, let''s make sure we understand the essence of the question  since we''re increasing by a set percent each year, what we really have here is a compound interest problem. The problem basically boils down to:
Principle investment on Jan 1, 1992: $k
interest rate per year: c%
total ...”






Stuart Kovinsky
posted a reply to remainder problem
in the Problem Solving forum
“Hi!
Picking numbers is a great approach to solving many number property questions.
Here, our constraints are that n/9 must have a remainder of 8 and n must be even. What''s the smallest number that satisfies these constraints? n=8 (8/9 has a quotient of 0 and a remainder of 8).
Now let''s ...”



Stuart Kovinsky
posted a reply to abc
in the Problem Solving forum
“Hi, those will indeed have different results, but since 6/2 doesn''t satisfy the condition that ab^2/c is even, we can ignore that possibility.
Remember, we take the equation in the question stem as a given; accepting that the equation is true, we now check to see which statement MUST also be ...”



Stuart Kovinsky
posted a reply to Single eqn solving??
in the Problem Solving forum
“Hi!
We can solve this question superduper quickly via backsolving. Since we want the minimum number of copper coins, let''s start with the smallest answer, (E).
(E) 0 copper means $2.80 from brass  since 280 is not a multiple of 25, wrong!
(D) 1 copper means $2.60 from brass  since 260 ...”






Stuart Kovinsky
posted a reply to Remainder R
in the Data Sufficiency forum
“Picking numbers is a very efficient way to solve number property DS questions.
From the question stem, we know that (4+7n)/3 has a remainder of r; we want to know that value. What do we need? Information about n.
1) n+1 is a multiple of 3.
If n=2 (we''re allowed to pick 2 since 2+1 is a ...”



Stuart Kovinsky
posted a reply to Sets problem
in the Data Sufficiency forum
“Let''s solve using the most powerful rule for data sufficiency: number of equations vs number of unknowns.
First, picture (sorry, I''m not good at computer diagrams!) a Venn diagram with 3 circles. There are 7 different sections: Only R, only S, only T, RS overlap, RT overlap, ST overlap, RST ...”



Stuart Kovinsky
posted a reply to usage of will and would
in the Sentence Correction forum
“For the first one I''d say "there is hope that the economy will grow". You would only use "would grow" if you''re adding a "but" to the end. For example, "I had hoped that the economy would grow, but it shrunk." (Or "I hoped that the economy would grow, ...”



Stuart Kovinsky
posted a reply to Confused  Any Ideas
in the Problem Solving forum
“From the question stem, we know that n is an integer. Accordingly, we know that sqrt(3+x) is an integer. What numbers have roots that are integers? Perfect squares.
Consequently, (3+x) must be a perfect square, i.e. 1, 4, 9, 16, 25, 36, ...
Now we just need to plug in each answer to see ...”



Stuart Kovinsky
posted a reply to usage of will and would
in the Sentence Correction forum
“Hi,
would is NOT the past tense of will. Would is used in conditionals, e.g. "I would go to Harvard if I were to get an 800 on my GMAT".
Would can be used in different tenses. For example:
I would have gone to Harvard if I had gotten an 800 on my GMAT.
"Will" ...”



Stuart Kovinsky
posted a reply to function h(n) number properties
in the Problem Solving forum
“Here''s the takeaway: if h(100) is divisible by every prime from 1 to 50, then h(100)+1 CANNOT be a multiple of any of those numbers.
What Bill was saying is that the greatest common factor of any TWO consecutive integers is 1. Since h(100) and h(100)+1 are consecutive integers, then any prime ...”



Stuart Kovinsky
posted a reply to Airline Fleet  GMAT Prep
in the Problem Solving forum
“You can think of it that way, but you have to count the actual number of years starting from the beginning of 1980. I guess technically you''d hit your target 8 years and 364 days after you start, but that''s still 9 years, not 8. (If you start on Jan 1st 1980, you have your 9th change on Dec 31st ...”



Stuart Kovinsky
posted a reply to numbers 2
in the Problem Solving forum
“Hi,
I''m happy to explain the concepts, but first it''s important to note that the wording of both questions is definitely NOT what you''d see on the GMAT. Also, there are only 4 answer choices and, of course, on the real GMAT there will be 5. Please always post the source of your questions so ...”



Stuart Kovinsky
posted a reply to Airline Fleet  GMAT Prep
in the Problem Solving forum
“Hi! You could solve this question very quickly by brute force  just make a chart and keep track of what happens each year. Remember, on the GMAT you get points for picking the right answer, not for HOW you arrive at that answer. Sometimes brute force is quicker than algebra.
Year A planes ...”



Stuart Kovinsky
posted a reply to OG 13 #229 How many of the integers...
in the Problem Solving forum
“Here''s the #1 thing to remember when using the OG: it''s a great source of questions, but a horrible source of explanations. Especially for math, OG explanations are rarely the most efficient way to solve problems.
Since the biggest answer given is 5, plug ''n play is a great alternative way ...”



Stuart Kovinsky
posted a reply to if b < 1 and 2x  b = 0
in the Problem Solving forum
“Hi! Like many GMAT questions, we should start by simplifying the question itself.
We know that b < 1 and that 2xb=0. We can rewrite the equation as:
2x = b
Putting the two statements together:
2x = b < 1
2x < 1
x < 1/2
Now we need to find the answer that MUST be true, ...”



Stuart Kovinsky
posted a reply to Probability of cars
in the Problem Solving forum
“Hi!
Lots of good solutions already posted, so I''m just going to focus on your actual question.
When we made the calculation to get 192, we were working on the basis that order DID matter. If you think about those possibilities, you''ll see that we''ve over counted.
For example, if the ...”



Stuart Kovinsky
posted a reply to Thought process on remainders
in the Problem Solving forum
“Hi,
for the GMAT, your goal is to be as efficient as possible. While you could certainly derive a fancy formula to solve this type of problem, brute force is almost certainly quicker.
Since we want all the numbers that leave a remainder of 1 when divided into 16, what we really want is the ...”



Stuart Kovinsky
posted a reply to Quadratic Equation
in the Data Sufficiency forum
“Hi!
There are two problems with your analysis, one of which may just have been a typo.
First, the minor issue: (C) is correct if you require both statements in combination; based on the rest of your post, I''m going to assume that you meant that you thought the correct answer should be (D), ...”



Stuart Kovinsky
posted a reply to Challengestatistics
in the Data Sufficiency forum
“Hi!
You seem to have misinterpreted the question as "what is the smallest possible number in the set?", when in fact it''s simply "what is the smallest number in the set?"
With (1) alone, there''s no way to determine the actual value of x, y or z, so (1) is insufficient.
...”



Stuart Kovinsky
posted a reply to Angles
in the Problem Solving forum
“Hi!
You''d definitely benefit from drawing out a clock on this question (as you would on pretty much any geometry question). Sadly, computergenerating diagrams is not one of my strengths, so we''ll just visualize.
Let''s think about where the hands are at 4:20: the little hand is on the 4 ...”






Stuart Kovinsky
posted a reply to Confusion with wording of option (2) ?
in the Data Sufficiency forum
“Hi,
the key word is "any".
(2) says that the difference between ANY two factors of n is odd; read ANY as EVERY (they mean the same thing).
So, if n=12, then we have lots of pairs of factors that do NOT have an odd difference, e.g.:
31=2
42=2
62=4
and so on...
The ...”









Stuart Kovinsky
posted a reply to Combinations Problem
in the Problem Solving forum
“Hi!
Let''s start with Step 1 of the Kaplan Method for PS: analyzing the question stem.
We''re told that there are 2 different sizes of pad  let''s call them small and large ("s" and "l"). There are also 4 different colours, b, g, y and p.
We''re allowed to make 2 ...”

