What sort of prep can I start doing for the GMAT?
Last week we looked at a problem from the SAT. Today, we’ll introduce the first in a series of problems that you’re likely to see on the GMAT.
I don’t think that the math classes I’ve taken to date will prepare me for the GMAT.
Don’t worry! Similar to what you find on the SAT, GMAT math is not particularly advanced, but you will need a bit of practice to refresh some concepts and brush up on your skills.
Okay, show me a problem.
Enough talking, let’s jump into a question that you could encounter on the GMAT.
If p/q < 1, and p and q, are positive integers, which of the following must be greater than 1 ?
(A) √(p/q)
(B) p/q2
(C) p/2q
(D) q/p2
(E) q/p
So how do we solve this?
First, let’s review the language and the question. p and q are positive integers, which means that they are numbers like 1, 5, or 23. The question presents us with an inequality (p/q < 1) and asks us to evaluate how the answer choices compare to another potential inequality (>1).
An easy but flawed way to approach this problem would be to randomly pick two numbers for p and q and test them in the solutions. Let’s pick p=2 and q=5. While this satisfies p/q < 1 and the first three answer choices are easily eliminated, answer choices D and E both yield solutions greater than 1. So now we’re stuck.
Okay coach, what’s a better way?
Based on the question stem, to satisfy p/q < 1, we know that q must be greater than p. Since we do not know the magnitude of p or q, let’s assign q a value of p + 1. Now let’s review the answer choices, inserting p + 1 for q:
(A) √(p/(p+1)). p/(p+1) will be a value less than 1, so its square root will also be less than 1.
(B) p/(p+1)2. Since (p+1)2 will be a value greater than p, this fraction will be less than 1.
(C) p/2(p+1). As 2(p+1) results in a value greater than p, the answer choice yields a value less than 1.
(D) (p+1)/p2. This one is tricky; the answer changes for different values of p. If p = 1, p + 1 > p2, so the resulting fraction is greater than 1 while for p values above 1, the opposite is true. Hence we cannot say for sure that the answer must be greater than 1.
(E) (p+1)/p. This fraction can be rewritten as p/p + 1/p = 1 + 1/p (keep in mind that this second term may be 2/p or 3/p or 4/p, etc.). This proves that the fraction given in this answer choice will always be greater than 1. The correct answer is E.
Tune in later this month for the next installment of the Math Mechanic.
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