GMATPrep Question

Chick wrote:Are positive integers p and q both greater than n?

(1) p - q is greater than n.

(2) q > p

Answer: C

Hi Chick,

The question is asking whether BOTH p and q are greater than n. And we know that both p and q are positive--this is important.

(1) p - q is greater than n.

When you subtract q (which is a positive number) from p, you have some number that is greater than n. Therefore, p itself is definitely greater than n. But you don't know whether q is greater than n; insufficient.

(2) q > p

As there is no information about n, this statement is automatically insufficient.

(1) + (2):

From (1), we know that p is greater than n. From (2), we know that q is greater than p. Therefore, both are greater than n.

The statements are not sufficient by themselves; together they are sufficient.

Choose C.

Hi Testluv,

I'm bit confused here. From 1, we know that p-q > n and from 2, q>p .. when we combine, as q>p, would it not result p-q as a negative number..

hence, when we subtract any 2 +ve numbers, the resultant would be a positive number.. therfore p&q ( both) are greater than n ( -ve number)..

Please correct me if I understood something wrong..

Regards,
Viju

viju9162 wrote:Hi Testluv,

I'm bit confused here. From 1, we know that p-q > n and from 2, q>p .. when we combine, as q>p, would it not result p-q as a negative number..

hence, when we subtract any 2 +ve numbers, the resultant would be a positive number.. therfore p&q ( both) are greater than n ( -ve number)..

Please correct me if I understood something wrong..

Regards,
Viju

No, you are not wrong. That is also correct, and while I thought of mentioning that, you don't actually have to observe that p - q is negative in order to see that they are both greater than n.

Yes - I think it's A.

A) p-q>n

If both p and q is positive no matter what numbers you choose it will prove that n is less than both. For example, p = 3 and q = 5 so p-q=-2 which is greater than n so n would have to be less than -2
Likewise if p = 5 and q = 3 the difference is 2 so 2>n so n would have to be less than 2.

What is the OA?

adamsmith2009 wrote:Yes - I think it's A.

A) p-q>n

If both p and q is positive no matter what numbers you choose it will prove that n is less than both. For example, p = 3 and q = 5 so p-q=-2 which is greater than n so n would have to be less than -2
Likewise if p = 5 and q = 3 the difference is 2 so 2>n so n would have to be less than 2.

What is the OA?

Chick already posted the OA; it's C. Viju was not suggesting that the answer was A. Instead, viju was pointing out another way of figuring out that the answer is C.

From (1), we know that p- q > n. P can = 4, and q can = 1. Then 4 - 1= 3, and so, with these numbers, 3 > n. But because q =1, in this case, you could have: n > q. Of course, with the numbers you've picked in your post, q > n. So, q may be greater or less than n; that's why (1) is insufficient.

If you are going to pick numbers in DS, then you need to pick different kinds of numbers that satisfy the statement in an effort to prove that the statement is insufficient.

Thank you Testluv for the explanation.

Regards,
Viju