VJesus12 wrote: ↑

Sun Mar 07, 2021 2:31 pm

If \(p\) and \(q\) are positive integers and \(pq = 24,\) what is the value of \(p ?\)

(1) \(\dfrac{q}6\) is an integer.

(2) \(\dfrac{p}2\) is an integer.

Answer: E

Source: Official Guide

Solution:

Question Stem Analysis:

We need to determine the value of p, given that pq = 24 and both p and q are positive integers. We see that p (and q) are factors of 24. Therefore, p (and q) can be one of the following integers:

1, 2, 3, 4, 6, 8, 12, and 24

Statement One Alone:

Since q/6 is an integer, q is 6, 12, or 24, and p will then be 4, 2, or 1, respectively. Since p can take on more than one value, statement one alone is not sufficient.

Statement Two Alone:

Since p/2 is an integer, p is 2, 4, 6, 8, 12, or 24. Since p can take on more than one value, statement two alone is not sufficient.

Statements One and Two Together:

From the two statements, we see that p can still be either 2 or 4. Since p can take on more than one value, both statements are not sufficient.

Answer: E