Is the product pqr divisible by 12?
(1) p is a multiple of 3
(2) q is a multiple of 4
Data Sufficiency
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Target question: Is the product pqr divisible by 12?
At first glance, it LOOKS like the correct answer is C.
However, we are not told whether ALL of the numbers (p, q and r ) are integers.
Sure, statements 1 and 2 indirectly tell us that p and q are divisible by 3 and 4, but r may or may not be an integer.
Given this, we can go straight to.....
Statements 1 and 2 combined
Statement 1 tells us that p² - q² = 128
Statement 2 tells us that p² - q² = 128
There are many values of p, q and r that satisfy BOTH statements. Here are two:
Case a: p = 3, q = 4 and r = 1. In this case, pqr = (3)(4)(1) = 12, which is divisible by 12. So, the answer to the target question is YES, pqr IS divisible by 12
Case b: p = 3, q = 4 and r = 0.5. In this case, pqr = (3)(4)(0.5) = 6, which is not divisible by 12. So, the answer to the target question is NO, pqr is NOT divisible by 12
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent