Data Sufficiency

aditya67 wrote: ↑

Wed Mar 25, 2020 10:40 am

Is the product pqr divisible by 12?
(1) p is a multiple of 3
(2) q is a multiple of 4

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