Bunuel wrote:
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 12Case 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 12Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
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