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Is PQ > 1?

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Is PQ > 1?

by M7MBA » Sun Dec 10, 2017 10:58 am
Is PQ > 1?

(1) P^Q = 1
(2) Q = -1

The OA is C.

I don't understand why both statements together are sufficient to solve this DS question. Experts, can you help me please?
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by DavidG@VeritasPrep » Sun Dec 10, 2017 11:17 am
M7MBA wrote:Is PQ > 1?

(1) P^Q = 1
(2) Q = -1

The OA is C.

I don't understand why both statements together are sufficient to solve this DS question. Experts, can you help me please?
Statement 1:
Case 1: P = 1; Q = 1. PQ = 1, and so is not greater than 1. The answer is NO.
Case 2: P =1; Q = 50. PQ = 50, so is greater than 1. The answer is YES.
Because we can answer YES or NO, this statement alone is not sufficient.

Statement 2: Nothing about P, so not sufficient.

Together, Now we know P^(-1) = 1. The only way that can happen is if P = 1. If P =1 and Q= -1, then PQ = -1, and the answer to the question is a definitive NO. The statements together are sufficient. The answer is C
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by [email protected] » Sun Dec 10, 2017 12:57 pm
Hi M7MBA,

We're asked if (P)(Q) > 1. This is a YES/NO question. We can solve it by TESTing VALUES and/or by using Number Property Rules.

1) P^Q = 1

With the equation in Fact 1, we know that one of the following must be occurring:
A) P = 1 and Q is ANY value
B) P = ANY value and Q = 0

With the first example, the product (P)(Q) could be greater than 1 (a YES answer), equal to 1 (a NO answer) or less than 1 (also a NO answer).
With the second example, the product (P)(Q) will always be 0, so the answer to the question is NO.
Fact 1 is INSUFFICIENT.

2) Q = -1

Fact 2 tells us nothing about the value of P, so there's no way to answer the question.
Fact 2 is INSUFFICIENT.

Combined, we know...
P^Q = 1
Q = -1
So (P)^(-1) = 1. The only solution to this equation is P=1, so (1)(-1) = -1 and the answer to the question is ALWAYS NO.
Combined, SUFFICIENT.

Final Answer: C

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