Is PQ > 1? GMAT Data Sufficiency

byRituparna Nath Content Writer at Study Abroad Exams

Question: Is PQ > 1?

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

Statement 1 and Statement 2 is sufficient
Statement 1 and Statement 2 is insufficient
Statement 1 and Statement 2 are insufficient but sufficient in theory
Statement 1 is insufficient and Statement 2 is sufficient
Statement 1 is sufficient and Statement 2 is insufficient

“Is PQ > 1?”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Quantitative Review 2017". GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. This particular GMAT data sufficiency question assesses candidates’ critical thinking and hypervigilance. An abstract problem-solving question is mainly given and most of the difficulty comes from obtuse or clever wording, candidates usually miss it.

Solution and Explanation:

Approach Solution 1:

We are asked if (P)(Q) > 1. This is a simple YES/NO question. We can solve it by using TEST VALUES or Number Property Rules.
Let us solve this equation one statement at a time

1) P^Q = 1
With the equation in statement 1, we know that one of the following must be occurring:
P = 1 and Q is ANY value
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.
Statement 1 is INSUFFICIENT.

2) Q = -1
Since Statement 2 tells us nothing about the value of P, so there's no way to answer the question.
So statement 2 is INSUFFICIENT.
Combining statements 1 and 2:
if q=-1 and p^q =1
This will give us, p = 1, q=-1 which is Sufficient.
To answer the question Is PQ > 1?, the answer is C

Correct Answer: C

Approach Solution 2:

Let us try to take another approach to find if PQ > 1. This is a very simple approach we are taking here,
If we take the value of P as 1, we will get 1 regardless of the value of Q.
If Q=0, p can be any value.
From 2nd statement
P can have any value, which makes it both true and false.
Both of these are required.
When we consider both statements,
We get Q=-1 (given) and P=1. This implies that PQ = -1 <1 .
So it suffices to say that PQ>1 is always SUFFICIENT.
To answer the question Is PQ > 1?, the answer is C

Correct Answer: C

Approach Solution 3:

From statement 1 we get -

P (PQ - 1) = 0
P = 0, PQ = 1; we get PQ =1

From statement 2 we get -

P (PQ - 1) = 0
Q = 0, PQ = 1 - you get PQ =1

Then we get P = 0 and Q = 0 but individual values are required P or Q.

In both statements we get PQ = 1, hence, should be sufficient.

Correct Answer: C

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Is PQ > 1? GMAT Data Sufficiency

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