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12 Mar 2023, 06:53
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A
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Difficulty:
75%
(hard)
Question Stats:
50% (02:15) correct
50%
(02:56)
wrong
based on 78
sessions
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If P and Q are positive integers, then is (P+2)(Q-1) an even number?
(1) \(\frac{P}{3Q}\) is an even integer
(2) \(\frac{Q}{\sqrt{P}-3}\) is a positive odd integer
(1) \(\frac{P}{3Q}\) is an even integer
(2) \(\frac{Q}{\sqrt{P}-3}\) is a positive odd integer
12 Mar 2023, 07:38
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Bunuel
Question
(P+2)(Q-1) = even number ?
PQ + 2Q - P - 2 = even number
PQ - P= even - 2Q + 2
P(Q-1) = even
The expression will hold true under two conditions
- P is even OR
- Q is odd
So, the question essentially wants us to find whether P is even OR Q is odd.
Statement 1
(1) \(\frac{P}{3Q}\) is an even integer
Multiplying 3Q on both sides, we get
P = even
This statement is sufficient as one of the conditions is met. Hence, we can eliminate B, C and E.
Statement 2
(2) \(\frac{Q}{\sqrt{P}-3}\) is a positive odd integer
We cannot comment on the even-odd nature of P or Q based on this expression. Let's take the following cases
Case 1: P = 16 ; Q = 3
In this case, P = even and Q = odd; hence the response to the question is Yes!
Case 2: P = 25 ; Q = 6
In this case, P = odd and Q = even; hence the response to the question is No!
The statement alone is not sufficient.
We can eliminate B.
Option A
04 Jul 2025, 04:17
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