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20 Sep 2022, 00:21
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A
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Difficulty:
25%
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Question Stats:
77% (01:05) correct
23%
(00:53)
wrong
based on 52
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Is the positive integer p a multiple of positive integer q?
(1) When p is divided by q, the result is an integer.
(2) When q is divided by p, the result is not an integer.
(1) When p is divided by q, the result is an integer.
(2) When q is divided by p, the result is not an integer.
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Updated on: 20 Sep 2022, 22:33
Originally posted by SaquibHGMATWhiz on 20 Sep 2022, 03:58.
Last edited by SaquibHGMATWhiz on 20 Sep 2022, 22:33, edited 1 time in total.
Last edited by SaquibHGMATWhiz on 20 Sep 2022, 22:33, edited 1 time in total.
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Solution:
Pre-Analysis:
- We are asked if a positive integer p is a multiple of positive integer q or not
- Or we are asked if \(\frac{p}{q}=\) positive integer or not
- This is a yes-no question
Statement 1: When p is divided by q, the result is an integer
- According to this statement, \(\frac{p}{q}=\) positive integer
- Based on our pre-analysis, this is exactly what the question is asking us
- Thus, statement 1 alone is sufficient and we can eliminate options B, C and E
Statement 2: When q is divided by p, the result is not an integer
- From this information, we cannot say if p is a multiple of q or not. Let us take 2 cases:
- Case 1: \(p = 4\) and \(q=2\)
- \(\frac{q}{p}=\) not an integer
- p is multiple of q
- Case 1: \(p = 3\) and \(q=2\)
- \(\frac{q}{p}=\) not an integer
- p is not a multiple of q
- Case 1: \(p = 4\) and \(q=2\)
- We are getting two distinct answers
Hence the right answer is Option A
20 Sep 2022, 07:37
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Given information: p is a positive integer, q is a positive integer
To determine: If positive integer p is a multiple of positive integer q OR \(\frac{p}{q}\) = Integer
(1) When p is divided by q, the result is an integer.
Given that \(\frac{p}{q}\) = Integer
Exactly what we are looking for
SUFFICIENT
(2) When q is divided by p, the result is not an integer.
\(\frac{q}{p}\) is NOT AN INTEGER
\(q = 2, p = 4; \frac{q}{p} \neq\) Integer; \(\frac{p}{q}\) = Integer
\(q = 2, p = 5; \frac{q}{p} \neq\) Integer; \(\frac{p}{q} \neq\) Integer
NOT SUFFICIENT
Answer - A
