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21 Apr 2013, 06:07
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
47% (01:11) correct
53%
(01:24)
wrong
based on 170
sessions
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If p and q are positive integers, is every factor of p a factor of q?
(1) p is a factor of q.
(2) The product of the prime factors of p is a factor of q.
(1) p is a factor of q.
(2) The product of the prime factors of p is a factor of q.
21 Apr 2013, 07:15
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If p and q are positive integers, is every factor of p a factor of q?
(1) p is a factor of q. Since p is a factor of q (q/p=integer), then obviously every factor of p will be a factor of q. Sufficient.
(2) The product of the prime factors of p is a factor of q. If p=36 and q=6, then the product of the prime factors of p (2*3=6) IS a factor of q but not every factor of p is a factor of q (for example 36 is not a factor of 6). Though if p=q=6, then we'll have that every factor of p a factor of q. Not sufficient.
Answer: A.
(1) p is a factor of q. Since p is a factor of q (q/p=integer), then obviously every factor of p will be a factor of q. Sufficient.
(2) The product of the prime factors of p is a factor of q. If p=36 and q=6, then the product of the prime factors of p (2*3=6) IS a factor of q but not every factor of p is a factor of q (for example 36 is not a factor of 6). Though if p=q=6, then we'll have that every factor of p a factor of q. Not sufficient.
Answer: A.
21 Oct 2021, 00:22
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Bunuel
Hi Bunuel,
Hope you are doing well.
Request you to clear my doubt. My doubt is can we read 'every factor of p a factor of q?' as is p=q.
Because, in my opinion, an integer must be the same as another integer for every factor to be the same.
Waiting for your response ahead and many thanks in advance.
