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If p is divisible by 7 and q is divisible by 6, pq must have
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12 Aug 2018, 15:40
12 Aug 2018, 15:40
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Question Stats:
41% (00:52) correct
58% (00:51) wrong based on 67 sessions
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If p is divisible by 7 and q is divisible by 6, pq must have at least how many factors greater than 1?
(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight
(A) One
(B) Three
(C) Six
(D) Seven
(E) Eight
Re: If p is divisible by 7 and q is divisible by 6, pq must have
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15 Aug 2018, 08:18
15 Aug 2018, 08:18
Expert Reply
Explanation
This problem is most easily solved with an example. If p = 7 and q = 6, then pg = 42, which has the factors 1 & 42, 2 & 21, 3 & 14, and 6 & 7. That’s 8 factors, but read carefully!
The question asks how many factors greater than 1, so the answer is 7. Note that choosing the smallest possible examples (p = 7 and q = 6) was the right move here, since the question asks “at least how many factors … ?” If testing p = 70 and q = 36, many, many more factors would have resulted.
The question asks for the minimum.
This problem is most easily solved with an example. If p = 7 and q = 6, then pg = 42, which has the factors 1 & 42, 2 & 21, 3 & 14, and 6 & 7. That’s 8 factors, but read carefully!
The question asks how many factors greater than 1, so the answer is 7. Note that choosing the smallest possible examples (p = 7 and q = 6) was the right move here, since the question asks “at least how many factors … ?” If testing p = 70 and q = 36, many, many more factors would have resulted.
The question asks for the minimum.
Re: If p is divisible by 7 and q is divisible by 6, pq must have
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29 May 2025, 18:56
29 May 2025, 18:56
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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