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Joined: 17 Jan 2011
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If q is a positive integer, is p*q/q^(1/2) an integer?
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Updated on: 02 Dec 2017, 05:26
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59% (00:44) correct 41% (00:39) wrong based on 190 sessions
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If \(q\) is a positive integer, is \(p\frac{q}{\sqrt{q}}\) an integer? (1) \(q = p^2\) (2) \(p\) is a positive integer M0220 Attachment:
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Originally posted by ravsg on 27 Apr 2011, 19:57.
Last edited by Bunuel on 02 Dec 2017, 05:26, edited 2 times in total.
Renamed the topic and edited the question.



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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16 Nov 2014, 21:20
1) q=p^2 take the square root on both sides p=(sqroot)q
so p*(q/(sqroot)q) = (sqroot)q * q/(sqroot)q = q and from definition we know that q is a positive integer. sufficient
2)p is an integer let p=2 and q=3 then the equation becomes 2 * 3 / (sqroot)3 which is not an integer let p=2 and q=4 then the equations becomes 2 * 4 / (sqroot)4 = 4 which is an integer insufficient
Answer is A



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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17 Nov 2014, 00:39



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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17 Nov 2014, 03:25
Expression given pq/q^1/2
this can be further simplified as (pq/q^1/2)*(q^1/2)/q^1/2 this will reduced to pq^1/2
1)q=p^2 since q is positive integer the main expression will be =p^2. is an integer. Sufficient 2)p is positive integer. this does not provide any solution. Insufficient
Answer is A



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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17 Nov 2014, 10:29
statement 1: sufficient If q=p^2 and q is a positive integer, then p must also be an integer. After plugging in p^2 for Q in the question , then after reducing you see that it is equal to p^2.
statement 2: insufficient If q=9 and p=2 then plug into the equation to get 6 as your answer. However, if you plug in q=6 and p=2, the equation does not equal an integer. not enough info.
Answer A!



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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02 Dec 2017, 05:21
In A  q = p^2 , => sqroot(q) = sqroot(p^2); sqroot(q) = p
Question = p* q / sqroot(q) = p * q / p = q.
It is given q is positive hence it is positive.



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Re: If q is a positive integer, is p*q/q^(1/2) an integer?
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13 Jan 2019, 01:53
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