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GRE math Challenge #43-If N = 3^x*5^y, where x and y

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soumya1989
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GRE math Challenge #43-If N = 3^x*5^y, where x and y [#permalink] New post   28 Feb 2015, 03:27
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If \(N = 3^x*5^y\), where x and y are positive integers, and N has 12 positive factors, what is the value of N?

Column AColumn B
9 is not a factor125 is a factor


A. Only Column A is sufficient.
B. Only Column B is sufficient.
C. Column A and B both are needed
D. Column A and B both are insufficient
E. None of the columns are needed.
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Kentuckycats19
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Re: GRE math Challenge #43 [#permalink] New post   26 Mar 2015, 16:31
That is not a GRE question, just FYI.

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soumya1989
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Re: GRE math Challenge #43 [#permalink] New post   31 Mar 2015, 09:10
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Yes you are right!
The idea is to solve maths problems regardless what exam it is. Just to challenge brains. :wink:
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Peter
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Re: GRE math Challenge #43-If N = 3^x*5^y, where x and y [#permalink] New post   11 Mar 2018, 05:38
soumya1989 wrote:
If \(N = 3^x*5^y\), where x and y are positive integers, and N has 12 positive factors, what is the value of N?

Column AColumn B
9 is not a factor125 is a factor


A. Only Column A is sufficient.
B. Only Column B is sufficient.
C. Column A and B both are needed
D. Column A and B both are insufficient
E. None of the columns are needed.



For me, the ans would be A, we are told that \(N = 3^x*5^y\), where x and y are positive integers, and N has 12 positive factors.

then (x+1)(y+1)=12. Let us do some prime factorization of 12.

12=2*6=1*12=3*4 We should rule out the pair 1*12 since x+1 or y+1=1, then x or y=0. Yet, we are told that x and y are positive integers. Now for cloumn A, we are told that 9 is not a factor of N. This leads us to know x=1 and y=5. then \(N = 3^1*5^5\).

For column B, we are told that 125 is a factor. That means that y>=3. So, y would be 3 or 5. B can't help us decide the value of N.

ANS:A
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