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# If n and m are positive integers and m is a factor of 6^2, what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 59674
If n and m are positive integers and m is a factor of 6^2, what is the  [#permalink]

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20 Nov 2019, 00:07
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65% (hard)

Question Stats:

54% (02:12) correct 46% (02:08) wrong based on 50 sessions

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If n and m are positive integers and m is a factor of 6^2, what is the greatest possible number of integers that can be equal to both 3n and 6^2/m ?

A. Zero
B. One
C. Three
D. Four
E. Six

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Re: If n and m are positive integers and m is a factor of 6^2, what is the  [#permalink]

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20 Nov 2019, 11:28
Bunuel wrote:
If n and m are positive integers and m is a factor of 6^2, what is the greatest possible number of integers that can be equal to both 3n and 6^2/m ?

A. Zero
B. One
C. Three
D. Four
E. Six

Are You Up For the Challenge: 700 Level Questions

Now m can be any of the factors 1, 2,3,4,6,9,12,18,36...
But 36/m =3n.....12=mn
So for all m as factors of 12, n is a positive integer.
So m can be 1,2,3,4,6,12 and corresponding values of n too are 12,6,4,3,2,1
Hence 6 values of 3n.

E
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Re: If n and m are positive integers and m is a factor of 6^2, what is the  [#permalink]

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22 Nov 2019, 09:03
Question implies to me that M is in the expnent? ^(m/2) or not?
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Re: If n and m are positive integers and m is a factor of 6^2, what is the  [#permalink]

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24 Nov 2019, 23:48
Bunuel wrote:
If n and m are positive integers and m is a factor of 6^2, what is the greatest possible number of integers that can be equal to both 3n and 6^2/m ?

A. Zero
B. One
C. Three
D. Four
E. Six

Are You Up For the Challenge: 700 Level Questions

6^2 has 9 factors( $$2^2*3^2$$)
Since 3n is a multiple of 3, for 3n to be equal to 6^2/m, we have to count only those factors which comprise 3 or multiple of 3
out of 9 multiple 2^0,2^1, 2^2 have nothing to do with multiple of 3
so 6 factors
E:)
Re: If n and m are positive integers and m is a factor of 6^2, what is the   [#permalink] 24 Nov 2019, 23:48
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