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# If m is a positive integer, is 13 a factor of m?

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Math Expert
Joined: 02 Sep 2009
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If m is a positive integer, is 13 a factor of m?  [#permalink]

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06 Oct 2017, 05:49
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35% (medium)

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73% (01:08) correct 27% (01:12) wrong based on 49 sessions

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If m is a positive integer, is 13 a factor of m?

(1) 117m is the square of an integer
(2) m/117 is the square of an integer

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Joined: 12 Feb 2017
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Re: If m is a positive integer, is 13 a factor of m?  [#permalink]

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06 Oct 2017, 06:19
1
1
(1) 117m is the square of an integer
lets factorize 117 first
117= 13*9
= 13 * 3^2
It is given that 117m is a square.
means 13 * 3^2 * m is a square.
so in order to be a square, m must be at least 13. (m can also take different values. eg: 13*4^2, 13^3 etc)

Hence in any case, 13 will be the factor of m. So Statement 1 is sufficient.

(2)m/117 is the square of an integer
means m/117 has to be an integer
m/(13*9) ----> must be an integer.
so m must be divisible by both 13 and 9.

Hence Statement 2 is Sufficient.

Kudos if it helps.
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Re: If m is a positive integer, is 13 a factor of m?  [#permalink]

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06 Oct 2017, 08:28
Bunuel wrote:
If m is a positive integer, is 13 a factor of m?

(1) 117m is the square of an integer
(2) m/117 is the square of an integer

IS M = 13a ,

from 1

117m = square of an integer .... 3^2 * 13*m and m is +ve integer , thus m is in the form 13a .... suff

from 2

m/3^2*13 = x^2 , m has to be in the form 13a and min value of x^2 = 1... suff

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Re: If m is a positive integer, is 13 a factor of m?  [#permalink]

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06 Oct 2017, 08:38
If m is a positive integer, is 13 a factor of m?

(1) 117m is the square of an integer
117 = 3^2 * 13
Since 117m is a square , so there should at least another 13 in m .
Sufficient

(2) m/117 is the square of an integer
m/(3^2 * 13) is square of an integer
m should have at least one 13 .
Sufficient

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Re: If m is a positive integer, is 13 a factor of m?  [#permalink]

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06 Oct 2017, 10:26
Yes/no type Qs
13 is factor of m ?
St-1 117 m is square of a integer, means
Prime factors of 117 is 3x3x13... to make a square of integer m has to be 13. Suffcient
St- m/117 is square of integer.. to make square 13 has to cancel out with m . m is 13-Sufficient'

Re: If m is a positive integer, is 13 a factor of m? &nbs [#permalink] 06 Oct 2017, 10:26
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