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# If 'm' is an integer and 35!/3^m is an integer, then what could be the

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If 'm' is an integer and 35!/3^m is an integer, then what could be the [#permalink]

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22 Nov 2017, 09:13
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If 'm' is an integer and $$\frac{35!}{3^m}$$ is an integer, then what could be the maximum possible value of 'm'?
A) 15
B) 12
C) 10
D) 9
E) Cannot be determined
[Reveal] Spoiler: OA

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If 'm' is an integer and 35!/3^m is an integer, then what could be the [#permalink]

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22 Nov 2017, 10:16
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souvonik2k wrote:
If 'm' is an integer and $$\frac{35!}{3^m}$$ is an integer, then what could be the maximum possible value of 'm'?
A) 15
B) 12
C) 10
D) 9
E) Cannot be determined

$$\frac{35}{3} + \frac{35}{3^2} + \frac{35}{3^3} = 11+3+1 =15$$

Option A

Refer article by Bunuel to know the formula

https://gmatclub.com/forum/everything-a ... 85592.html
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Re: If 'm' is an integer and 35!/3^m is an integer, then what could be the [#permalink]

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22 Nov 2017, 10:56
souvonik2k wrote:
If 'm' is an integer and $$\frac{35!}{3^m}$$ is an integer, then what could be the maximum possible value of 'm'?
A) 15
B) 12
C) 10
D) 9
E) Cannot be determined

35! is the product of all the number from 1 to 35.

Starting from 1 till 35,
there are 11 multiples of 3, 3 multiples of $$9(3^2)$$ and only 1 multiple of $$27(3^3)$$

Therefore, m has a maximum value of $$11+3+1 = 15$$(Option A)
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Re: If 'm' is an integer and 35!/3^m is an integer, then what could be the   [#permalink] 22 Nov 2017, 10:56
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