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# If m, n, and p are positive integers, mnp= ?

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Senior SC Moderator
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If m, n, and p are positive integers, mnp= ?  [#permalink]

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23 Mar 2017, 00:17
3
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Difficulty:

95% (hard)

Question Stats:

32% (01:08) correct 68% (01:13) wrong based on 124 sessions

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If m, n, and p are positive integers, mnp= ?

1) $$m^4*np=2,835$$

2) p=7

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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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23 Mar 2017, 03:15
ziyuen wrote:
If m, n, and p are positive integers, mnp= ?

1) $$m^4*np=2,835$$

2) p=7

1) $$m^4*np=2,835$$

$$m^4*n*p = 3^4*5*7$$

$$n*p$$ can be ---> (1*56), (5*7), (7*5),(56*1) Insufficient.

2) p=7 Clearly insufficient.

(1)&(2) Sufficient at first glance but we should not forget about $$1$$. $$m^4$$ can bee either $$3^4$$ or $$1^4$$ ---- $$1^4*2835$$ or $$3^4*56$$. Still insufficient.

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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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15 Aug 2017, 08:17
Could you, please, elaborate on where 1*56 and 56*1 pairs for n*p are coming from? To me m can be either 1 or 3, if it is 3 then n*p=5*7=35.If m is 1 then n*p=2,835. I don't see how n*p can equal 56...Thanks
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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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15 Aug 2017, 09:35
venstein wrote:
Could you, please, elaborate on where 1*56 and 56*1 pairs for n*p are coming from? To me m can be either 1 or 3, if it is 3 then n*p=5*7=35.If m is 1 then n*p=2,835. I don't see how n*p can equal 56...Thanks

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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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15 Aug 2017, 09:56
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hazelnut wrote:
If m, n, and p are positive integers, mnp= ?

1) $$m^4*np=2,835$$

2) p=7

E is correct. Consider the following:

m = 1, n = 3^4*5, p = 7 --> mnp = 2,835;
m = 3, n = 5, p = 7 --> mnp = 105.

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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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02 Oct 2017, 19:54
Pay attention to special case in which m = 1!
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Re: If m, n, and p are positive integers, mnp= ?  [#permalink]

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03 Oct 2017, 00:00
hazelnut wrote:
If m, n, and p are positive integers, mnp= ?

1) $$m^4*np=2,835$$

2) p=7

Factorization of 2835 =3^4*5*7

But we are not told that n and p have to be prime so following cases are possible
1*3
35*1
5*7
7*5
So insufficient
p=7
it does not provide information for other variable so insufficient

Together we know p=7 then n=5
Hence together they are sufficient

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Re: If m, n, and p are positive integers, mnp= ? &nbs [#permalink] 03 Oct 2017, 00:00
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