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

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VP
Joined: 14 Nov 2016
Posts: 1103

Kudos [?]: 1053 [1], given: 377

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

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23 Mar 2017, 00:17
1
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6
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Difficulty:

95% (hard)

Question Stats:

28% (01:04) correct 72% (01:10) wrong based on 104 sessions

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

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

2) p=7
[Reveal] Spoiler: OA

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Kudos [?]: 1053 [1], given: 377

Senior Manager
Joined: 13 Oct 2016
Posts: 367

Kudos [?]: 389 [0], given: 40

GPA: 3.98
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.

Kudos [?]: 389 [0], given: 40

Intern
Joined: 09 Jun 2017
Posts: 12

Kudos [?]: 0 [0], given: 55

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

Kudos [?]: 0 [0], given: 55

Director
Joined: 21 May 2013
Posts: 532

Kudos [?]: 66 [0], given: 477

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

Kudos [?]: 66 [0], given: 477

Math Expert
Joined: 02 Sep 2009
Posts: 41695

Kudos [?]: 124574 [1], given: 12079

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

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15 Aug 2017, 09:56
1
KUDOS
Expert's post
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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Kudos [?]: 124574 [1], given: 12079

Re: If m, n, and p are positive integers, mnp= ?   [#permalink] 15 Aug 2017, 09:56
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