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# If m and n are positive integers and mn = 30, what is the value of m ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51101
If m and n are positive integers and mn = 30, what is the value of m ?  [#permalink]

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16 Dec 2017, 00:34
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Difficulty:

35% (medium)

Question Stats:

62% (01:06) correct 38% (00:58) wrong based on 46 sessions

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If m and n are positive integers and mn = 30, what is the value of m ?

(1) n is an odd prime.
(2) m and n are consecutive integers.

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Joined: 12 Aug 2015
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Schools: Boston U '20 (M)
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Re: If m and n are positive integers and mn = 30, what is the value of m ?  [#permalink]

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16 Dec 2017, 00:46
Lets see.
The best course of action is off course a hit and trail.
I would not sit around and make all the pairs of product = 30

Statement 1 ->

(3,10)
(5,6)

Not sufficient
Statement 2 => Hmm
(5,6)
(6,5)

Not sufficient

Combining them up ->

n=5 and m=6

Hence sufficient.

SMASH THAT C.

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Re: If m and n are positive integers and mn = 30, what is the value of m ?  [#permalink]

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16 Dec 2017, 00:48
Bunuel wrote:
If m and n are positive integers and mn = 30, what is the value of m ?

(1) n is an odd prime.
(2) m and n are consecutive integers.

$$mn=30 =>m=\frac{30}{n}$$. $$30$$ is divisible by $$n$$ as $$m$$ is a positive integer

Statement 1: $$n$$ could be $$3$$ or $$5$$. so no unique value for $$m$$. Insufficient

Statement 2: if $$n=6$$, $$m=5$$ & if $$n=5$$, $$m=6$$. No unique value. Insufficient

Combining 1 & 2, we know $$n$$ is odd prime. So $$n=5$$ & $$m=6$$. Sufficient

Option C
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Re: If m and n are positive integers and mn = 30, what is the value of m ?  [#permalink]

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16 Dec 2017, 09:07
Bunuel wrote:
If m and n are positive integers and mn = 30, what is the value of m ?

(1) n is an odd prime.
(2) m and n are consecutive integers.

So, possible solutions for mn (positive integers) = 30 is {30-1,15-2,10-3,6-5}.

(1) n is an odd prime. Then n = 3 and m = 10 or n = 5 and m = 5. Insufficient.

(2) m and n are consecutive integers. Then, m = 6 and n = 5 or m = 5 and n = 6. Insufficient.

(3) Combining both, we know that they are consecutive and that n is an odd prime, so n = 5 and m = 6. Sufficient.

Re: If m and n are positive integers and mn = 30, what is the value of m ? &nbs [#permalink] 16 Dec 2017, 09:07
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