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# If m and n are positive integers and mn = 24, what is the value of m ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
If m and n are positive integers and mn = 24, what is the value of m ?  [#permalink]

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19 Jan 2018, 10:54
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25% (medium)

Question Stats:

84% (01:36) correct 16% (01:33) wrong based on 64 sessions

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If m and n are positive integers and mn = 24, what is the value of m ?

(1) n is the square of a prime number.
(2) m is the product of two distinct prime numbers.

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Joined: 23 Feb 2017
Posts: 58
If m and n are positive integers and mn = 24, what is the value of m ?  [#permalink]

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19 Jan 2018, 11:28
m and n positive integer and mn = 24

m = 1 and n= 24 or m = 24 and n = 1
m = 2 and n= 12 or m = 12 and n = 2
m = 3 and n= 8 or m = 8 and n = 3
m = 4 and n= 6 or m = 6 and n = 4

(1) n is the square of a prime number.
n= 4 and m= 6 Sufficient

(2) m is the product of two distinct prime numbers.
m= 3*2=6 and n = 4 Sufficient

Ans D
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Joined: 28 Jan 2015
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Re: If m and n are positive integers and mn = 24, what is the value of m ?  [#permalink]

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20 Jan 2018, 12:22
mandeey wrote:
m and n positive integer and mn = 24

m = 1 and n= 24 or m = 24 and n = 1
m = 2 and n= 12 or m = 12 and n = 2
m = 3 and n= 8 or m = 8 and n = 3
m = 4 and n= 6 or m = 6 and n = 4

(1) n is the square of a prime number.
n= 4 and m= 6 Sufficient

(2) m is the product of two distinct prime numbers.
m= 3*2=6 and n = 4 Sufficient

Ans D

I agree with ANS D, but I approached this question differently.

Rather than state all the factors of "mn = 24", I just factorized it:

mn = 24 = 2^3 * 3

(1) n is the square of a prime number.

The only possible value to n is 2^2 = 4, so m = 2*3 = 6.

Sufficient.

(2) m is the product of two distinct prime numbers.

In this case, the only two distinct prime numbers are 2 and 3, so again m = 2*3 = 6.

Sufficient.

Ans D.
Re: If m and n are positive integers and mn = 24, what is the value of m ?   [#permalink] 20 Jan 2018, 12:22
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