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# If m and n are positive integers, what is the value of 3/m + n/4 ?

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Senior Manager
Joined: 04 Sep 2017
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If m and n are positive integers, what is the value of 3/m + n/4 ?  [#permalink]

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21 Sep 2019, 19:20
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Difficulty:

55% (hard)

Question Stats:

61% (01:43) correct 39% (01:49) wrong based on 72 sessions

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If m and n are positive integers, what is the value of 3/m + n/4 ?

(1) mn = 12

(2) 3/m is in lowest terms and n/4 is in lowest terms.

DS65291.01

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Kudos
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Posts: 8326
Re: If m and n are positive integers, what is the value of 3/m + n/4 ?  [#permalink]

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21 Sep 2019, 22:20
If m and n are positive integers, what is the value of 3/m + n/4 ?

$$\frac{3}{m} + \frac{n}{4} =\frac{12+mn}{4n}$$

(1) mn = 12
If m=3 and n=4....$$\frac{12+mn}{4n}=\frac{12+12}{4*4}=\frac{3}{2}$$
If m=1 and n=12....$$\frac{12+mn}{4n}=\frac{12+12}{4*12}=\frac{1}{2}$$
Insufficient

(2) 3/m is in lowest terms and n/4 is in lowest terms.
This means that m is NOT a multiple of 3 and n is NOT a multiple of 2 .
We know nothing about m and n.
m and n could be 4 and 3 OR 7 and 7..
Insufficient

Combined..
mn=12=1*12=2*6=3*4..
m and n can be 1 and 12 or 12 and 1 ...NO, m can NOT be a multiple of 3 and n can NOT be a multiple of 2 ...
m and n can be 2 and 6 or 6 and 2.......NO, n cannot be a multiple of 2
m and n cannot be 3 and 4 ...NO, m can NOT be a multiple of 3 and n can NOT be a multiple of 2 ...
So, ONLY possibility is m and n can be 4 and 3...
m=4 and n=3....$$\frac{12+mn}{4n}=\frac{12+12}{4*3}=2$$
Sufficient

B
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Re: If m and n are positive integers, what is the value of 3/m + n/4 ?  [#permalink]

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14 Nov 2019, 12:02
What is the logic for lowest term to not be a multiple of those integers?

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If m and n are positive integers, what is the value of 3/m + n/4 ?  [#permalink]

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19 Nov 2019, 11:27
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shaonkarim wrote:
What is the logic for lowest term to not be a multiple of those integers?

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when it is a multiple, the fraction wont be in its lowest term e.g . 3/12,3/9,3/6..... is not in its lowest term right? why? because 12 is a multiple of 3 and 9,6 are all multiples of 3.
lowest term for 3/12= 1/4 , 3/9=1/3 ...etc

now 3/7 ,3/8,3/5,3/13.......is in its lowest term right? why? because seven (7) aint a multiple if three (3) , we can also say 3 and 7 ,3 and 8 ........are co-prime
got it?
If m and n are positive integers, what is the value of 3/m + n/4 ?   [#permalink] 19 Nov 2019, 11:27
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