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..
answer will be different
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
_________________

What is the logic for lowest term to not be a multiple of those integers?

Posted from my mobile device

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?
_________________

Hi, it should be \(\frac{12+mn}{4m}\)

Only when m is not a multiple of 3 it is in its lowest form, otherwise we could divide both numerator and denominator by 3.
Same for n. The lowest multiple is 2.
_________________

1. \(\frac{3}{m} + \frac{n}{4}\) can be simplified to \(\frac{12 + mn}{4m}\)

Option A - Insufficient
Even if we plug in \(mn = 12\), then a variable \(m\) still remains in the denominator - \(\frac{24}{4m} = \frac{6}{m}\)

Option B - Insufficient
Says that the two fractions are in the lowest terms, which means that these fractions cannot be simplified any further e.g. \(\frac{3}{4}\) or \(\frac{1}{4}\)

Combining both statements
\(m * n = 12\) can have the following values of \(m\) and \(n\)

a. 1 * 12 or 12 * 1
b. 3 * 4 or 4 * 3
c. 2 * 6 or 6 * 2

Out of the above 6 combinations a., c. and first combination from b. can be eliminated because these do not meet the second statement e.g. \(n = 12\) gives \(\frac{12}{4} = 3\) but second statement states that the fractions are in the lowest terms or cannot be simplified further.

Only b. survives the test of the second statement which gives fractions that cannot be simplified any further i.e. \(\frac{3}{m} = \frac{3}{4}\) and \(\frac{n}{4} = \frac{4}{3}\)

\(m = 4\) and \(n = 3\) can be plugged in to yield \(\frac{3}{4} + \frac{3}{4} = 1.5\)

Ans. C
_________________

Solution:

Statement One Only:
mn = 12

If m = 12 and n = 1, then 3/m + n/4 = 3/12 + 1/4 = 1/4 + 1/4 = 1/2.

On the other hand, if m = 6 and n = 2, then 3/m + n/4 = 3/6 + 2/4 = 1/2 + 1/2 = 1.

We see that statement one alone is not sufficient to answer the question.


Statement Two Only:
3/m is in lowest terms and n/4 is in lowest terms.

If m = n = 1, then 3/m + n/4 = 3/1 + 1/4 = 3 1/4 = 3.25.

On the other hand, if m = 2 and n = 3, then 3/m + n/4 = 3/2 + 3/4 = 9/4 = 2.25.

We see that statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statement one, we can conclude that {m, n} must equal {1, 12}, {2, 6} or {3, 4}. Using statement two, we see that the only way 3/m and n/4 can both be in lowest terms is if m = 4 and n = 3. Thus, 3/m + n/4 = 3/4 + 3/4 = 3/2.

Statements one and two together are sufficient to answer the question:

Answer: C
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________