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

Question

(1) mn = 12

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

DS65291.01

chetan2u · Accepted Answer

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

shaonkarim · Answer

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

Posted from my mobile device

Staphyk · Answer

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?

lcueto · Answer

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

hemantbafna · Answer

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.

Pritishd · Answer

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

ScottTargetTestPrep · Answer

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

akshitam27 · Answer

What does lowest form exactly mean here?

Shouldn't it be the forms when 3/m and n/4 are the lowest which happens when we combine statements and take my = 12 and n = 1 and also when m = 6 and n = 2 making the sum = 0.5 and instead when we take m = 4 and n = 3 the sum is 1.5 and even the individual terms are higher in this case.

mikemcgarry   Bunuel

Bunuel · Answer

An irreducible fraction  (or  fraction in lowest terms ,  simplest form  or  reduced fraction ) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered).

So, a/b is a fraction in lowest terms when it cannot be further reduced. For example, 3/4 is in lowest terms, because you cannot reduce it further while 3/6 is NOT in lowest terms, because you can reduce it further and get 1/2, which is in lowest terms.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards