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

[BTGmoderatorDC]

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.




OA C

Source: Official Guide

[Jay@ManhattanReview]

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.

OA C

Source: Official Guide

We have to get the value of 3/m + n/4.

3/m + n/4 = (12 + mn)/4m

Let's take each statement one by one.

(1) mn = 12

(12 + mn)/4m = (12 + 12)/4m = 6/m. We do not know the value of m. Given that mn = 12 and m and n are positive integers, there can be six possible values of m: (1) m = 1 and n = 12; (2) m = 12 and n = 1; (3) m = 3 and n = 4; (4) m = 4 and n = 3; (5) m = 2 and n = 6; and (6) m = 6 and n = 2. Thus, the value of 6/m is not unique sufficient.

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

It means that the fractions 3/m and n/4 cannot be further reduced. Thus, 3 and m are co-prime and n and 4 are co-prime. Still, there are many possible values of m and n; for example m = n = 7, and m = 8 and n = 5, etc. Thus, the unique value of 3/m + n/4 cannot be determined. Insufficient.

(1) and (2) together

Let's list down the six possible sets of values of m and n.

(1) m = 1 and n = 12: The value of n is not qualified as 12 and 4 are not co-prime.

(2) m = 12 and n = 1: The value of m is not qualified as 12 and 3 are not co-prime.

(3) m = 3 and n = 4: The value of m is not qualified as 3 and 3 are not co-prime.

(4) m = 4 and n = 3: The values of m and n are qualified. This is a possible solution. Thus, 3/m + n/4 = 3/4 + 3/4 = 3/2.

(5) m = 2 and n = 6: The value of n is not qualified as 6 and 4 are not co-prime.

6) m = 6 and n = 2: The value of m is not qualified as 6 and 3 are not co-prime.

Thus, m = 4 and n = 3 and 3/m + n/4 = 3/4 + 3/4 = 3/2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

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.




OA C

Source: Official Guide

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