gmatt1476
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
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