BTGmoderatorDC wrote: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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