If a, b and c are positive integers and a/6 + b/5 = c/30, is c divisible by 5?
(1) b is divisible by 5
(2) a is even
To clear the fractions in the question stem, multiply each side by 30:
30 * (a/6 + b/5) = 30 * (c/30)
5a + 6b = c
c = 5a + 6b.
Statement 1: b is divisible by 5
If a=1 and b=5, then c = 5*1 + 6*5 = 35.
If a=2 and b=20, then c = 5*2 + 6*20 = 130.
In each case, c is a multiple of 5.
Perhaps one more case to confirm:
If a=3 and b=100, then c = 5*3 + 6*100 = 615.
In every case, c is a multiple of 5.
SUFFICIENT.
Statement 2: a is even
If a=2 and b=20, then c = 130, as shown above.
In this case, c is a multiple of 5.
If a=2 and b=1, then c = 5*2 + 6*1 = 16.
In this case, c is NOT a multiple of 5.
INSUFFICIENT.
The correct answer is
A.
Statement 1 indicates the following:
b = 5k, where k is a positive integer.
Implication:
c = 5a + 6*(5k) = 5(a + 6k) = 5 * integer.
Thus, c is a multiple of 5.
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