If a, b, and c are positive integers, and a/6 + b/5 = c/30, is c divisible by 5?

[BTGModeratorVI]

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.

Answer: A
Source: Veritas Prep

[Brent@GMATPrepNow]

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.

Answer: A
Source: Veritas Prep

Target question: Is c divisible by 5?

Given: a/6 + b/5 = c/30
First let's eliminate the fractions by multiplying both sides of the equation be the least common multiple of 6, 5 and 30.
So, we'll multiply both sides by 30 to get: 5a + 6b = c

Statement 1: b is divisible by 5
We can apply a useful divisibility rule that says: "If j is divisible by x and k is divisible by x, then (j+k) is divisible by x"
We can ready see that 5a is divisible by 5.
And, if b is divisible by 5, then we know that 6b is divisible by 5.
So, by the above rule, we know that 5a + 6b is divisible by 5.
Since 5a + 6b = c, we can conclude that c IS divisible by 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: a is even
There are several cases that satisfy statement 2. Here are two:
Case a: a = 2 and b = 5. we know that c = 5a + 6b. So, c = 5(2) + 6(5) = 40, which is divisible by 5. In this case, c IS divisible by 5
Case b: a = 2 and b = 1. we know that c = 5a + 6b. So, c = 5(2) + 6(1) = 16, which is NOT divisible by 5. In this case, c is NOT divisible by 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent