If i, a and b are integers, is 4(3b + 2) = 5a? (1) If i is

[BTGmoderatorDC]

If i, a and b are integers, is 4(3b + 2) = 5a?

(1) If i is divided by 5 the quotient is a and the remainder is 3
(2) If i is divided by 12 the quotient is b and the remainder is 11

OA C

Source: Economist Gmat

[Brent@GMATPrepNow]

If i, a and b are integers, is 4(3b + 2) = 5a?

(1) If i is divided by 5 the quotient is a and the remainder is 3
(2) If i is divided by 12 the quotient is b and the remainder is 11

Target question: Is 4(3b + 2) = 5a?

Statement 1: If i is divided by 5 the quotient is a and the remainder is 3
ASIDE: There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

So, we can take the given information and write: i = 5a + 3
Since we have no information about b, there's no way to answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: If i is divided by 12 the quotient is b and the remainder is 11
We can write: i = 12b + 11
Since we have no information about a, there's no way to answer the target question.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that i = 5a + 3
Statement 2 tells us that i = 12b + 11
Since both equations are set equal to i, we can write: 12b + 11 = 5a + 3
Subtract 3 from both sides to get: 12b + 8 = 5a
Factor left side to get: 4(3b + 2) = 5a
The answer to the target question is YES, it IS the case that 4(3b + 2) = 5a
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent