Brent@GMATPrepNow wrote:b, c, d, e, f and g are different positive integers. When b is divided by c, the remainder is d. When e is divided by f, the remainder is g. What is the value of d+g?

(1) b + e = 16
(2) c + f = 6

Answer: B
Source: www.gmatprepnow.com
Difficulty level: 650

Given: b, c, d, e, f and g are different positive integers. When b is divided by c, the remainder is d. When e is divided by f, the remainder is g.

Target question: What is the value of d+g?

Statement 1: b + e = 16
There are several cases that satisfy statement 1. Here are two:
Case a: b = 5, c = 2, d = 1, e = 11, f = 4 and g = 3. In this case, the answer to the target question is d + g = 1 + 3 = 4
Case b: b = 5, c = 2, d = 1, e = 11, f = 7 and g = 4. In this case, the answer to the target question is d + g = 1 + 4 = 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: c + f = 6
If c + f = 6, then it MUST be the case that one value (c or f) is 4 and the other value is 2.
How do we know this?
Well, c and f can't both equal 3, since all 6 values are DIFFERENT
Also, neither value can be 0, since we're told all 6 values are POSITIVE
And, the numbers cannot be 1 and 5, because if we divide by 1, we get a remainder of 0, and we're told all 6 values are POSITIVE.
So, the two values must be 2 and 4.

---ASIDE---
Useful remainder property
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
-----------

When we apply the above property, we can conclude that d < c and g < f
So, the GREATEST possible value of d+g is 4.
We also know that d+g cannot add to 3, because the only way to get a sum of 3 is for the numbers to be 1 and 2, and we already
accounted for the 2 when we concluded that one one value (c or f) is 4 and the other value is 2.
Using similar logic, we can show that d+g cannot add to 2 or 1 either.
So, it MUST be the case that d + g = 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Aside: here's one way to for d+g to equal 4:
b = 5, c = 2, d = 1, e = 11, f = 4 and g = 3. In this case, the answer to the target question is d + g = 1 + 3 = 4

Cheers,
Brent