helen.xia@mbawatch wrote:If a, b, and c are positive distinct integers, is (a/b)/c an integer?

1) c = 2
2) a = b + c

Target question: Is (a/b)/c an integer?

Since (a/b)/c = a/bc, we can rephrase the target question as . . .
Rephrased target question: Is a/bc an integer?

Given: a, b, and c are distinct positive integers

Statement 1: c = 2
There are several values for a, b and c that satisfy this condition. Here are two:
Case a: a = 4, b = 1, and c = 2, in which case a/bc IS an integer
Case b: a = 1, b = 3, and c = 2, in which case a/bc is NOT an integer
Since we cannot answer the rephrased target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a = b + c
Take the rephrased target question and replace a with b + c to get:
Is (b+c)/bc an integer?
The answer here is NO. (b+c)/bc is definitely NOT an integer.
Here's why.
(b+c)/bc = b/bc + c/bc
= 1/c + 1/b

Since b and c are positive AND distinct integers, the possible values for 1/c and 1/b are 1/1, 1/2, 1/3, 1/4, 1/5, etc.
As you can see, there's no way that ANY two (different) fractions could ever add to be an integer
Answer = B

Cheers,
Brent