Target question: What is the value of b + c ?
Statement 1: ab + cd + ac + bd = 6
Rearrange terms: ab + ac + bd + cd = 6
Factor the a out of the first two terms to get: a(b + c) + bd + cd = 6
Factor the d out of the last two terms to get: a(b + c) + d(b + c) = 6
Rewrite as: (a + d)(b + c) = 6
There are infinitely many values of a, b, c and d that satisfy the equation (a + d)(b + c) = 6. Here are two:
Case a: a + d = 1 and b + c = 6. In this case, the answer to the target question is b + c = 6
Case b: a + d = 2 and b + c = 3. In this case, the answer to the target question is b + c = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a + d = 4
Since we're given NO INFORMATION about b and c, we cannot answer the target question with certainty.
So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that (a + d)(b + c) = 6
Statement 2 tells us that a + d = 4
Take the first equation and replace a + d with 4
We get: (4)(b + c) = 6
So, is MUST be the case that b + c = 1.5
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
