Walkabout wrote:
What is the value of b + c ?
(1) ab + cd + ac + bd = 6
(2) a + d = 4
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 = 6Case b:
a + d = 2 and
b + c = 3. In this case, the answer to the target question is
b + c = 3Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a + d = 4Since 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 = 4Take the first equation and replace
a + d with
4We get: (
4)(
b + c) = 6
So, is MUST be the case that
b + c = 1.5Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent