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

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