Last Updated on May 9, 2023
GMAT OFFICIAL GUIDE DS –
Solution:
We need to determine the value of b + c.
Statement One Alone:
ab + cd + ac + bd = 6
We start by rearranging terms and then factoring out common terms.
ab + ac + cd + bd = 6
a(b + c) + d(c + b) = 6
(b + c)(a + d) = 6
We see that we do not have enough information to determine the value of b + c. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
a + d = 4
Only knowing that a + d = 4 is not enough to determine the value of b + c. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two we know that (b + c)(a + d) = 6 and that a + d = 4. Thus,
(b + c)(4) = 6
b + c = 6/4 = 3/2
Statements one and two together are sufficient to answer the question.
Answer: C
