Practice GMAT Data Sufficiency Question

a, b, c, and d are integers; abcd≠0; what is the value of cd?

A)	Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)	Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)	BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D)	EACH statement ALONE is sufficient.
E)	Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Correct Answer: C

Evaluate Statement (1) alone.
1. Cross-multiply:
  c/b = 2/d
  cd = 2b
2. Since b could be any integer, the value of cd cannot be definitively determined. For example, if b = 2, then cd = 4. However, if b = 3, then cd = 6.
3. Since we cannot determine the value of cd, Statement (1) is NOT SUFFICIENT.
Evaluate Statement (2) alone.
1. Simplify by dividing common terms:
  b³a⁴c = 27a⁴c
  b³ = 27; (divided by a⁴c)
  b = 3
2. By knowing that b = 3, there is no information about the value of cd. (Do not make the mistake of importing the information from Statement (1) into your evaluation of Statement (2)).
3. Since we cannot determine the value of cd, Statement (2) is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
1. Combining Statements (1) and (2), you know that b = 3 and cd = 2b.
2. By plugging b = 3 into cd=2b, you know that cd = 2(3) = 6. Combining Statements (1) and (2), you can find a definitive value of cd.
Statements (1) and (2), when taken together, are SUFFICIENT. Answer C is correct.