Practice GMAT Data Sufficiency Question
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a, b, c, and d are integers; abcd≠0; what is the value of cd?
- c/b = 2/d
- b3a4c = 27a4c
Correct Answer: C
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Evaluate Statement (1) alone.
- Cross-multiply:
c/b = 2/d
cd = 2b
- 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.
- Since we cannot determine the value of cd, Statement (1) is NOT SUFFICIENT.
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Evaluate Statement (2) alone.
- Simplify by dividing common terms:
b3a4c = 27a4c
b3 = 27; (divided by a4c)
b = 3
- 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)).
- Since we cannot determine the value of cd, Statement (2) is NOT SUFFICIENT.
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Evaluate Statements (1) and (2) together.
- Combining Statements (1) and (2), you know that b = 3 and cd = 2b.
- 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.
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