Table of Contents / Nội Dung Chính

### QUESTION

If *b *≠ 0, does *a* equal *b* ?

STATEMENT 1:

^{a2}⁄_{b2} + 4 = 5

STATEMENT 2:

^{17a + 4b}⁄_{7} = 3a

**ANSWER SELECTION**

**(B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. (THIS IS CORRECT!)**

(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

**ANSWER EXPLANATION**

We want to determine if there is sufficiency to say that *a* always equal *b* or *a* never equals *b*.

Statement (1) is the equation . Subtracting 4 from both sides of this equation, we have . Multiplying both sides of this equation by *b*^{2}, we have *a*^{2} = *b*^{2}. Now having *a*^{2} = *b*^{2} does not mean that we must have *a* = *b*. It is also possible that *a* = –*b*. For examples, if *a* = 4 and *b* = 4, then *a*^{2} = *b*^{2}, and in this case, *a* = *b*, so the answer to the question is “yes.” However, if *a* = 4 and *b* = -4, then *a*^{2} = *a*^{2}, and in this case *a* is not equal to *b*, so the answer to the question is “no.” Statement (1) is insufficient. We can eliminate choices (A) and (D).

Statement (2) is the equation . Let’s try to rewrite this equation. Multiplying both sides of this equation by 7, we have 17*a* + 4*b* = 21*a*. Subtracting 17*a* from both sides, we have 4*b* = 4*a*. Dividing both sides of this equation by 4, we have *b* = *a*. Thus, *a* = *b*. We can answer the question with a “yes.” We have determined that *a* does equal *b*. Statement (2) is sufficient. **Choice (B) is correct.**

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**Tags:** gmat, GMAT Quantitative