GMAT Question of the Day – 12/12/2020

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.

(D) EITHER statement BY ITSELF is sufficient to answer the question.

(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

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 b², we have a² = b². Now having a² = b² 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 a² = b², and in this case, a = b, so the answer to the question is “yes.” However, if a = 4 and b = -4, then a² = a², 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 17a + 4b = 21a. Subtracting 17a from both sides, we have 4b = 4a. 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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