GMAT Question of the Day – 11/1/2021

QUESTION

What is the value of a ?

STATEMENT 1:

a ² = b²

STATEMENT 2:

b – a = -12

ANSWER SELECTION

(A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

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

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

(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

CORRECT ANSWER IS C.

Statement (1): insufficient. All we know is that the square of a equals the square of b. a can have any real value. Thus, we can have a = 3 and b = 3. We can have a = 7 and b = 7. Let’s note that we must have a = b or a = –b. So a and bdo not have to be equal. a can be the negative of b. Since a can have any real value, statement (1) is insufficient. We can thus eliminate choices (A) and (D).

Statement (2): insufficient. Solving for a, we have that a = b + 12. However, since we have no value for b, it is impossible to determine the value for a. Eliminate choice (B).

Statements (1) and (2): sufficient. We know from statement (1) that a = b or that –a = b. Looking at statement (2), we know that it must be the latter, for a cannot equal a + 12. So, substitute –a for b in the equation b – a = -12. Then -a – a = -12, or -2a = -12. Thus, we can find the value of a. The statements taken together are sufficient. Choice (C) is correct.

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