Solutions

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Question

If x is a nonzero number, which of the three numbers x, 1/x and x^2 is greatest?

I. -1 < x < 1

II. x is negative


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Hard

Solution

Option B is the correct answer.


Option Analysis

Statement I is insufficient: -1 < x < 1. If x=1/2, then x=1/2, 1/x=2, and x^2=1/4, so 1/x has the greatest value but if x is negative, then both x and 1/x are negative and x^2=positive, so x^2 has the greatest value. Not sufficient.

Statement II is sufficient: x is negative. For negative x both x and 1/x are negative and x^2=positive, so x^2 has the greatest value. Sufficient.


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