Solutions
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Question
a is a nonzero integer. Is a^a greater than 1?
I. a < -1
II. a is even
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
MediumSolution
Option A is the correct answer.
Option Analysis
Statement I is sufficient: a < -1. So, a could be -2, -3, -4, … If a is a negative even integer, then a^a will be a positive fraction less than 1 (for example, if a = -2, then a^a = (-2)^(-2) = 1/4) and if a is a negative odd integer, then a^a will be a negative fraction greater than -1 (for example, if a = -3, then a^a = (-3)^(-3) = -1/27). In any case the result is less than 1. Sufficient.
Statement II is insufficient: a is even. If a = 2, then a^a = 4 > 1 but if a = -2, then a^a = 1/4 < 1. Not sufficient.