Solutions
Get detailed explanations to advanced GMAT questions.
Question
If m and n are integers and x > 0, what is the value of x^m+x^n?
I. x^m=81
II. 1+x^(n−m)=10
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
EasySolution
Option C is the correct answer.
Option Analysis
Statement I is insufficient: x^m=81. No info about n. Not sufficient.
Statement II is insufficient: 1+x^(n−m)=10 –> x^(n−m)=9 –> (x^n)/(x^m)=9 –> x^n=9x^m –> x^m+x^n=10x^m. Not sufficient.
Together I and II, x^m+x^n=10*x^m=10∗81. Sufficient.
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