Get detailed explanations to advanced GMAT questions.

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.

Option C is the correct answer.

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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