Solutions

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Question

What is the value of 6^x*6^y ?

I. 2^(x+y) = 32

II. 3^(x+y) = 243


 

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

Medium

Solution

Option D is the correct answer.


Option Analysis

6^x∗6^y=6^x+y, so to find the value of 6^x*6^y we need to find the value of x + y.

Statement I is sufficient: 2^(x+y) = 32 –> 2x+y=25 –> equate the powers: x + y = 5. Sufficient.

Statement II is sufficient: 3^(x+y) = 243 –> 3x+y=35 –> equate the powers: x + y = 5. Sufficient.


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