GMAT Math : Powers & Roots of Numbers
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #1291 : Data Sufficiency Questions
Statement 1: 
Statement 2: 
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 alone is not enough to determine whether 
Assume both statements are true. 
Example Question #3401 : Gmat Quantitative Reasoning
Let 
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
We examine two examples of situations in which both statements hold.
Example 1:
Then
32 is not a perfect square, so 
Example 2:
Then 
In both cases, both statements hold, but in only one, 
Example Question #1293 : Data Sufficiency Questions
Simplify:
When we are faced with a radical in the denominator of a fraction, the first step is to multiply the top and bottom of the fraction by the numerator:
We can then reduce the fraction to:
Example Question #1294 : Data Sufficiency Questions
Statement 1: 
Statement 2: 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient to answer the question.
Either statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient to answer the question.
Both statements TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient to answer the question.
Both statements TOGETHER are insufficient to answer the question.
Both statements TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient to answer the question.
A negative integer to an even power is positive:
Example:
A negative integer to an odd power is negative:
Example:
A positive integer to an odd power is positive:
Example:
So, as seen in the first two statements, knowing only that base 
The answer is that both statements together are sufficient to answer the question, but neither statement alone is sufficient.
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