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If m and n are integers greater than 1, is m^n>500?

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by Max@Math Revolution » Mon Aug 27, 2018 1:35 am

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[Math Revolution GMAT math practice question]

If m and n are integers greater than 1, is m^n>500?

1) n>8
2) n>2m
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Aug 27, 2018 5:47 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If m and n are integers greater than 1, is m^n > 500?

1) n > 8
2) n > 2m
Target question: Is m^n > 500?

Given: m and n are integers greater than 1

Statement 1: n > 8
We're told that m and n are integers greater than 1
So, the SMALLEST possible value of m is 2
And, if n > 8, the SMALLEST possible value of n is 9
When we plug in these SMALLEST values, we get: m^n = 2^9 = 512
So, the SMALLEST possible value of m^n is 512
So, m^n must be greater than or equal to 512
The answer to the target question is YES, m^n IS greater than 500
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n > 2m
There are several values of m and n that satisfy statement 2. Here are two:
Case a: m = 2 and n = 5. In this case, m^n = 2^5 = 32. So, the answer to the target question is NO, m^n is NOT greater than 500
Case b: m = 2 and n = 9. In this case, m^n = 2^9 = 512. So, the answer to the target question is YES, m^n IS greater than 500
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Aug 29, 2018 12:49 am
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

If a question states "greater than", then we should find the minimum value because all data are greater than the minimum. Considering condition 1), the minimum value is m^n=2^9=512>500, so the answer is 'yes' and condition 1) is sufficient.

Condition 2)
If m = 2, n = 100, then 2^{100} > 500 and the answer is 'yes'.
If m = 2, n = 5, then 2^5 = 32 < 500 and the answer is 'no'.
Thus, condition 2) is not sufficient, since we don't have a unique solution.

Therefore, A is the answer.

Answer: A
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