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

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If m and n are integers greater than 1, is m^n>500?  [#permalink]

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New post 27 Aug 2018, 01:41
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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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Re: If m and n are integers greater than 1, is m^n>500?  [#permalink]

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New post 27 Aug 2018, 01:50
If \(m\) and \(n\) are integers greater than \(1\), is \(m^n>500\)?

\(1) n>8\)
Let us take m as minimum = 2 and minimum value of n =9
So min value of \(m^n=2^9=516\)
So yes it is always >500
Sufficient

\(2) n>2m\)
Again min value of m=2 and that of n is 2m+1=5
So min value of m^n =2^5=32 <500
But if m is 5, Ans is yes >500
Insufficient

A
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Re: If m and n are integers greater than 1, is m^n>500?  [#permalink]

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New post 27 Aug 2018, 05:48
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MathRevolution 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
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Re: If m and n are integers greater than 1, is m^n>500?  [#permalink]

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New post 29 Aug 2018, 00:53
=>

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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Re: If m and n are integers greater than 1, is m^n>500?  [#permalink]

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New post 05 Sep 2018, 09:54
MathRevolution wrote:
[Math Revolution GMAT math practice question]

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

\(1) n>8\)
\(2) n>2m\)


Statement One Alone:

n>8

We see that n is at least 9, and m is at least 2. Since 2^9 = 512 > 500, then m^n will certainly be greater than 500.

Statement one alone is sufficient.

Statement Two Alone

n>2m

We can’t determine whether m^n > 500 by knowing only that n > 2m. For example, if m = 2 and n = 5, then m^n = 2^5 = 32 is not greater than 500. On the other hand, if m = 3 and n = 7, then m^n = 3^7 = 2187 is greater than 500.

Statement two alone is not sufficient.

Answer: A
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Re: If m and n are integers greater than 1, is m^n>500?   [#permalink] 05 Sep 2018, 09:54
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