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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If m and n are integers greater than 1, is m^n>500?  [#permalink]

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27 Aug 2018, 01:41
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Difficulty:

65% (hard)

Question Stats:

50% (01:30) correct 50% (01:55) wrong based on 179 sessions

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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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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 8795 Re: If m and n are integers greater than 1, is m^n>500? [#permalink] ### Show Tags 27 Aug 2018, 01:50 1 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 _________________ GMAT Club Legend Joined: 11 Sep 2015 Posts: 4999 Location: Canada GMAT 1: 770 Q49 V46 Re: If m and n are integers greater than 1, is m^n>500? [#permalink] ### Show Tags 27 Aug 2018, 05:48 Top Contributor 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 Cheers, Brent _________________ If you enjoy my solutions, you'll love my GMAT prep course. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 9270 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m and n are integers greater than 1, is m^n>500? [#permalink] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2800
Re: If m and n are integers greater than 1, is m^n>500?  [#permalink]

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05 Sep 2018, 09:54
1
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.

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

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10 May 2019, 21:43
chetan2u wrote:
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

2^9=512 not 516. Thank you very much for explaining though

$$2) n>2m$$
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] 10 May 2019, 21:43