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# If m and n are positive integers and m^2 + n^2 = 40, what is

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Director
Joined: 21 Dec 2009
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Concentration: Entrepreneurship, Finance
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If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]

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01 Nov 2012, 07:56
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Difficulty:

5% (low)

Question Stats:

90% (02:14) correct 10% (01:46) wrong based on 78 sessions

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If m and n are positive integers and m^2 + n^2 = 40, what is the value of m^3 + n^3?

A. 72
B. 224
C. 320
D. 512
E. 1,600

Pls try algebra method...
Of course, plugging nos easily gives 2 and 6(m and n being integers), but i attempted algebra first
and was wasting time.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 01 Nov 2012, 08:01, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Joined: 19 Apr 2012
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Re: If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]

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01 Nov 2012, 12:16
Hey,

i have tried it this way:

You need to integers which squared are equal 40.

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
Stop. The integers can't be greater than 6 or we will score above 40.

The second integer need to be picked up the same way.
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36

The only pair that matches is 6^2 + 2^2 = 40.

So 6^3 + 2^3 = 224.

Senior Manager
Joined: 13 Aug 2012
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Re: If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]

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10 Dec 2012, 23:35
I tried algebraic method. I think it will eat up my life in the test. Haha! Nonetheless, I would like to see how that is done.

I just selected from the possible values of $$m^2$$ and $$n^2$$: $$1,4,9,16,25,36$$ and selected $$2^2$$ and $$6^2$$

$$m^3 + n^3=2^3 + 6^3 = 224$$
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Intern
Joined: 21 May 2013
Posts: 29
Location: India
Concentration: Finance, Marketing
GMAT 1: 660 Q49 V32
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Kudos [?]: 6 [0], given: 8

Re: If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]

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11 Aug 2013, 04:57
If you try to solve it through algebra you will definitely spend the whole 75 minutes on it alone ..while picking numbers will help you to solve easily..just see which numbers fit as M and N to make the given equation possible...
Re: If m and n are positive integers and m^2 + n^2 = 40, what is   [#permalink] 11 Aug 2013, 04:57
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