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

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If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]  01 Nov 2012, 06:56
00:00

Difficulty:

15% (low)

Question Stats:

91% (02:17) correct 9% (01:11) wrong based on 55 sessions
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, 07:01, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]  01 Nov 2012, 11:16
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.

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Re: If m and n are positive integers and m^2 + n^2 = 40, what is [#permalink]  10 Dec 2012, 22:35
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
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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]  11 Aug 2013, 03:57
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, 03:57
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