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# If m and n are integers and x>0, what is value of x^m + x^n?

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If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]  20 Jun 2014, 04:23
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If m and n are integers and x > 0, what is the value of $$x^m + x^n$$?

(1) $$x^m = 81$$

(2) $$1 + x^{n-m} = 10$$
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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]  20 Jun 2014, 04:36
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If m and n are integers and x > 0, what is the value of $$x^m + x^n$$?

(1) $$x^m = 81$$. No info about n. Not sufficient.

(2) $$1 + x^{n-m} = 10$$ --> $$x^{n-m} = 9$$ --> $$\frac{x^n}{x^m}=9$$ --> $$x^n =9x^m$$ --> $$x^m + x^n=10x^m$$. Not sufficient.

(1)+(2) $$x^m + x^n=10x^m=10*81$$. Sufficient.

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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]  20 Jun 2014, 04:52
newbornmuse wrote:
If m and n are integers and x > 0, what is the value of $$x^m + x^n$$?

(1) $$x^m = 81$$

(2) $$1 + x^{n-m} = 10$$

x^m + x^n= x^m(1+x^n-m)---------------------------A)

st1 x^m=81 insufficient as no information about n is provided

st2 (1 + x^n-m) =10

as seen from 'A' we still need the value of x^m to calculate the value of x^m+x^n hence insufficient

combining 1 and 2 we can substitute the value of 1 + x^n-m and x^m in 'A' to calculate the total value which is 81*10=810 hence C
Re: If m and n are integers and x>0, what is value of x^m + x^n?   [#permalink] 20 Jun 2014, 04:52
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