If m and n are integers and x>0, what is value of x^m + x^n? : GMAT Data Sufficiency (DS)
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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]

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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) $$1 + x^{n-m} = 10$$
[Reveal] Spoiler: OA
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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

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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]

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

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09 Oct 2016, 12:47
I concluded that statement 2 was sufficient.

This is what I did.

X^m + X^n = 1 + (X^n)/(X^m)

Statement 2: 1 + (X^n)*(X^-m) = 10 ---> 1 + (X^n)/(X^m) = 10

Hence: X^m + X^n = 1 + (X^n)/(X^m) = 10 ---> Sufficient.

Can anyone please explain me what am I doing wrong?

Thank you.
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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

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09 Oct 2016, 23:04
EBITDA wrote:
I concluded that statement 2 was sufficient.

This is what I did.

X^m + X^n = 1 + (X^n)/(X^m)

Statement 2: 1 + (X^n)*(X^-m) = 10 ---> 1 + (X^n)/(X^m) = 10

Hence: X^m + X^n = 1 + (X^n)/(X^m) = 10 ---> Sufficient.

Can anyone please explain me what am I doing wrong?

Thank you.

How did you get the highlighted part?
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If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

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10 Oct 2016, 00:02
The question asks us for the value of: X^m + X^n

If we divide this expression by X^m, we get: 1 + (X^n)/(X^m)

Per statement 2: 1 + (X^n)/(X^m) = 10.

Hence, statement 2 allows us to know what is the value of the initial expression.

Where am I making the error?
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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

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10 Oct 2016, 00:07
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EBITDA wrote:
The question asks us for the value of: X^m + X^n

If we divide this expression by X^m, we get: 1 + (X^n)/(X^m)

Per statement 2: 1 + (X^n)/(X^m) = 10.

Hence, statement 2 allows us to know what is the value of the initial expression.

Where am I making the error?

I see what you are doing there but it's wrong. We need the value of x^m + x^n. When you divide this by x^m, you get the value of (x^m + x^n)/x^m, not x^m + x^n.
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Re: If m and n are integers and x>0, what is value of x^m + x^n? [#permalink]

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13 Oct 2016, 11:36
I choose C but I was wondering if my approach was correct?
Here is what I did :
1) insuff.
2) insuff.

C) Given 1+x^n−m=10 I rewrote as 1+ x^n/x^m = 10 then substitute x^m from 1)
I got 1+ x^n/81 = 10
81+x^n=810
x^n=729
So If I got x^n and x^m to answer the question.

But is it a correct way to arrive at solution?
thank you
Re: If m and n are integers and x>0, what is value of x^m + x^n?   [#permalink] 13 Oct 2016, 11:36
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