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

(1) $x^m=81$

(2) $1+x^{n−m}=10$

Answer Choices

Correct answer marked below

Statement (1) ALONE is sufficient

Statement (2) ALONE is sufficient

BOTH statements TOGETHER are sufficient

Correct

EACH statement ALONE is sufficient

Statements (1) and (2) TOGETHER are NOT sufficient

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Comments

AravindMay 1

Hmm, this one took me a second. I kept trying to solve for x directly from (1) and got stuck, until I realized there are multiple integer values of m that work. That's the whole trap I think.

PanshulMay 4

same here, I plugged in m=4 and x=3 and thought I was done lol

AmberMay 10

thanks, this was helpful! The 1+x^(n-m) part confused me at first but rewriting it as x^m + x^n over x^m made it click.

MohamedSep 10

wait how do the two statements combine exactly? I get that (1) gives you x^m but I'm lost on how (2) helps find n-m without knowing x

EyadSep 11

from (2) you can get x^(n-m) as a number, and since you already know x^m from (1), you can piece it together

AbhilashaApr 29

is this really 505-555? felt harder than that to me, the exponent manipulation is sneaky. got C though finally.

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

If mmm and nnn are integers and x>0x > 0x>0, what is the value of xm+xnx^m+x^nxm+xn(1) xm=81x^m=81xm=81(2) 1+xn−m=101+x^{n−m}=101+xn−m=10