This is how GMAT prep solved it and it makes sense:

Statement 1

X^m = 81 insufficient as there we need two equations for two variables (n & m), therefore insufficient

Statement 2

1 + x^n - m = 10

we can try to solve it and see what gives us

so... x^n-m = 10 -1

we get ...

x^n-m = 9

we can then separate both n-m by doing the reciprocals:

then we get x^n / x^m = 9. This is why statement 2 is not sufficient since we cannot find the value of "n". Therefore, not sufficient.

Now, we are left with statements 1 + 2 and see if the problem can be solved

Remember statement 1? x^m = 81

Remember your result from statement 2?

now you can replace x^m = 81 in your second statement where x^n / 81 = 9. Then we can take x^n = 9*81, which is 279.

Then we have as a result that x^n = 279 and x^m = 81. Now you only need to sum both.... 81 + 279 = 810. Therefore, the answer is "C" not because we got "810" but because the problem can be solved. This is what data sufficiency questions are asking you to determine...can the problem be solved? In this case only when both statements are combined the problem can be solved.

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