# SAT question

## Homework Statement

let x and y be positive integers and n = x^y
If n + n^(1/2) + n ^(1/3) = 76, then x cannot equal
A. 64
B. 16
C. 8
D. 4
E. 2

## The Attempt at a Solution

i really don't know how to approach this question. i tried simplifying the powers and write them in terms of x and y, e.g. x^y + x^(y/2) + x ^(y/3) = 76 and i expressed the answers as powers of 2 but i couldn't find a way out.

Tom Mattson
Staff Emeritus
Gold Member
Start by letting x=64. Then by inspection it is clear that for y=1, you get 76. Then try to express 64 as integer powers of the other answer choices. If you do that then you will find the one answer choice that doesn't work by exhausting the answer choices that do work.

2, 4 and 8 can be expressed as integer powers of 64. but actually the answer is 8 but not 16... :S

HallsofIvy
Homework Helper
2, 4 and 8 can be expressed as integer powers of 64. but actually the answer is 8 but not 16... :S

And how exactly did you decide that? Since 82= 64, taking x= 8, y= 2 obviously does satisfy the equation and x= 8 is not the answer.

awww..... i'm terribly sorry!!!

thanks a loot for helping

HallsofIvy