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Homework Help: SAT question

  1. Apr 19, 2008 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant equations

    3. 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.
  2. jcsd
  3. Apr 19, 2008 #2

    Tom Mattson

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    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.
  4. Apr 20, 2008 #3
    2, 4 and 8 can be expressed as integer powers of 64. but actually the answer is 8 but not 16... :S
  5. Apr 20, 2008 #4


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    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.
  6. Apr 20, 2008 #5
    awww..... i'm terribly sorry!!!

    i misread the answer off the book.....

    thanks a loot for helping
  7. Apr 21, 2008 #6


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    Do we get to share in the loot?
  8. Apr 21, 2008 #7
    ok, loot = lot!! ;)
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