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Topic: Solution to a Mathematics GRE question
Replies: 6   Last Post: May 10, 2008 3:24 AM

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Bill Daly

Posts: 69
Registered: 12/8/04
Re: Solution to a Mathematics GRE question
Posted: May 10, 2008 3:24 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 27, 9:14 pm, monkeyboy <fsen...@lynx.neu.edu> wrote:
> I recently started doing a Mathematics GRE exam just for fun. I've
> been cruising through the calculus questions, but have hit an algebra
> problem that stumped me. Unfortunately detailed solutions are not
> provided, only the correct answer, could some one point me in the
> right direction...
>
> Question:
> Let x and y be positive integers such that 3x + 7y is divisible by 11.
> Which of the following must also be divisible by 11?
>
> Solution:
> 4x - 9y
>
> Thanks


Sheesh, everybody is making heavy weather of this question. The
complete solution to 3x + 7y = 0 (mod 11) is given by x = 4t, y = 3t
(mod 11), for an arbitrary integer t. Thus, 4x - 9y = 4(4t) - 9(3t) =
-11t (mod 11), i.e. 4x - 9y = 0 (mod 11).



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