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What will be X^4 + Y^4 remainder?

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udit_g
 Post subject: What will be X^4 + Y^4 remainder?
 Post Posted: Fri Jul 03, 2009 5:01 am 
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Students


Posts: 6
What is the remainder when X^4 + Y^4 divide by 5

A) X-Y divided by 5 gives remainder 1
B) X+Y divided by 5 gives remainder 2

My answer is C and remainder is 2

We can easily found pair of number for which A and B are not self sufficient

Combining these,
(X+Y+X-Y) mod 5 = 3 mod 5
2X mod 5 = 3 mod 5
this gives X mod 5 = 4 as it can be satisfied for X = 4, 9 ....

Similarly, (X+Y-X+Y) mod 5 = 1 mod 5
i.e 2Y mod 5 = 1 mod 5 gives Y mod 5 = 3 as it is satisfied for Y = 3, 8...

so now X mod 5 = 4 and Y mod 5 = 3
i.e X^4 mod 5 = 4^4 mod 5 = 6 mod 5 = 1mod 5
Y^4 mod 5 = 1 mod 5

so X^4 + Y^4 mod 5 = (1+1) mod 5 = 2 mod 5

hence remainder 2.

Please let me know if reasoning and answer is correct.
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RonPurewal
 Post subject: Re: What will be X^4 + Y^4 remainder?
 Post Posted: Fri Jul 10, 2009 6:57 am 
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ManhattanGMAT Staff


Posts: 7146
again, what is the source of this question?

this is the GMATPREP MATH FOLDER, which is for GMATPREP SOFTWARE questions only.

i'm quite sure that this is NOT an official gmatprep question.
it's much too "theory heavy", and much too light on the clever manipulations and shortcuts that characterize real gmat problems, to be an official problem.
--

at this point you have 2 options:
(1) if this problem is really from the GMATPREP SOFTWARE, then please upload a screen shot as proof;
(2) if not, post this problem in the GENERAL MATH FOLDER, and CITE THE SOURCE of the problem (original source - don't cite other forums, for instance).

thanks.
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