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gmat question pack 1 hard remainder

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by fangtray » Tue May 15, 2012 7:29 am
If x and y are integers, what is the remainder when x^2 + y^2 is divided by 5?
1. When x-y is divided by 5, the remainder is 1
2. When x+y is divided by 5, the remainder is 2
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Source: — Data Sufficiency |
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by jai123oct » Tue May 15, 2012 7:46 am
i think the answer is E as we do not know the quotients in both the case so even if we combine both the statements we cannot get the answer.

as x-y = 5k+1

and x+y = 5r+2

so we cannot get the value of x^2 + y^2 .

but can we find the value of x and y individually thats my question and then square it before dividing by 5 ; to get the answer but can we solve the above for value of x and y .
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by karthikgmat » Tue May 15, 2012 6:53 pm
both statements together we get a solution when x = 4 ; y =3

C is answer
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by karthikgmat » Tue May 15, 2012 7:01 pm
assume x-y divided by 5 remainder 1

so , x-y = 5r+1

x+y divided by 5 remainder 2

x+y = 5s+2

square of (x+y) + square of (x-y) = 2(square of x+ square of y) = (5r+1)^2 + (5s+2)^2

x^2+ y^2 = [5*(r^2+s^2)+(1+4)+10r+10s] / 2

= 5*[(r^2+s^2+1+2r+2s)/2]

so it is clearly divisible y 5
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