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14 Apr 2006, 02:48
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What is the remainder when x^2+y^2 is divided by 5, where x and y are positive integer?
1). When x+y is divided by 5, the remainder is 1.
2). When x-y is divided by 5, the remainder is 2.
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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14 Apr 2006, 04:21
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Hello, I think it's C.
1) x+y= 5a + 1, not sufficient alone
consider x=3 and y=3
and
x=5 y=1
2) x-y= 5b + 2, not sufficient alone
consider x=3 and y=1
and
x=5 y=3
1+2) instead of calculating x^2 + y^2, use numbers and find the pattern
x=4 and y=2 fit both equations; the final remainder if (x^2 + y^2)/5 is 0
... all values that fit are made up of x=4 and y=2 just that constants (multiples of 5 in this case) are added; for example x=9 y=7 constant 5,
1) x+y= 5a + 1, not sufficient alone
consider x=3 and y=3
and
x=5 y=1
2) x-y= 5b + 2, not sufficient alone
consider x=3 and y=1
and
x=5 y=3
1+2) instead of calculating x^2 + y^2, use numbers and find the pattern
x=4 and y=2 fit both equations; the final remainder if (x^2 + y^2)/5 is 0
... all values that fit are made up of x=4 and y=2 just that constants (multiples of 5 in this case) are added; for example x=9 y=7 constant 5,
14 Apr 2006, 04:42
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For problems such as above, is the best way really trial and error - pluggin in various numbers to see if a statement is sufficient? Is there a faster way?
