Last doubt of 2009

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Out of (m+1) given integers two of them can always be chosen such that there
(a) difference is divisible by m
(b) Sum is divisible by m
(c) Product is divisible by m
(d)none of these

#Mathematics #Algebra

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sanchit ·2009-12-31 10:42:32

i think the answer is (d)

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Tush Watts ·2009-12-31 10:45:42

Nops ans is (a)

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sanchit ·2009-12-31 10:47:42

arre .........but how..........can u give me a hint..................

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Lokesh Verma ·2010-01-01 01:02:10

answer is a because any numbers can leave a remainder of either 0, 1, 2, ... m-1

two numbers among m+1 leave the same reaminder on division by m

hence their difference is divisible by m

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Tush Watts ·2010-01-01 01:11:41

ok.... any integer can be written as , x = m q +r where 0 â‰¤r â‰¤ m-1

x _i= m q₁ + r
x_j = m q₂ + r

So, x_i - x_j is divisible by m

Thanx a lot sir [1]

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Last doubt of 2009

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