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Question

# Given that p,q,r,s,t,u are integers and p+q+r+s+t+u=2005, what is the minimum value of (-1)p + (-1)q +(-1)r +(-1)s +(-1)t +(-1)u ?

A
-2
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B
-3
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C
none of these
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Solution

## The correct option is C none of thesep + q + r + s + t + u = 2005 of the 6 integers, the number of integers that can be odd is 5,3 or 1. In the expression (-1)p+ (-1)q +(-1)r +(-1)s +(-1)t +(-1)u 1)When one integer is even and the others are odd, then only one among is +1 and others are -1 each. Hence the sum of the terms is -5 + 1 = -4. 2)When three of the integers are even, then three of the terms are +1 each and the remaining three are -1 each. Hence the sum is 0. 3)When five of the integers are even, then five terms will be +1 each and the other term is -1. Hence the sum is 4. ∴The minimum value of the sum is -4.

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