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
• B. -3
• C. none of these

Answer 1

The correct option is C none of these

p + 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.