Bunuel wrote:

GMAT CLUB'S FRESH QUESTION:

If x and y are positive integers, then what is the value of \((–1)^x + (–1)^y + (–1)^x*(–1)^y\) ?

(1) x does not have a prime factor greater than 1.

(2) y is a common factor of all prime numbers between 101 to 202

Given x, y > 0

Asked is value of Expression E = \((–1)^x + (–1)^y + (–1)^x*(–1)^y\)

We know that (-1)^{even} = 1 & (-1)^{odd} = -1

Hence we have cases

(i) x = even, y = even, then E = 1 + 1 + 1*1 = 3

(ii) x = even, y = odd, then E = 1 - 1 + 1*(-1) = -1

(iii) x = odd, y = odd, then E = (-1) + (-1) + (-1)*(-1) = -1

(iv) x = odd, y = even, then E = (-1) + 1 + (-1)*1 = -1

Statement 1: x does not have a prime factor greater than 1. Therefore x = 1, hence x = odd

We have from cases (iii) & (iv), for x = odd, y = odd/even, E = -1

Hence statement 1 is Sufficient.

Statement 2: y is a common factor of all prime numbers between 101 to 202. Therefore y = 1, hence y = odd

We have cases (ii) & (iii), for y = odd, x = odd/even, E = -1

Hence Statement 2 is Sufficient.

Answer D.

Thanks,

GyM

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