Q.)Let X,Y and Z be distinct integers, that are odd and positive. Which one of the following statements cannot be true? [CAT Question, CAT 2000 Question, Number System, MBA Exam]

(a) is odd

(b) is even

(c) is even

(d)(X-Y)(Y+Z)(X+Y-Z) is odd

Solution :

(a) = odd*odd*odd*odd = odd

Hence, this statement is true.

(b) is even

= (odd-odd)(odd-odd) = even*even = even

Hence , this statement is true.

(c) is even

= (odd+odd-odd)(odd+odd-odd)(odd+odd) = (odd+odd-odd)(odd+odd-odd)*even = even

Hence, this statement is true.

(d)(X-Y)(Y+Z)(X+Y-Z) is odd

(X-Y)(Y+Z)(X+Y-Z) = (odd-odd)(odd+odd)(odd+odd-odd) = even*even*(even-odd) = even

Hence, this statement is false.

Hence, OPTION(d)