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CAT Question – Expression Result in Odd or Even Value

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) XY{Z}^{2} is odd
(b) {(X-Y)}^{2}Z is even
(c){(X+Y-Z)}^{2}(X+Y) is even
(d)(X-Y)(Y+Z)(X+Y-Z) is odd

Solution :
(a) XY{Z}^{2} = odd*odd*odd*odd = odd

Hence, this statement is true.

(b) {(X-Y)}^{2}Z is even

{(X-Y)}^{2}Z = (odd-odd)(odd-odd) = even*even = even

Hence , this statement is true.

(c){(X+Y-Z)}^{2}(X+Y) is even

{(X+Y-Z)}^{2}(X+Y) = (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)


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