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CAT Question – Expression Result in Odd or Even Value

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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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