Properties of Odd and Even Integers

CAT 2001 Slot 1 · QA · Easy · Number Systems

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Let x,yx, y and zz be distinct integers. xx and yy are odd and positive, and zz is even and positive. Which one of the following statements cannot be true?

  1. A.

    y(x−z)2y(x - z)^2 is even

  2. B.

    y2(x−z)y^2(x - z) is odd

  3. C.

    y(x−z)y(x - z) is odd

  4. D.

    z(x−y)2z(x - y)^2 is even

Answer

A

Explanation

xx is odd, zz is even   ⟹  (x−z)\implies (x - z) is odd   ⟹  (x−z)2\implies (x - z)^2 is odd. yy is odd, so y(x−z)2=odd×odd=oddy(x - z)^2 = \text{odd} \times \text{odd} = \text{odd}. Therefore, y(x−z)2y(x - z)^2 can never be even.

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