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# Number Systems : Odd and Even Numbers : Quant Question

This question is a Number Systems question. Explains concepts on odd and even numbers and operations on these numbers.

#### Question

Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
1. (x - z)2 y is even
2. (x - z) y2 is odd
3. (x - z) y is odd
4. (x - y)2 z is even
5. (x + y)3 z is even
Correct Answer - (x - z)2 y is even. Choice (1)

(x - z)2 y is even cannot be true.

x is odd and z is even. Therefore, x - z is odd.
And y is odd.
Therefore, (x - z)2 will be odd and (x - z)2 y will be odd.

Level of difficulty : Easy to Moderate

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