# 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?

- (x - z)
^{2} y is even
- (x - z) y
^{2} is odd
- (x - z) y is odd
- (x - y)
^{2} z is even
- (x + y)
^{3} z is even

Correct Answer -

**(x - z)**^{2} y is even. Choice (1)

#### Explanatory Answer

(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.

Correct answer is choice (1)

Level of difficulty : Easy to Moderate

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