If x is an integer, then which of the following statements

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If x is an integer, then which of the following statements about x^2 - x - 1 is true?

A) It is always odd.
B) It is always even.
C) It is always positive.
D) It is even when x is even and odd when x is odd.
E) It is even when x is odd and odd when x is even.

OA A

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by Ian Stewart » Thu Apr 18, 2019 5:38 pm
Lots of ways to do this, for example:

x^2 - x - 1 = x(x-1) - 1

Notice x(x-1) is the product of two consecutive integers, so it is the product of one odd and one even integer, and must therefore be even. When we subtract 1 from this product, we get an odd number, so x(x-1) - 1 is odd.
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by Scott@TargetTestPrep » Tue Apr 23, 2019 6:23 pm
BTGmoderatorDC wrote:If x is an integer, then which of the following statements about x^2 - x - 1 is true?

A) It is always odd.
B) It is always even.
C) It is always positive.
D) It is even when x is even and odd when x is odd.
E) It is even when x is odd and odd when x is even.
If x is even, then x^2 - x - 1 = even - even - odd = even - odd = odd.

If x is odd, then x^2 - x - 1 = odd - odd - odd = even - odd = odd.

So x^2 - x - 1 is always odd.

Answer: A

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