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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Wed Apr 17, 2019 4:52 pm

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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

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Wed Apr 17, 2019 4:52 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8178; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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