What is the range of the solutions to the equation |x^2 â€“

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Aug 26, 2019 6:04 am

BTGmoderatorDC wrote:What is the range of the solutions to the equation |xÂ² - 1| = 0 ?

A. 0
B. 1
C. 2
D. 3
E. 5

If |xÂ² - 1| = 0, then we can be certain that: xÂ² - 1 = 0
Add 1 to both sides: xÂ² = 1
So, EITHER x = 1 OR x = -1

Range of solutions = 1 - (-1) = 2

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Aug 27, 2019 5:17 pm

BTGmoderatorDC wrote:What is the range of the solutions to the equation |x^2 - 1| = 0 ?

A. 0
B. 1
C. 2
D. 3
E. 5

OA C

Source: Veritas Prep

The only way |x^2 - 1| = 0 is if x^2 - 1 = 0. Let's solve it:

x^2 - 1 = 0

(x - 1)(x + 1) = 0

x = 1 or x = -1

Thus, the range is 1 - (-1) = 2.

Answer: C

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