If x(x + 1) = x + 1, what are all the possible values of x ?

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

Re: If x(x + 1) = x + 1, what are all the possible values of x ?

by Brent@GMATPrepNow » Wed Dec 02, 2020 9:25 am

BTGModeratorVI wrote: ↑
Thu Nov 26, 2020 1:11 pm
If x(x + 1) = x + 1, what are all the possible values of x ?

A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1

Answer: E
Source: GMAT prep

Given: x(x + 1) = x + 1
Note: Some students will be tempted to divide both sides of the equation by (x + 1) to get x = 1.
However, since we don't know the value of x, we may be inadvertently dividing both sides by 0, which is a big no-no

Instead, let's first expand the left side to get: x² + x = x + 1
Subtract x from both sides: x² = 1
From here we can see that, EITHER x = 1 OR x = -1

Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Re: If x(x + 1) = x + 1, what are all the possible values of x ?

by swerve » Thu Dec 03, 2020 10:45 am

BTGModeratorVI wrote: ↑
Thu Nov 26, 2020 1:11 pm
If x(x + 1) = x + 1, what are all the possible values of x ?

A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1

Answer: E
Source: GMAT prep

\(x(x + 1) = x + 1\)

Do not cancel the \((x+1)\) from both sides, it's a trap.

Subtract \((x+1)\) from both sides

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

\(\Rightarrow x = \pm 1\)

Therefore, E

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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

Re: If x(x + 1) = x + 1, what are all the possible values of x ?

by Scott@TargetTestPrep » Sat Dec 05, 2020 5:57 pm

BTGModeratorVI wrote: ↑
Thu Nov 26, 2020 1:11 pm
If x(x + 1) = x + 1, what are all the possible values of x ?

A. -1 only
B. 0 only
C. 1 only
D. -1 and 0
E. -1 and 1

Answer: E

Solution:

If x = -1, we see that both sides of the equation will be 0. Thus, a value of x is -1.

If x ≠ -1, divide both sides of the equation by x + 1 and we’ll have x = 1. Thus, another value of x is 1.

Answer: E

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