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

Question

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

PS21184

yashikaaggarwal · Answer

Answer is supposedly E

Equation is x(x+1)=x+1
Let's put x=0
0(0+1)=0+1
0≠1 (incorrect)

Put x=1
1(1+1)=1+1
1(2)=2
2=2 (correct)

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

Only E is satisfying both 1&-1
Therefore Answer is E

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Ravixxx · Answer

Test values... is more funny

-1
 -1*(-1+1) = -1+1 
 -1(0) = 0  Ok

0 
 0*(0+1)=0+1 
 0=1  NO

1
 1(1+1)=1+1 
 2=2  OK

Answer E

hiranmay · Answer

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 -->   correct : x(x + 1) = x + 1 => x^2+x=x+1 =>x^2=1 => x=+1 or -1

GMATinsight · Answer

RULE : Don't cancel the variable part (x+1 in this case)unless we know that it's non-zero

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

i.e. either x+1 = 0 or x-1 = 0

i.e. either x = -1 or x = 1

ANswer: Option E

Abhishek009 · Answer

x(x + 1) = x + 1

Or,  x^2 + x = x + 1

Or,  x^2 = 1

Hence,  x = -1  &  x = +1 , Answer must be (E)

BrentGMATPrepNow · Answer

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

NitishJain · Answer

x(x + 1) = x + 1

Do not cancel the (x+1) from both sides, its a trap.

Subtract (x+1) from both sides

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

==> x = +1, -1

E.

ScottTargetTestPrep · Answer

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

BlueRocketAsh · Answer

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

Answer E

Kinshook · Answer

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

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

x = 1 or -1

IMO E

bumpbot · Answer

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

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

Prep Toolkit

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