Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x

Question

Competition Mode Question

Is  x^3 − 1 = 0  ?

(1)  x^2 = 1

(2)  x^2 = x

unraveled · Answer

Is  x^3 − 1 = 0 ?

(1)  x^2 = 1 
 x^2 - 1 = 0 
x = 1 YES 
or 
x = - 1 NO

INSUFFICIENT

(2)  x^2 = x 
 x^2 - x = 0 
 x(x - 1) = 0 
x = 0 NO
OR
x = 1 YES

INSUFFICIENT

Together 1 and 2 
x = 1 YES

SUFFICIENT.

Answer C.

eakabuah · Answer

Is x^3 - 1 = 0?

Statement 1: x^2=1
This means x=1 or x=-1
Insufficient because when x=1 x^3 - 1 = 0 but when x=-1, x^3 - 1 = -2

Statement 2: x^2=x
This mean x=0 or x=1
Insufficient. When x=0, x^3 - 1 = -1, but when x=1, x^3 - 1 = 0.

1+2
Sufficient since we know that x=1 is common to both statements, hence x=1 and x^3 - 1 =0

The answer is C.

CareerGeek · Answer

Question: Is  x^3 − 1=0  ?

(1)  x^2 = 1 
-->  x = 1  or  -1 
-->  x^3 = 1  or  -1  -->  Insufficient

(2)  x^2 = x 
-->  x^2 - x = 0 
-->  x(x - 1) = 0 
-->  x = 0  or  1 
-->  x^3 = 0  or  1  -->  Insufficient

Combining (1) & (2),
-->  x = 1  ONLY -->  Sufficient

Option C

freedom128 · Answer

(1) x^2 = 1 --> x=-1 or x=1
If x=-1, then x^3 − 1 = -2 (no)
If x=1, then x^3 − 1 = 0 (yes)
NOT SUFFICIENT

(2) x^2 = x --> x=0 or x=1
If x=0, then x^3 − 1 = -1 (no)
If x=1, then x^3 − 1 = 0 (yes)
NOT SUFFICIENT

(1)+(2) turns out we havwe only single solution: x=1, then x^3 − 1 = 0 (yes)
SUFFICIENT

FINAL ANSWER IS (C)

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Archit3110 · Answer

#1
x^2=1
x= +/-1 insufficient
#2
x^2-x=0
x= 0 or x= 1
insufficient
from 1&2 
x= 1
IMO C

Is x3−1=0 ?

(1) x2=1

(2) x2=x

madgmat2019 · Answer

For x^3-1=0
 
X can only be 1

1) from this X can be 1,-1..... INSUFFICIENT
2) from this X can be 0,1.... INSUFFICIENT

Combining both we can get X=1

OA:C

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GMATinsight · Answer

Question: Is x^3 = 1?

Statemnt 1 : x^2 = 1

i.e. x =  + 1
i.e. x^3 =  + 1

NOT SUFFICIENT

Statement 2 : x^2 = x

i.e. x = 0 or 1
i.e. x^3 = 0 or 1

NOT SUFFICIENT

COmbining the two statements

x^3 = 1

SUFFICIENT

Answer: Option C

Papist · Answer

Is x^3 - 1 = 0?

In other words, we are trying to find out if x^3 is equal to 1

(1) "x^2 = 1"
x could be equal to 1, which would make the equation correct. However, x could also equal -1, which would make the equation incorrect. INSUFFICIENT.

(2) "x^2 = x"
x could equal 1, which would make the equation correct. However, x could also equal 0, which would make the equation incorrect. INSUFFICIENT.

(1+2) The only value of x that satisfies both statements is 1, so we can definitively say the equation is correct. SUFFICIENT.

Answer: (C)

exc4libur · Answer

(1) insufic
x^2-1=0, (x-1)(x+1)=0, x={1,-1}

(2) insufic
x^2=x, x^2-x=0, x(x-1)=0, x={0,1}

(1/2) sufic
x=1

Ans (C)

globaldesi · Answer

Is  x^3−1=0  ?

(1)  x^2=1

(2)  x^2=x

Is  x^3−1=0  ? or x = 1
(1)  x^2=1

x can be 1 or -1 (Not sufficient)

(2)  x^2=x 
or  x^2-x =0 
or  x(x-1)=0 
thus x = 0 ,1
Not sufficient

Combine both
only value common is 1
thus 
 x^3−1=0   , sufficient
Thus C

lacktutor · Answer

Is  x^{3} —1 =0  ??? 
—>  x^{3} =1  —>  x= 1  ???

(Statement1):  x^2 = 1 
—> ( x—1)(x+1)= 0 
 x= 1  and  x= —1 
Insufficient

(Statement2):  x^{2} = x 
—>  x( x—1) = 0 
 x = 0  and  x= 1 
Insufficient

Taken together 1&2, 
Only  x= 1  satisfies the both statements 
Sufficient

Answer (C)

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chaitralirr · Answer

Is $x^3 − 1 = 0$ ?

we need to find if X^3-1=0 or X^3=1

(1) $x^2 = 1$

X^2=1 means X=1 this means X^3-1 =0 Hence statement 1 is sufficient.

(2) $x^2 = x$

X^2=X Therefore X^2-X=0, X(X-1)=0 means X=0 or X=1

if X=0 the |X^3-1|= 1 
If X=1 the X=0 hence insufficient

statement 1 is sufficient IMO A

Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x

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