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Math Expert V
Joined: 02 Sep 2009
Posts: 65241
Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (00:42) correct 26% (00:52) wrong based on 43 sessions

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Competition Mode Question

Is $$x^3 − 1 = 0$$ ?

(1) $$x^2 = 1$$

(2) $$x^2 = x$$

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Sloan MIT School Moderator V
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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.

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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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

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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
(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

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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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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Joined: 23 Mar 2020
Posts: 85
Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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.

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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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

(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)
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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
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Director  D
Joined: 25 Jul 2018
Posts: 731
Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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1
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

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GMAT Club Legend  V
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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#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
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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

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

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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x  [#permalink]

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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 Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x   [#permalink] 31 Mar 2020, 21:53

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