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

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Bunuel
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Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 02:15
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A
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C
D
E

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Is \(x^3 − 1 = 0\) ?

(1) \(x^2 = 1\)

(2) \(x^2 = x\)
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C
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 02:32
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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.
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 02:40
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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.
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 02:57
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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] New post   31 Mar 2020, 03:19
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(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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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 04:00
#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] New post   31 Mar 2020, 09:04
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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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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 09:25
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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

Answer: Option C
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 12:31
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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)
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 12:41
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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] New post   31 Mar 2020, 21:37
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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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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 22:35
1
Kudos
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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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink] New post   31 Mar 2020, 22:53
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
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Re: Is x^3 − 1 = 0 ? (1) x^2 = 1 (2) x^2 = x [#permalink]
31 Mar 2020, 22:53
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