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# Is x^3 - 1 = 0

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Manager
Joined: 02 Mar 2018
Posts: 69
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
Is x^3 - 1 = 0  [#permalink]

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Updated on: 05 Aug 2018, 09:45
00:00

Difficulty:

35% (medium)

Question Stats:

55% (00:54) correct 45% (00:46) wrong based on 31 sessions

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Is $$x^3 − 1 = 0$$ ?

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

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

Originally posted by gsingh0711 on 05 Aug 2018, 08:57.
Last edited by generis on 05 Aug 2018, 09:45, edited 1 time in total.
Edited and formatted the question, renamed the topic
Manager
Joined: 02 Mar 2018
Posts: 69
Location: India
GMAT 1: 640 Q51 V26
GPA: 3.1
Re: Is x^3 - 1 = 0  [#permalink]

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05 Aug 2018, 08:58
Explanation:

Question can be rewritten as: Is x3 = 1.

Considering statement 1:
x2 = 1
⇒ x = 1 or −1
⇒ x3 = 1 or −1, i.e. x3 may or may not be 1.

Since we are not getting a definite answer from above statement, statement 1 itself is not sufficient to provide the answer.

Considering statement 2:
x2 = x
⇒ x2 − x = 0
⇒ x(x − 1) = 0
⇒ x = 0 or x − 1 = 0
⇒ x = 0 OR x = 1
⇒ x3 = 0 or 1, i.e. x3 may or may not be 1.

Since we are not getting a definite answer from above statement, statement 1 itself is not sufficient to provide the answer.

Considering statement 1 and 2:
x = 1 is the only value which satisfies both the statements.
⇒ x3 = 1

Since we are getting a definite answer from combination of statements, i.e. ,statement 1 and 2 are sufficient to provide the answer.

I think, I deserve a kudus LOL
Manager
Status: Studying SC
Joined: 04 Sep 2017
Posts: 116
GPA: 3.6
WE: Sales (Computer Software)
Re: Is x^3 - 1 = 0  [#permalink]

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05 Aug 2018, 15:29
gsingh0711 wrote:
Is $$x^3 − 1 = 0$$ ?

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

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

Question Is x = 1?

(1) x = 1 or -1

Yes and No. Not Sufficient

(2) x = 0 or 1

No and Yes. Not Sufficient

(1) + (2) x = 1

Yes. Sufficient.

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Re: Is x^3 - 1 = 0 &nbs [#permalink] 05 Aug 2018, 15:29
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