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Is x^3 - 1 = 0

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Manager
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Joined: 02 Mar 2018
Posts: 70
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Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
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Is x^3 - 1 = 0  [#permalink]

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New post Updated on: 05 Aug 2018, 10:45
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  35% (medium)

Question Stats:

62% (01:00) correct 38% (00:45) wrong based on 21 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, 09:57.
Last edited by generis on 05 Aug 2018, 10:45, edited 1 time in total.
Edited and formatted the question, renamed the topic
Manager
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Joined: 02 Mar 2018
Posts: 70
Location: India
Schools: IIMA , IIMA PGPX"20
GMAT 1: 640 Q51 V26
GPA: 3.1
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Re: Is x^3 - 1 = 0  [#permalink]

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New post 05 Aug 2018, 09:58
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.

Answer: C.

I think, I deserve a kudus LOL
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Re: Is x^3 - 1 = 0  [#permalink]

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New post 05 Aug 2018, 16:29
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.


Answer: C
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Re: Is x^3 - 1 = 0 &nbs [#permalink] 05 Aug 2018, 16:29
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