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# Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0

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Math Expert
Joined: 02 Sep 2009
Posts: 52119
Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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04 Dec 2018, 02:09
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Difficulty:

55% (hard)

Question Stats:

56% (00:50) correct 44% (01:02) wrong based on 157 sessions

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Is x an even number?

(1) x^3 + x^2 = 0

(2) x^2 + |x| = 0

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Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
WE: Marketing (Energy and Utilities)
Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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04 Dec 2018, 02:28
1
Bunuel wrote:
Is x an even number?

(1) x^3 + x^2 = 0

(2) x^2 + |x| = 0

from stmt 1:
x^3 + x^2 = 0
this would be true for x=-1 and 0
not sufficient

from 2:
x^2 + |x| = 0[

when x=0 only possible hence sufficient IMO B
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Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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04 Dec 2018, 06:19
1
It's a Yes/No Data Sufficiency i.e the options must suggest a bold Yes or a bold No.

1. x^3+x^2=0
=> (x^2)(x+1)=0
We state that either x=0 or x=-1. Not sufficient.

2. x^2+|x|=0
Positive+Positive=0 only when the value is 0.
Hence x is even.

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Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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Updated on: 04 Dec 2018, 08:38
1
(1) x^3 + x^2 = 0
$$x^2$$(x+1)=0 => $$x^2$$=0 or x+1=0 => x=0 or x=-1
We have 2 values of x. NOT SUFFICIENT

(2)$$x^2$$ + |x| = 0
Squaring both sides. $$x^4$$+$$x^2$$=0 => $$x^2$$($$x^2$$+1)=0 =>$$x^2$$=0 or $$x^2$$=-1(not possible as square root of negative number is an imaginary number) Thus x=0 SUFFICIENT.

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Originally posted by topper97 on 04 Dec 2018, 06:42.
Last edited by topper97 on 04 Dec 2018, 08:38, edited 1 time in total.
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Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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04 Dec 2018, 08:30
topper97 wrote:
(1) x^3 + x^2 = 0
$$x^2$$(x+1)=0 => $$x^2$$=0 or x+1=0 => x=0 or x=-1
We have 2 values of x. NOT SUFFICIENT

(2)$$x^2$$ + |x| = 0
Squaring both sides. $$x^4$$+$$x^2$$=0 => $$x^4$$($$x^2$$+1)=0 =>$$x^2$$=0 or $$x^2$$=-1(not possible as square root of negative number is an imaginary number) Thus x=0 SUFFICIENT.

you made a mistake here mate: factoring out the x^2, leaves us with x^2(x^2+1)

best gota900
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Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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04 Dec 2018, 08:44
1
gota900 wrote:

you made a mistake here mate: factoring out the x^2, leaves us with x^2(x^2+1)

best gota900

Thanks friend. Done.

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Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0  [#permalink]

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24 Dec 2018, 00:31
Bunuel wrote:
Is x an even number?

(1) x^3 + x^2 = 0

(2) x^2 + |x| = 0

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Re: Is x an even number? (1) x^3 + x^2 = 0 (2) x^2 + |x| = 0 &nbs [#permalink] 24 Dec 2018, 00:31
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