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# What is the value of x^6/(x^2+1)?

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Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

What is the value of x^6/(x^2+1)? [#permalink]

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02 Oct 2017, 23:59
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Question Stats:

53% (00:47) correct 47% (01:03) wrong based on 64 sessions

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What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x
[Reveal] Spoiler: OA

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Kudos [?]: 132595 [0], given: 12326

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Joined: 08 Jul 2010
Posts: 1847

Kudos [?]: 2335 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: What is the value of x^6/(x^2+1)? [#permalink]

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03 Oct 2017, 00:18
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

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Re: What is the value of x^6/(x^2+1)? [#permalink]

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03 Oct 2017, 07:38
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep

Kudos [?]: 3 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132595 [0], given: 12326

Re: What is the value of x^6/(x^2+1)? [#permalink]

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03 Oct 2017, 07:45
sandeep211986 wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep

Correct, except if |x| = –x, x can be 0 too: |0| = -0 = 0.
_________________

Kudos [?]: 132595 [0], given: 12326

SVP
Joined: 08 Jul 2010
Posts: 1847

Kudos [?]: 2335 [0], given: 51

Location: India
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Re: What is the value of x^6/(x^2+1)? [#permalink]

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03 Oct 2017, 10:32
sandeep211986 wrote:
GMATinsight wrote:
Bunuel wrote:
What is the value of $$\frac{x^6}{x^2+1}$$?

(1) |x| = –x
(2) x^2 = x

Question : x^6/(x^2+1) = ?

Statement 1: |x| = –x

i.e. x is LESS than or EQUAL to 0

x = 0, x^6/(x^2+1) = 0
x = -1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

Statement 2: x^2 = x
i.e. x = 0 or 1
x = 0, x^6/(x^2+1) = 0
x = 1, x^6/(x^2+1) = 1/2

NOT SUFFICIENT

COmbining the two statements

x = 0
i.e. x^6/(x^2+1) = 0
SUFFICIENT

I have a small query .

As per my understanding |x| = –x means that x is negative while |x| = x means that x is either positive or 0.

Regards,
Sandeep

0 is neither positive nor negative therefore

-0 = +0 = 0

Hence, |x| = -x means that x≤0

Other way around, x can be anything that satisfies the expression |x| = -x and zero satisfies this expression.

You might need this clarification for many other good questions as well.

Posted from my mobile device
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GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

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Kudos [?]: 2335 [0], given: 51

Re: What is the value of x^6/(x^2+1)?   [#permalink] 03 Oct 2017, 10:32
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