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Bunuel
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What is the value of x^6/(x^2+1)? 02 Oct 2017, 23:59
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C
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Difficulty:

55% (hard)

Question Stats:

51% (01:25) correct 49% (01:22) wrong based on 237 sessions

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

(1) |x| = –x
(2) x^2 = x
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C
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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What is the value of x^6/(x^2+1)? 03 Oct 2017, 00:18
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Bunuel
What is the value of \(\frac{x^6}{x^2+1}\)?

(1) |x| = –x
(2) x^2 = x
Show more

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

Answer: Option C
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What is the value of x^6/(x^2+1)? 03 Oct 2017, 07:38
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Bunuel
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

Answer: Option C
Show more

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.
Experts can you please clarify.

Regards,
Sandeep
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What is the value of x^6/(x^2+1)? 03 Oct 2017, 07:45
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sandeep211986
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Bunuel
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

Answer: Option C

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.
Experts can you please clarify.

Regards,
Sandeep
Show more

Correct, except if |x| = –x, x can be 0 too: |0| = -0 = 0.
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What is the value of x^6/(x^2+1)? 03 Oct 2017, 10:32
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sandeep211986
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Bunuel
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

Answer: Option C

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.
Experts can you please clarify.

Regards,
Sandeep
Show more
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.

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What is the value of x^6/(x^2+1)? 16 Apr 2018, 09:09
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Statement 1: lxl=-x, lxl+x=0, Lets take two cases, one x is negative number other x is positive number
if x is positive then equation becomes, x+x=0, 2x=0, x=0
if x is negative then equation becomes, l-xl + (-x) =0, x-x=0, infinite soltions
Insufficient
Statement 2: Solving equation 2 gives x = 0 or 1. Insufficient

Statement 1 & 2 together gives, x = 0, hence the question will have unique value of 0.

Answer is C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
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What is the value of x^6/(x^2+1)? 21 Dec 2023, 22:28
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