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98 < x< 102

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Carcass

Verbal Expert

Joined: 18 Apr 2015

Posts: 18184

GRE 1: Q160 V160

98 < x< 102 [#permalink]

20 Oct 2017, 02:38

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This question is part of GREPrepClub - The Questions Vault Project

\(98 < x < 102\)

\(103 < y < 107\)

Quantity A	Quantity B
\(y - x\)	\(\|y - x\|\)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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IlCreatore

Director

Joined: 03 Sep 2017

Posts: 518

Re: 98 < x< 102 [#permalink]

20 Oct 2017, 06:19

Given that y is always greater than x, we can say that both quantities are always positive. Moreover, given that the result of y-x is positive, means that the absolute value on quantity B is superfluous. Thus, the two quantities are exactly the same. Answer C

GreenlightTestPrep

GRE Instructor

Joined: 10 Apr 2015

Posts: 4909

Re: 98 < x< 102 [#permalink]

09 Aug 2019, 15:09

Expert Reply

Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project

\(98 < x < 102\)

\(103 < y < 107\)

Quantity A	Quantity B
\(y - x\)	\(\|y - x\|\)

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Regardless of which x and y values you choose to use, the y-value will ALWAYS be greater than the x-value.
So, y - x will ALWAYS be POSITIVE.

This means y - x = |y - x| for any pair of values we choose to use.

Answer: C

Cheers,
Brent
_________________

Brent Hanneson – Creator of GreenlightTestPrep.com

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INEQUALITIES/Absolute Value/Modulus