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Math Expert V
Joined: 02 Sep 2009
Posts: 58416
If |x – 3| = 5, what is the value of x?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 83% (00:47) correct 17% (00:50) wrong based on 239 sessions

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If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

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Manager  Joined: 05 Jun 2015
Posts: 77
Location: United States
WE: Engineering (Transportation)
Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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x>3. x = 8
x<3, x = -2

(1) x < 0

=>x =- 2

(2) x^3 = –8
=> x <0

x = -2

Both choice are sufficient.
Option D
Intern  Joined: 23 Oct 2016
Posts: 32
Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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lx-3l=5

So basically, we have to know whether the value inside the absolute is positive or negative, that is, we have to know if x-3>0 or x-3<0. So knowing the range of possible value of x would be sufficient.

Statement1: x<0, so x if for sure less than 3, so lx-3l=3-x (to make the value inside the absolute positive)=5 =>x=-2 => sufficient

Statement2: x^3=-8, so x=-2 => sufficient

Answer is D. Both statements are sufficient
Senior Manager  Joined: 06 Jun 2016
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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Bunuel wrote:
If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

IMO D
Given
x-3=5 when x>0 ==> x=8
3-x=5 when x<0 ==> x=-2
what is the value of x?

statement 1
says that x<0 giving the value of x as -2
Sufficient

Statement 2
x^3=-8 ==> x=-2
Sufficient

Hence D
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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Bunuel wrote:
If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

from the given statement, x is either -2 or 8.

1. x<0 -> x must be -2. sufficient.
2. x^3 = -8, x must be -2. sufficient.

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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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Bunuel wrote:
If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

Question : What is the value of x?
Given, |x – 3| = 5
i.e. x = 8 or -2

Statement 1:: x < 0
i.e. x must be only -2, Hence
SUFFICIENT

Statement 2:: x^3 = –8
i.e. x must be only -2 out of 8 or -2, Hence
SUFFICIENT

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Current Student B
Joined: 08 Oct 2016
Posts: 49
Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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I'm sorry to ask, but are these questions actually 600-700 level? Seem to easy.

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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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1
gillyelephant wrote:
I'm sorry to ask, but are these questions actually 600-700 level? Seem to easy.

Posted from my mobile device

Yes this question is 600-700 level questions due to the following facts

1) This question is a DS question
2) Question requires the properties of Inequality and Absolute value which is supposed to be a difficult topic
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Current Student P
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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gillyelephant wrote:
I'm sorry to ask, but are these questions actually 600-700 level? Seem to easy.

Posted from my mobile device

Lol i agree, this was very easy but you will be surprised how many people would select C. Its a C trap answer. Under test conditions with stress, many people will carry over the -2 vs 8 mindset, and see X cube is -8 and quickly select C and move on.
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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Bunuel wrote:
If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

2 ways to approach absolute value

Pos

x-3 =5
x =8

Neg

-l x -3l =5
-x + 3 =5
-x = 2
x= -2

D
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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Bunuel wrote:
If |x – 3| = 5, what is the value of x?

(1) x < 0
(2) x^3 = –8

Question : x = ?

Given |x – 3| = 5

x – 3 = 5 or x - 3 = -5

x = 8 or x = -2

St 1: x < 0

means -2 is the valid answer as -2 < 0 Sufficient

St 2: x^3 = -8

x = -2 Sufficient

(D)
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Re: If |x – 3| = 5, what is the value of x?  [#permalink]

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_________________ Re: If |x – 3| = 5, what is the value of x?   [#permalink] 04 Jul 2019, 05:01
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