GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 11 Nov 2019, 19:49

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# How many integer solutions are there to the inequality |x+8|<x?

Author Message
TAGS:

### Hide Tags

Economist GMAT Tutor Representative
Joined: 06 Aug 2019
Posts: 107
How many integer solutions are there to the inequality |x+8|<x?  [#permalink]

### Show Tags

13 Oct 2019, 01:06
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:49) correct 26% (01:26) wrong based on 82 sessions

### HideShow timer Statistics

How many integer solutions are there to the inequality $$|x+8|<x$$?

A. 0

B. 2

C. 3

D. 8

E. 16

_________________
Economist GMAT Tutor
http://econgm.at/KvjVSi
(866) 292-0660
VP
Joined: 20 Jul 2017
Posts: 1044
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: How many integer solutions are there to the inequality |x+8|<x?  [#permalink]

### Show Tags

13 Oct 2019, 03:18
1
TheEconomistGMAT wrote:
How many integer solutions are there to the inequality $$|x+8|<x$$?

A. 0

B. 2

C. 3

D. 8

E. 16

x can never take negative values as Modulus |x+8| can never be negative

Also, when x is 0 or positive |x+8| is always greater than x

So, no values of x satisfies the above inequality

IMO Option A
Intern
Joined: 25 Aug 2018
Posts: 1
Re: How many integer solutions are there to the inequality |x+8|<x?  [#permalink]

### Show Tags

14 Oct 2019, 07:59
1) if, X +8 <0, -(x+8)<x, ==> X <-8 or x >-4, so no integer solutions.
2) if, X +8 >0, (x+8)<x, ==> X so no integer solutions.

Economist GMAT Tutor Representative
Joined: 06 Aug 2019
Posts: 107
Re: How many integer solutions are there to the inequality |x+8|<x?  [#permalink]

### Show Tags

15 Oct 2019, 22:03
1

Official Explanation

The issue in this question is an inequality combined with an absolute value. Note that this inequality is of the variable form (i.e., variables on both sides). Thus, the two-scenario approach will not necessarily work. Instead, plug in numbers to find out what the inequality really means.

First note that an absolute value can never be less than zero or a negative number, so x must be positive. Try some positive values of xx and see what happens.

Plug in x=2
|x+8|=|2+8|=|10|=10
This is NOT smaller than x=2 Therefore, x cannot equal 2.

Try other positive values of x Plug in x=3
|x+8|=|3+8|=|11|=11
This is NOT smaller than x=3. Therefore, x cannot equal 3.

Plug in x=0.5
|x+8|=|0.5+8|=|8.5|=8.5
This is NOT smaller than x=0.5 Therefore, x cannot equal 0.5.

Notice a pattern? For every positive value of x, the left side of the equation will always be greater than the right side. Thus, |x+8||x+8| will never be smaller than x, and there are no values of x that satisfy the inequality.

_________________
Economist GMAT Tutor
http://econgm.at/KvjVSi
(866) 292-0660
Re: How many integer solutions are there to the inequality |x+8|<x?   [#permalink] 15 Oct 2019, 22:03
Display posts from previous: Sort by