It is currently 20 Nov 2017, 01:09

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x is a number between -5 and 15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 16 Mar 2017
Posts: 13

Kudos [?]: 10 [0], given: 15

If x is a number between -5 and 15 [#permalink]

Show Tags

New post 19 Sep 2017, 08:26
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

71% (00:55) correct 29% (00:40) wrong based on 139 sessions

HideShow timer Statistics

If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0
[Reveal] Spoiler: OA

Kudos [?]: 10 [0], given: 15

1 KUDOS received
Director
Director
avatar
P
Joined: 25 Feb 2013
Posts: 558

Kudos [?]: 254 [1], given: 34

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
GMAT ToolKit User Reviews Badge
If x is a number between -5 and 15 [#permalink]

Show Tags

New post 19 Sep 2017, 08:37
1
This post received
KUDOS
2
This post was
BOOKMARKED
petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0


Given, \(-5<x<15\). Add -5 to both sides of the inequality

\(-5-5<x-5<15-5\) or \(-10<x-5<10\)

This can be written as \(|x-5|<10\)

Option C

Kudos [?]: 254 [1], given: 34

2 KUDOS received
Director
Director
avatar
P
Joined: 22 May 2016
Posts: 983

Kudos [?]: 341 [2], given: 592

If x is a number between -5 and 15 [#permalink]

Show Tags

New post 19 Sep 2017, 10:25
2
This post received
KUDOS
petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0

We know: -5 < x < 15

To find the range expressed in an absolute value inequality (or equation) you can use a fairly easy method. If needed, sketch a number line.

1) Find the midpoint,* which is 5, exactly halfway between -5 and 15.

2) Think about "distance from" to set up the expression, LHS

|x| = the distance of x from 0 on the number line

Similarly, |x - 5| is the distance of x from 5, the midpoint. (The point from which distance is measured has "moved" from 0 to 5, the midpoint of THIS range.)

That's the LHS

3) RHS?

Now use 5, midpoint, and 10, distance, as the "distance from": -5 is a distance of 10 from 5, and 15 is a distance of 10 from 5

The x here is not inclusive.

The distance of x from 5 cannot be 10 (which would be |x - 5| = 10), but it can be anything up to 10, namely

|x - 5| < 10

ANSWER C

You can check. (In fact, because these numbers are very manageable, if you got really stuck, you could work from the answer choices.)

|x - 5| < 10, remove absolute value bars, check the two cases

Case 1:
x - 5 < 10
x < 15

Case 2:
x - 5 > -10
x > -5

Together: -5 < x < 15 - Correct

ANSWER C

*Midpoint
\(\frac{(-5 + 15)}{2}\) = 5

Kudos [?]: 341 [2], given: 592

Manager
Manager
User avatar
G
Joined: 30 May 2012
Posts: 220

Kudos [?]: 82 [0], given: 151

Location: United States (TX)
Concentration: Finance, Marketing
GPA: 3.3
WE: Information Technology (Consulting)
Premium Member
Re: If x is a number between -5 and 15 [#permalink]

Show Tags

New post 21 Sep 2017, 17:25
petrified17 wrote:
If x is a number between -5 and 15, which of following equations represents the range of x?

A) |x| - 5 < 10
B) |x| + 5 < 10
C) |x - 5| < 10
D) |x + 5| < 10
E) |x + 5| < 0



It is important to note that, unless mentioned in the prompt, one needs to assume that the endpoints (-5 and 15) are not inclusive. As in, -5<x<15 and NOT \(-5\leq{x}\leq{15}\)

Kudos [?]: 82 [0], given: 151

Re: If x is a number between -5 and 15   [#permalink] 21 Sep 2017, 17:25
Display posts from previous: Sort by

If x is a number between -5 and 15

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.