Last visit was: 25 Apr 2026, 08:32 It is currently 25 Apr 2026, 08:32
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,882
 [29]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,882
 [29]
If x is an integer, then how many values of x will satisfy the equatio Updated on: 20 Sep 2018, 07:58
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:05.
Last edited by EgmatQuantExpert on 20 Sep 2018, 07:58, edited 5 times in total.
2
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

63% (01:44) correct 37% (01:43) wrong based on 1222 sessions

History

Date
Time
Result
Not Attempted Yet
Different methods to solve absolute value equations and inequalities- Exercise Question #2

If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?

Options

    a) 0
    b) 1
    c) 2
    d) 3
    e) 4

Previous Question | Next Question


To read the article: Different methods to solve absolute value equations and inequalities

ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
T1101
User avatar
Joined: 07 Aug 2018
Last visit: 18 Nov 2021
Posts: 79
Own Kudos:
358
 [7]
Given Kudos: 247
Location: United States (MA)
GMAT 1: 560 Q39 V28
GMAT 2: 670 Q48 V34
GMAT 2: 670 Q48 V34
Posts: 79
Kudos: 358
 [7]
If x is an integer, then how many values of x will satisfy the equatio Updated on: 20 Sep 2018, 08:05
Originally posted by T1101 on 13 Sep 2018, 10:36.
Last edited by T1101 on 20 Sep 2018, 08:05, edited 2 times in total.
7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
My Approach:

Ix-10I will always be positive and in order for ||x-10|-6|=4 to be true |x-10|=2 or |x-10|=10

|x-10|=2



1.
x-10=2
x=12

2.
-x+10=2
x=8

--> x=12 or x=8

|x-10|=10



1.
x-10=20
x=20

2.
-x+10=10
x=0

Left with four values: 0,8,10,12
So Answer: E



Please correct me if I am wrong!!

Edited! Was wrong first time...
General Discussion
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,882
 [4]
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,882
 [4]
If x is an integer, then how many values of x will satisfy the equatio Updated on: 20 Sep 2018, 21:06
Originally posted by EgmatQuantExpert on 13 Sep 2018, 03:10.
Last edited by EgmatQuantExpert on 20 Sep 2018, 21:06, edited 4 times in total.
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post

Solution


Given:
    • We are given that x is an integer, and
    • We are also given an absolute value equation, ||x - 10| - 6| = 4

To find:
    • We need to find the number of values of x, that satisfy the given equation

Approach and Working:
    • As seen in the previous question, the first step is to substitute |x - 10| as t, which gives
      o |t - 6| = 4
    • Now, applying the definition of |x|, as learnt in the article, we can write |t - 6| = 4 as,
      o t - 6 = 4, if t ≥ 6
         Implies, t = 10, which is greater than 6
         Now, substituting back t as |x - 10|, we get, |x - 10| = 10
         This again gives two cases,
        Case -1: x – 10 = 10, if x ≥ 10
         Implies, x = 20, which is greater than 10
         Thus, x = 20, is a possible value of x
        Case -2: x – 10 = -10, if x < 10
         Implies, x = 0, which is also a possible value
      o And, t - 6 = -4, if t < 6
         Implies, t = 2, which is less than 6
         Now, substituting back t as |x - 10|, we get, |x - 10| = 2
         This again gives two cases,
        Case -1: x – 10 = 2, if x ≥ 10
         Implies, x = 12, which is greater than 10
         Thus, x = 12, is a possible value of x
        Case -2: x – 10 = -2, if x < 10
         Implies, x = 8, which is less than 10
         Thus, x = 8, is also a possible value
    • Thus, the only possible values of x that satisfy the given equation are 0, 8, 12 and 20.
    • Therefore, the number of possible values of x is 4.

Hence, the correct answer is option E.

Answer: E

User avatar
rahul16singh28
User avatar
Joined: 31 Jul 2017
Last visit: 09 Jun 2020
Posts: 428
Own Kudos:
503
 [1]
Given Kudos: 752
Location: Malaysia
Schools: INSEAD Jan '19
GPA: 3.95
WE:Consulting (Energy)
Schools: INSEAD Jan '19
Posts: 428
Kudos: 503
 [1]
If x is an integer, then how many values of x will satisfy the equatio Updated on: 14 Sep 2018, 04:41
Originally posted by rahul16singh28 on 13 Sep 2018, 10:46.
Last edited by rahul16singh28 on 14 Sep 2018, 04:41, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
Different methods to solve absolute value equations and inequalities- Exercise Question #2

If x is an integer, then how many values of x will satisfy the equation ||x - 10| - 6| = 4?

Options

    a) 0
    b) 1
    c) 2
    d) 3
    e) 4

Previous Question | Next Question


To read the article: Different methods to solve absolute value equations and inequalities

Show more

Basically, here we have to find values of x for which |x-10| = 2,10.

So, x = 0,8,12,20

Hence, E.
avatar
mittu
avatar
Joined: 07 Jan 2018
Last visit: 16 Oct 2019
Posts: 9
Own Kudos:
2
 [1]
Given Kudos: 10
Posts: 9
Kudos: 2
 [1]
If x is an integer, then how many values of x will satisfy the equatio 14 Sep 2018, 04:39
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
x={0,8,12,20}
So isn't the answer E?

Posted from my mobile device
User avatar
sayankh
User avatar
Joined: 08 Apr 2018
Last visit: 08 Feb 2023
Posts: 15
Own Kudos:
10
 [1]
Given Kudos: 3
Posts: 15
Kudos: 10
 [1]
If x is an integer, then how many values of x will satisfy the equatio 14 Sep 2018, 07:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer would be 'E', 4 possible values of 'x' {0,8,12,20}.
avatar
HimoGMAT
avatar
Joined: 22 Apr 2017
Last visit: 27 Jun 2019
Posts: 5
Own Kudos:
5
Given Kudos: 115
Posts: 5
Kudos: 5
If x is an integer, then how many values of x will satisfy the equatio 20 Sep 2018, 07:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert

Solution


Given:
    • We are given that x is an integer, and
    • We are also given an absolute value equation, ||x - 10| - 6| = 4

To find:
    • We need to find the number of values of x, that satisfy the given equation

Approach and Working:
    • As seen in the previous question, the first step is to substitute |x - 10| as t, which gives
      o |t - 6| = 4
    • Now, applying the definition of |x|, as learnt in the article, we can write |t - 6| = 4 as,
      o t - 6 = 4, if t ≥ 6
         Implies, t = 10, which is greater than 6
         Now, substituting back t as |x - 10|, we get, |x - 10| = 10
         This again gives two cases,
        Case -1: x – 10 = 10, if x ≥ 10
         Implies, x = 20, which is greater than 10
         Thus, x = 20, is a possible value of x
        Case -2: x – 10 = -10, if x < -10
         Implies, x = 0, which is not less than -10
         Thus, x = 0, is not a possible value
      o And, t - 6 = -4, if t < 6
         Implies, t = 2, which is less than 6
         Now, substituting back t as |x - 10|, we get, |x - 10| = 2
         This again gives two cases,
        Case -1: x – 10 = 2, if x ≥ 10
         Implies, x = 12, which is greater than 10
         Thus, x = 12, is a possible value of x
        Case -2: x – 10 = -2, if x < 10
         Implies, x = 8, which is less than 10
         Thus, x = 8, is also a possible value
    • Thus, the only possible values of x that satisfy the given equation are 8, 12 and 20.
    • Therefore, the number of possible values of x is 3.

Hence, the correct answer is option D.

Answer: D

Show more

Hello Payal

In solution mentioned by you:
The case 2 of lx-10l=10; there should be -(x-10)=10 if x<10
So x=0 if x<10. Which is a possible solution.
So the answer should be E.
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,657
Own Kudos:
20,882
Given Kudos: 165
Expert
Expert reply
Posts: 3,657
Kudos: 20,882
If x is an integer, then how many values of x will satisfy the equatio 20 Sep 2018, 08:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey HimoGMAT, mittu, rahul16singh28, T1101

You all are correct.
There was a typo error.
We have corrected the solution.

Regards
User avatar
sayankh
User avatar
Joined: 08 Apr 2018
Last visit: 08 Feb 2023
Posts: 15
Own Kudos:
10
Given Kudos: 3
Posts: 15
Kudos: 10
If x is an integer, then how many values of x will satisfy the equatio 20 Sep 2018, 08:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EgmatQuantExpert
Hey HimoGMAT, mittu, rahul16singh28, T1101

You all are correct.
There was a typo error.
We have corrected the solution.

Regards
Show more

You also might want to update the second last line, where it currently says the number of possible solutions is 3.
avatar
hibobotamuss
avatar
Joined: 28 Jun 2018
Last visit: 13 Oct 2019
Posts: 58
Own Kudos:
19
Given Kudos: 163
Posts: 58
Kudos: 19
If x is an integer, then how many values of x will satisfy the equatio 29 Sep 2018, 11:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u this one too please :(
User avatar
Ved22
User avatar
Joined: 18 Oct 2017
Last visit: 24 Apr 2026
Posts: 74
Own Kudos:
24
Given Kudos: 76
Location: India
Schools: ISB '21
Schools: ISB '21
Posts: 74
Kudos: 24
If x is an integer, then how many values of x will satisfy the equatio 23 Oct 2022, 04:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The best approach to solve this problem within 1 min is to plot the equation as a graph in coordinate axis.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
1,117
Posts: 38,985
Kudos: 1,117
If x is an integer, then how many values of x will satisfy the equatio 20 Mar 2025, 23:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109827 posts
Krunaal
Tuck School Moderator
852 posts