Last visit was: 26 Apr 2026, 07:26 It is currently 26 Apr 2026, 07:26
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
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 26 Apr 2026
Posts: 5,987
Own Kudos:
5,860
 [28]
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,987
Kudos: 5,860
 [28]
If x is an integer, What is the value of |x+5|+ |x-3|? 10 Jul 2019, 22:53
1
Kudos
Add Kudos
27
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

43% (02:10) correct 57% (02:03) wrong based on 246 sessions

History

Date
Time
Result
Not Attempted Yet
If x is an integer, What is the value of |x+5|+ |x-3|?

\(A. x^2<16\)
\(B. (x+1)^2<25\)
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
firas92
User avatar
Current Student
Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 616
Own Kudos:
1,766
 [5]
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
My Reviews
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
Posts: 616
Kudos: 1,766
 [5]
If x is an integer, What is the value of |x+5|+ |x-3|? Updated on: 07 Aug 2019, 08:03
Originally posted by firas92 on 11 Jul 2019, 01:17.
Last edited by firas92 on 07 Aug 2019, 08:03, edited 1 time in total.
2
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
The range -5≤x≤3 will give a unique value for |x+5|+ |x-3|

If x is outside this range, we can get multiple values

(1) \(x^2<16\)

|x|<4 or -4<x<4

Since x is an integer, the minimum value x can take is -3 and the maximum is 3

This lies within our favorable region -5≤x≤3

Sufficient

(2) \((x+1)^2<25\)

|x+1|<5 or -5<x+1<5 or -6<x<4

This means the minimum value x can take is -5 and the maximum is 3

Once again, this is within our favorable region -5≤x≤3

Sufficient

Answer is (D)
General Discussion
User avatar
wizardofoddz
User avatar
Joined: 19 Jul 2018
Last visit: 11 Feb 2020
Posts: 12
Own Kudos:
11
Given Kudos: 59
Posts: 12
Kudos: 11
If x is an integer, What is the value of |x+5|+ |x-3|? 11 Jul 2019, 23:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel I do not really follow the solution above. Some concepts seem to have been used without proper explanation. Could you please provide a solution to this that a beginner would understand? Thanks in advance.
User avatar
wizardofoddz
User avatar
Joined: 19 Jul 2018
Last visit: 11 Feb 2020
Posts: 12
Own Kudos:
11
 [4]
Given Kudos: 59
Posts: 12
Kudos: 11
 [4]
If x is an integer, What is the value of |x+5|+ |x-3|? 13 Jul 2019, 16:45
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Before we dive into this question, let's try and understand the properties of the modulus function

1. |x+a| has a domain (-infinity, infinity) and range [0, infinity).
2. |x+a| can be rewritten as |x-(-a)| and is nothing but the distance of x from (-a).
2. |x+a| divides the x axis into 3 regions:
a. x < -a
b. x = -a
c. x > -a

Therefore, the range of the function |x+5|+ |x-3| can be divided into 3 segments: 1. x<-5 2. -5≤x≤3 3. x>3

When x<-5:

1. One approach would be taking 2 random values of x (x1 and x2) such that x<-5 and checking the values of f(x) = |x+5|+ |x-3|. f(x1) and f(x2) produce different values. Therefore, value of f(x) can not be determined in this range.
2. Second approach would be to check out the graphs of the two functions, |x+5| and |x-3| in this range. We would see ascendent parallel lines with a negative slope. Therefore, f(x) decreases for decreasing x.

When x>3:

1. Here too, approach #1, would be taking 2 random values of x (x1 and x2) such that x>3 and checking the values of f(x) = |x+5|+ |x-3|. f(x1) and f(x2) produce different values. Therefore, value of f(x) can not be determined in this range.
2. Second approach would be to check out the graphs of the two functions, |x+5| and |x-3| in this range. We would see ascendent parallel lines with a positive slope. Therefore, f(x) increases for increasing values of x.

When -5≤x≤3:

The graphs of two functions are straight lines here that converge, intersect and diverge, with increasing x starting at -5 through 3, in this region with equal but opposite slopes. Therefore, for all x in this region, f(x) = 8.
The same can be verified by trying random values of x.

Therefore, let's now have a look at the statements to see whether they can help us determine whether x lies in our favorable range or not.

Statement 1: x^2<16

=> |x|<4 => -4<x<4. Since x is an integer, this translates to -3≤x≤3. This lies in the favorable range. Therefore this is sufficient.


Statement 2: (x+1)^2 <25

=> |x+1|<25 => -5<x+1<5 => -6<x<4. Since x is an integer, this translates to -5≤x≤3. This lies in the favorable range. Therefore this is sufficient.

Therefore, the answer is (D).

Posted from my mobile device
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,680
Own Kudos:
1,469
 [1]
Given Kudos: 607
Location: United States
Posts: 1,680
Kudos: 1,469
 [1]
If x is an integer, What is the value of |x+5|+ |x-3|? 26 Jul 2019, 11:52
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kinshook
If x is an integer, What is the value of |x+5|+ |x-3|?

\(A. x^2<16\)
\(B. (x+1)^2<25\)
Show more

given: x=integer, |x+5|+|x-3|=?

(1) \(x^2<16\): then |x|<4,…-4>x>4={-3,-2,-1,0,1,2,3}, when you replace any of these values in the equation, you get the same result, 8; sufficient.

(2) \((x+1)^2<25\): then, |x+1|<5,…-6<x<4={-5,-4…}, when you replace any of these values in the equation, you get the same result, 8; sufficient.

Answer (D).

Hey Bunuel or chetan2u, instead of testing all the values in the range, isn't there some way better?
User avatar
ishan261288
User avatar
Joined: 31 Oct 2018
Last visit: 04 Nov 2024
Posts: 15
Own Kudos:
17
Given Kudos: 285
WE:Research (Hospitality and Tourism)
Posts: 15
Kudos: 17
If x is an integer, What is the value of |x+5|+ |x-3|? 07 Aug 2019, 08:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can you explain why this happened
wizardofoddz
Since x is an integer, this translates to -3≤x≤3
Why suddenly range changed from -4 to 4 to -3 to 3?

wizardofoddz
Before we dive into this question, let's try and understand the properties of the modulus function

1. |x+a| has a domain (-infinity, infinity) and range [0, infinity).
2. |x+a| can be rewritten as |x-(-a)| and is nothing but the distance of x from (-a).
2. |x+a| divides the x axis into 3 regions:
a. x < -a
b. x = -a
c. x > -a

Therefore, the range of the function |x+5|+ |x-3| can be divided into 3 segments: 1. x<-5 2. -5≤x≤3 3. x>3

When x<-5:

1. One approach would be taking 2 random values of x (x1 and x2) such that x<-5 and checking the values of f(x) = |x+5|+ |x-3|. f(x1) and f(x2) produce different values. Therefore, value of f(x) can not be determined in this range.
2. Second approach would be to check out the graphs of the two functions, |x+5| and |x-3| in this range. We would see ascendent parallel lines with a negative slope. Therefore, f(x) decreases for decreasing x.

When x>3:

1. Here too, approach #1, would be taking 2 random values of x (x1 and x2) such that x>3 and checking the values of f(x) = |x+5|+ |x-3|. f(x1) and f(x2) produce different values. Therefore, value of f(x) can not be determined in this range.
2. Second approach would be to check out the graphs of the two functions, |x+5| and |x-3| in this range. We would see ascendent parallel lines with a positive slope. Therefore, f(x) increases for increasing values of x.

When -5≤x≤3:

The graphs of two functions are straight lines here that converge, intersect and diverge, with increasing x starting at -5 through 3, in this region with equal but opposite slopes. Therefore, for all x in this region, f(x) = 8.
The same can be verified by trying random values of x.

Therefore, let's now have a look at the statements to see whether they can help us determine whether x lies in our favorable range or not.

Statement 1: x^2<16

=> |x|<4 => -4<x<4. Since x is an integer, this translates to -3≤x≤3. This lies in the favorable range. Therefore this is sufficient.


Statement 2: (x+1)^2 <25

=> |x+1|<25 => -5<x+1<5 => -6<x<4. Since x is an integer, this translates to -5≤x≤3. This lies in the favorable range. Therefore this is sufficient.

Therefore, the answer is (D).

Posted from my mobile device
Show more
User avatar
freedom128
User avatar
Joined: 30 Sep 2017
Last visit: 01 Oct 2020
Posts: 939
Own Kudos:
1,377
 [1]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Products:
My Reviews
GMAT 1: 720 Q49 V40
Posts: 939
Kudos: 1,377
 [1]
If x is an integer, What is the value of |x+5|+ |x-3|? 07 Aug 2019, 11:08
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|x+5|+ |x-3|
= (x+5) - (x-3) = 8
---> if both x+5>0 and x-3<0 are satisfied. That gives us a combined range -5≤x≤3. If x is outside that range, we can get many x value.

(1) x^2<16
-4<x<4 where x is n integer.
x is within the abovementioned range -5≤x≤3. Thus, the equation give a singular result, that is a constant 8.
SUFFICIENT

(2) (x+1)^2<25
-5<x+1<5 or -6<x<4 where x is an integer. In other word, x is within the abovementioned range -5≤x≤3. Thus, the equation gives a singular solution, that is a constant 8.
SUFFICIENT

Answer is (D)
User avatar
wali786
User avatar
Joined: 04 Feb 2018
Last visit: 04 Dec 2022
Posts: 28
Own Kudos:
9
Given Kudos: 2
Posts: 28
Kudos: 9
If x is an integer, What is the value of |x+5|+ |x-3|? 22 Dec 2020, 17:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x is an integer, What is the value of |x+5|+ |x-3|? The question is asking for a Value not values. I can solves the conditions and get answer, but i cannot understand how to get the range and why would we get a range?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,988
Own Kudos:
1,118
Posts: 38,988
Kudos: 1,118
If x is an integer, What is the value of |x+5|+ |x-3|? 08 Mar 2022, 05:37
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
109837 posts
kingbucky
498 posts
Gmat860sanskar
212 posts