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Kinshook
Major Poster
Joined: 03 Jun 2019
Last visit: 10 Sep 2026
Posts: 6,127
Location: India
Schools: HBS '28 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
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Difficulty:
95%
(hard)
Question Stats:
47% (02:43) correct
53%
(02:50)
wrong
based on 376
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History
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How many integer values of x satisfy the equation |x-3|+|x-5|<|x-11| ?
A. 7
B. 8
C. 9
D. 10
E. 11
A. 7
B. 8
C. 9
D. 10
E. 11
we have 4 ranges to examine:
at (\(x≥11\)) ,---------> \(x-3+x-5<x-11\) --> (\(x<-3\)) --------------> no common valid values
at (\(11>x≥5\)) ,--> \(x-3+x-5<11-x\) --> (\(x<6.33\)) ------------> 5,6 are common
at (\(5>x≥3\)) ,----> \(x-3+5-x<11-x\) --> (\(x<9\)) ----------------> 3,4 are common
at (\(3>x\)) ,----------> \(3-x+5-x<11-x\) --> (\(x>-3\)) --------------> -2,-1,0,1,2 are common
so we got 9 values C
at (\(x≥11\)) ,---------> \(x-3+x-5<x-11\) --> (\(x<-3\)) --------------> no common valid values
at (\(11>x≥5\)) ,--> \(x-3+x-5<11-x\) --> (\(x<6.33\)) ------------> 5,6 are common
at (\(5>x≥3\)) ,----> \(x-3+5-x<11-x\) --> (\(x<9\)) ----------------> 3,4 are common
at (\(3>x\)) ,----------> \(3-x+5-x<11-x\) --> (\(x>-3\)) --------------> -2,-1,0,1,2 are common
so we got 9 values C
Coggi abhishek31,
please fine the attached image, hope i am able to answer the working principle of modulus questions like this.
please fine the attached image, hope i am able to answer the working principle of modulus questions like this.
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General Discussion
Posts: 72
Hi, can someone explain the working of this question
Hello,
I am interested too. I don't really know how to tackle this problem. Can someone please give us an explanation ?
I am interested too. I don't really know how to tackle this problem. Can someone please give us an explanation ?
Thank you very much ! I understand now ! 
Posts: 39
J2S2019
Thanks a lot. I get everything except for one thing:
how do you determine the ranges inequality signs? You had:
x<3, 3≤x<5, 5≤x<11 and x>11
How did you determine it's ≤ for some and not just <?
Vigasimrair
Joined: 06 Feb 2019
Last visit: 26 Mar 2021
Posts: 36
Location: Russian Federation
Schools: INSEAD Sept'21 Intake (WL)
GMAT 1: 690 Q45 V40
The thing is to understand that |x-3| means:
The distance between x and 3. So the given inequality states that the combined distance between x and 3 plus distance between x and 5 is less than distance between x and 11.
We can use the number line to easily count that there are 9 such x:
-2,-1,0,1,2,3,4,5,6.
Does it help?
Posted from my mobile device
The distance between x and 3. So the given inequality states that the combined distance between x and 3 plus distance between x and 5 is less than distance between x and 11.
We can use the number line to easily count that there are 9 such x:
-2,-1,0,1,2,3,4,5,6.
Does it help?
Posted from my mobile device
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