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07 Jul 2019, 23:42
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C
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Difficulty:
95%
(hard)
Question Stats:
47% (02:43) correct
53%
(02:50)
wrong
based on 376
sessions
History
Date
Time
Result
Not Attempted Yet
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
08 Jul 2019, 03:59
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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
05 Aug 2019, 21:31
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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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