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20 May 2020, 08:13
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a, b, and c are distinct positive integers less than 100. If \(|a - b| + |b - c| = |c – a|\), what is the maximum value possible for b?
A. 50
B. 96
C. 97
D. 98
E. 99
Are You Up For the Challenge: 700 Level Questions
A. 50
B. 96
C. 97
D. 98
E. 99
Are You Up For the Challenge: 700 Level Questions
Updated on: 30 Jan 2025, 05:16
Originally posted by BrushMyQuant on 17 Jul 2021, 09:51.
Last edited by BrushMyQuant on 30 Jan 2025, 05:16, edited 2 times in total.
Last edited by BrushMyQuant on 30 Jan 2025, 05:16, edited 2 times in total.
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧
Theory: |a - b| always means the distance between the points a and b on the number line. (Irrespective of the signs of a and b)
=> |a - b| -> Distance between a and b
=> |b - c| -> Distance between b and a
=> |c - a| -> Distance between c and a
\(|a - b| + |b - c| = |c – a|\)
This means that, distance between a and b + distance between b and c = distance between c and a
=> b lies between a and c
image-2.jpg [ 6.29 KiB | Viewed 10590 times ]
And we know that a,b,c are distinct positive integers less than 100
=> max value of c can be 99, making max value of b as 98
So, Answer will be D
Hope it helps!
Watch the following video to learn Basics of Absolute Values
Theory: |a - b| always means the distance between the points a and b on the number line. (Irrespective of the signs of a and b)
=> |a - b| -> Distance between a and b
=> |b - c| -> Distance between b and a
=> |c - a| -> Distance between c and a
\(|a - b| + |b - c| = |c – a|\)
This means that, distance between a and b + distance between b and c = distance between c and a
=> b lies between a and c
Attachment:
image-2.jpg [ 6.29 KiB | Viewed 10590 times ]
And we know that a,b,c are distinct positive integers less than 100
=> max value of c can be 99, making max value of b as 98
So, Answer will be D
Hope it helps!
Watch the following video to learn Basics of Absolute Values
20 May 2020, 09:43
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The sum of the distance between a and b and distance between b and c is equal to that between a and c. Hence, only following scenario is possible. 
Untitled.png [ 3 KiB | Viewed 12786 times ]
b<99; Max value b can take is 98.
Attachment:
Untitled.png [ 3 KiB | Viewed 12786 times ]
b<99; Max value b can take is 98.
