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a, b, and c are distinct positive integers less than 100. If |a - b| +

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Bunuel
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a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink] New post  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


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Re: a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink] New post  17 Jul 2021, 09:51
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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
image-2.jpg [ 6.29 KiB | Viewed 5432 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!

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a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink] New post  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.
Attachment:
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b<99; Max value b can take is 98.
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Re: a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink] New post  12 Aug 2021, 10:49
Bunuel wrote:
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


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The key to the solution is simple substitution and finding the right answer
let assume b=98 since if we chose 99 then the value cannot be equalised while maximising B
therefore we get the meaximum value thereafter and we take c=99
=>LHS = 98and rhs = 98

Therefore IMO D
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Re: a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink] New post  18 May 2023, 02:35
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Re: a, b, and c are distinct positive integers less than 100. If |a - b| + [#permalink]
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