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# Consider three distinct positive integers a, b, c all less than 100

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Retired Moderator
Joined: 25 Feb 2013
Posts: 1182
Location: India
GPA: 3.82
Consider three distinct positive integers a, b, c all less than 100  [#permalink]

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01 Dec 2017, 11:10
1
7
00:00

Difficulty:

65% (hard)

Question Stats:

60% (01:59) correct 40% (02:25) wrong based on 115 sessions

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Consider three distinct positive integers $$a$$, $$b$$, $$c$$ all less than $$100$$. If $$|a - b| + |b - c| = |c – a|$$, what is the maximum value possible for $$b$$ ?

A. 95
B. 96
C. 97
D. 98
E. 99

Source: Question Bank
Current Student
Joined: 22 Apr 2017
Posts: 106
Location: India
GMAT 1: 620 Q46 V30
GMAT 2: 620 Q47 V29
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GPA: 3.7
Re: Consider three distinct positive integers a, b, c all less than 100  [#permalink]

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01 Dec 2017, 11:26
4
3
niks18 wrote:
Consider three distinct positive integers $$a$$, $$b$$, $$c$$ all less than $$100$$. If $$|a - b| + |b - c| = |c – a|$$, what is the maximum value possible for $$b$$ ?

A. 95
B. 96
C. 97
D. 98
E. 99

Source: Question Bank

|a - b| + |b - c| = |c – a| the equation means that the sum of distance between B & A and C & B is equal to distance between C & A. Which means B is between C & A.

.....0........a...........b..........c . Since the maximum value of C can be 99(1<=A,B,C<100 and distinct), 98 is the maximum value of B.
Hence D.
##### General Discussion
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Re: Consider three distinct positive integers a, b, c all less than 100  [#permalink]

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03 Feb 2019, 23:32
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Re: Consider three distinct positive integers a, b, c all less than 100   [#permalink] 03 Feb 2019, 23:32
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