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

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 633

Kudos [?]: 317 [1], given: 39

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, 10:10
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1
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Difficulty:

55% (hard)

Question Stats:

59% (02:09) correct 41% (01:35) wrong based on 41 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
[Reveal] Spoiler: OA

Kudos [?]: 317 [1], given: 39

Manager
Joined: 22 Apr 2017
Posts: 76

Kudos [?]: 30 [2], given: 59

Location: India
Schools: MBS '20 (S)
GPA: 3.7
Re: Consider three distinct positive integers a, b, c all less than 100 [#permalink]

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01 Dec 2017, 10:26
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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.

Kudos [?]: 30 [2], given: 59

Re: Consider three distinct positive integers a, b, c all less than 100   [#permalink] 01 Dec 2017, 10:26
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# Consider three distinct positive integers a, b, c all less than 100

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