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

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

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New post 01 Dec 2017, 10:10
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Question Stats:

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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

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Re: Consider three distinct positive integers a, b, c all less than 100  [#permalink]

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New post 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.
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Re: Consider three distinct positive integers a, b, c all less than 100  [#permalink]

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New post 03 Feb 2019, 22:32
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Re: Consider three distinct positive integers a, b, c all less than 100   [#permalink] 03 Feb 2019, 22:32
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