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M16-37

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M16-37 [#permalink]

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(1) \(a \lt b \lt c\). Since given that \(a \lt b\) then \(|a-b|=-(a-b)=2\), so we have that \(b-a=2\). The same way, since given that \(b \lt c\) then \(|b-c|=-(b-c)=2\), so we have that \(c-b=2\). Sum these two equations: \((b-a)+(c-b)=2+2\), which simplifies to \(c-a=4\). Hence, \(|a-c|=4\). Sufficient.

(2) \(c-a \gt c-b\). Rearrange: \(a \lt b\). Not sufficient, consider \(a=0\), \(b=2\), \(c=4\) (\(|a-c|=4\)) and \(a=0\), \(b=2\), \(c=0\) (\(|a-c|=0\)).


Answer: A
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M16-37 [#permalink]

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New post 22 Nov 2015, 15:22
Bunuel wrote:
If \(|a - b| = |b - c| = 2\), what is the value of \(|a - c|\)?


(1) \(a \lt b \lt c\)

(2) \(c - a \gt c - b\)


my approach:

We can also write this question as:"if the distance between a and b, and, b and c is 2 then what is the distance between a and c ?"

1) if a < b < c then this is an arithmetic series with common difference 2. Which is a,b,c = a, a+2, a+4 thus the distance between a and c is 4. ===sufficient

2) if c-a > c-b (which is a < b) then c could be c= b+2 = a+4 or c= b-2 = a) ===insufficient

Answer A
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Re: M16-37 [#permalink]

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New post 22 Sep 2016, 09:32
Cannot these points be non co-linear?

On a coordinate plan, a @(-2,0) ; b @(0,0) ; c @(2,0) or (0,2)
and |a-b| etc represents distance between two points.
(in that case, (1) isn't sufficient)

Is there any flaw in this thinking?
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Re: M16-37 [#permalink]

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New post 23 Sep 2016, 03:04
rumanshu wrote:
Cannot these points be non co-linear?

On a coordinate plan, a @(-2,0) ; b @(0,0) ; c @(2,0) or (0,2)
and |a-b| etc represents distance between two points.
(in that case, (1) isn't sufficient)

Is there any flaw in this thinking?


a, b and c there represent numbers. If it were otherwise it would be mentioned.
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Re: M16-37 [#permalink]

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New post 02 Dec 2016, 16:55
Hi, could you please explain why this is true:

"Since given that a<ba<b then |a−b|=−(a−b)=2"

Thank you very much
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Re: M16-37 [#permalink]

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Re: M16-37 [#permalink]

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New post 03 Aug 2017, 10:13
why is B not sufficient? Can anyone explain
Thank you:D
Re: M16-37   [#permalink] 03 Aug 2017, 10:13
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