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# M16-37

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:00
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Difficulty:

65% (hard)

Question Stats:

53% (01:27) correct 47% (01:29) wrong based on 100 sessions

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If $$|a - b| = |b - c| = 2$$, what is the value of $$|a - c|$$?

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

(2) $$c - a \gt c - b$$
[Reveal] Spoiler: OA

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16 Sep 2014, 00:00
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Official Solution:

(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 $$a=0$$, $$b=2$$, $$c=0$$ ($$|a-c|=0$$).

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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

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Joined: 13 Jan 2016
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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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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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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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03 Dec 2016, 00:29
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nelliegu wrote:
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

|x| = -x, when x <= 0. Since a - b < 0, then |a−b|=−(a−b).
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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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# M16-37

Moderators: chetan2u, Bunuel

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