If |a - b| = |b - c| = 2 , what is |a - c| ? : GMAT Data Sufficiency (DS)
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# If |a - b| = |b - c| = 2 , what is |a - c| ?

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If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 03:09
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If |a - b| = |b - c| = 2 , what is |a - c| ?

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

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

(C) 2008 GMAT Club - m16#37
[Reveal] Spoiler: OA
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 03:40
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AndreG wrote:
How do I approach a question like the following:

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

1. $$a \lt b \lt c$$
2. $$c - a \gt c - b$$

(C) 2008 GMAT Club - m16#37

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

$$|a - b| = |b - c| = 2$$

Imagine the points on a number line. There is two possibilities, either a & c are on the same side of the line relative to b, or on the opposite sides. Also remember that |x-y| represents distance between x and y on the number line.

So if a & c ar on the same side then a=c. |a-c|=0
If they are on opposite sides, |a-c|=4

(1) $$a \lt b \lt c$$
a and c on opposite sides, answer is 4. Sufficient

(2) $$c - a \gt c - b$$
This only implies $$a \lt b$$
Insufficient to know where c is, same side or opposite side. Insufficient

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 04:51
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Expert's post
AndreG wrote:
How do I approach a question like the following:

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

1. $$a \lt b \lt c$$
2. $$c - a \gt c - b$$

(C) 2008 GMAT Club - m16#37

Generally for $$|x|$$:
When $$x\leq{0}$$, then $$|x|=-x$$;
When $$x\geq{0}$$, then $$|x|=-x$$.

(1) $$a<b<c$$ --> as $$a<b$$ ($$a-b<0$$) then $$|a - b|=2$$ becomes: $$-a+b=2$$, so $$b=2+a$$ and as $$b<c$$ ($${b-c}<0$$) then $$|b-c|=2$$ becomes: $${-b+c}=2$$. Substituting $$b$$ --> $$-2-a+c=2$$ --> $$a-c=-4$$ --> $$|a - c|=|-4|=4$$ . Sufficient.

(2) $$c-a>c-b$$ --> $$b-a>0$$ --> $$|a - b|=2$$ becomes: $$-a+b=2$$, so $$b=2+a$$ --> $$|b - c|=|a-c+2| = 2$$ --> either $$a-c=0$$ or $$a-c=-4$$. Not sufficient.

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 09:14
Thanks to the two of you!
While I do understand both solutions, I feel shrouded's is a lot faster, will that always be the case, or is this kind of just lucky for this particular question?
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 10:30
Thinking of |x-y| as distance between two points on a number line is a very neat trick and I find it very helpful in a lot of GMAT problems. You should def give it a shot first. Thinking visually is faster than algebraically solving in many cases

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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09 Oct 2010, 10:38
|a-b| = |b-c| = 2 can be written in 4 ways

1) a-b = b-c = 2 => a>b>c with a diff of 2
2) a-b = c-b = 2 => a=c
3) b-a = b-c = 2 => a=c
4) b-a = c-b = 2 => a<b<c with a diff of 2

A) a<b<c : based on the 4th statement above , we can say that |a-c| = 4
Sufficient
B) c-a > c-b : we can understand that a<b but there is no relationship with C.
Hence Insufficient

Ans : A

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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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16 Oct 2010, 04:38
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I always find these type of questions to be killer..
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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06 Jun 2014, 07:09
I don't think that even the options are required to answer this question

From question itself

|<-------------2------------->|<--------------2-------------->|
A------------------------------B--------------------------------C

|<----------------------------4--------------------------------->|

The question is badly framed and is definitely not GMAT.
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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06 Jun 2014, 07:36
If |a - b| = |b - c| = 2 , what is |a - c| ?

(1) $$a \lt b \lt c$$
(2) $$c - a \gt c - b$$

I don't think that even the options are required to answer this question

From question itself

|<-------------2------------->|<--------------2-------------->|
A------------------------------B--------------------------------C

|<----------------------------4--------------------------------->|

The question is badly framed and is definitely not GMAT.

There is noting wrong with the question. The second statement is NOT sufficient. Consider:
b=3, a=1, and c=1 --> |a - c| = 0.
b=3, a=1, and c=5 --> |a - c| = 4.

Hope it helps.
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Re: If |a - b| = |b - c| = 2 , what is |a - c| ? [#permalink]

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30 Jul 2015, 02:18
|a-b|=|b-c|=2 means that distance between a and b equal to that between b and c

Four possibilities in number line:
----a------b------c-------->
----c------b------a-------->
----a,c--------b----------->
----b----------a,c--------->

What is the |a-c|?

So, if b between a and c, the answer is 4; if a=c, the answer is 0

St.1 a<b<c, b between a and c, so answer is 4. SUFF

St.2 c-a>c-b => -a>-b => a<b. But we do not know where c. INSUFF

A
Re: If |a - b| = |b - c| = 2 , what is |a - c| ?   [#permalink] 30 Jul 2015, 02:18
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