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# GMAT Test M19#37

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GMAT Test M19#37 [#permalink]  09 Oct 2010, 04:09
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Question Stats:

75% (03:53) correct 25% (00:00) wrong based on 0 sessions
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
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Re: GMAT Test M19#37 [#permalink]  09 Oct 2010, 04:40
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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: GMAT Test M19#37 [#permalink]  09 Oct 2010, 05:51
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: GMAT Test M19#37 [#permalink]  09 Oct 2010, 10:14
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: GMAT Test M19#37 [#permalink]  09 Oct 2010, 11:30
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: GMAT Test M19#37 [#permalink]  09 Oct 2010, 11:38
|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: GMAT Test M19#37 [#permalink]  16 Oct 2010, 05:38
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I always find these type of questions to be killer..
Re: GMAT Test M19#37   [#permalink] 16 Oct 2010, 05:38
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