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

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09 Oct 2010, 04:40

2

This post received KUDOS

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

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

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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?

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

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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

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

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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

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.

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