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

Answer is (A) _________________

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1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

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