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M16 Q 37

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Manager
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M16 Q 37 [#permalink] New post 26 Jul 2012, 04:49
If \(|a - b| = |b - c| = 2\) , what is \(|a - c|\) ?

\(a \lt b \lt c\)
\(c - a \gt c - b\)

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

Statement (1) by itself is sufficient. We can write \(|a - b| = b - a = 2\) and \(|b - c| = c - b = 2\) . Plugging \(b = c - 2\) into the first equation, we get \(b - a = c - 2 - a = 2\) or \(c - a = 4\) . Thus, \(|a - c| = 4\) .

Statement (2) by itself is insufficient. Consider \(a = 0\) , \(b = 2\) , \(c = 4\) ( \(|a - c| = 4\) ) and \(a = c = 0\) , \(b = 2\) ( \(|a - c| = 0\) ).
The correct answer is A.


Does someone have an easier solution for this one? I have a hard time doing through this solution.
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Re: M16 Q 37 [#permalink] New post 26 Jul 2012, 08:45
teal wrote:
If \(|a - b| = |b - c| = 2\) , what is \(|a - c|\) ?

\(a \lt b \lt c\)
\(c - a \gt c - b\)

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

Statement (1) by itself is sufficient. We can write \(|a - b| = b - a = 2\) and \(|b - c| = c - b = 2\) . Plugging \(b = c - 2\) into the first equation, we get \(b - a = c - 2 - a = 2\) or \(c - a = 4\) . Thus, \(|a - c| = 4\) .

Statement (2) by itself is insufficient. Consider \(a = 0\) , \(b = 2\) , \(c = 4\) ( \(|a - c| = 4\) ) and \(a = c = 0\) , \(b = 2\) ( \(|a - c| = 0\) ).
The correct answer is A.


Does someone have an easier solution for this one? I have a hard time doing through this solution.


Good work!

I approached it graphically, using the meaning of absolute value, which is the distance on the number line between two points (numbers).
The main difficulty seems to be not to miss that a and c can be equal (in (2)).
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Re: M16 Q 37 [#permalink] New post 06 Jul 2014, 16:04
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In the GMATClub Tests, this question is written incorrectly: the inequality sign in 2) is reversed. 'c−a<c−b', whereas the answer indicates 'c−a>c−b'.
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Re: M16 Q 37 [#permalink] New post 06 Jul 2014, 16:12
Expert's post
Re: M16 Q 37   [#permalink] 06 Jul 2014, 16:12
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M16 Q 37

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