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# M16 Q 37

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Manager
Joined: 13 May 2010
Posts: 122

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26 Jul 2012, 05:49
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 $$a = c = 0$$ , $$b = 2$$ ( $$|a - c| = 0$$ ).

Does someone have an easier solution for this one? I have a hard time doing through this solution.
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)

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26 Jul 2012, 09:45
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 $$a = c = 0$$ , $$b = 2$$ ( $$|a - c| = 0$$ ).

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)).
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Joined: 12 Dec 2013
Posts: 25

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06 Jul 2014, 17:04
1
KUDOS
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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Please +1 KUDOS if my post helps. Thank you.

Math Expert
Joined: 02 Sep 2009
Posts: 39672

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06 Jul 2014, 17:12
bekerman wrote:
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'.

Thank you very much! Already edited.
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Re: M16 Q 37   [#permalink] 06 Jul 2014, 17:12
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# M16 Q 37

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