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# On the number line, the distance between point A and C is 5

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On the number line, the distance between point A and C is 5 [#permalink]  27 Jun 2008, 14:45
On the number line, the distance between point A and C is 5 and the distance between point B and point C is 20. Does point C lie between point A and point B?

a. The distance between point A and point B is 25
b.Point A lies to the left of point B.

My choice is C. I will wait for you to concur. Thanks
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Re: gmatprep - number line [#permalink]  27 Jun 2008, 14:57
it can be in the order of CAB also, if you apply only 2nd condition...you need both the statements to prove point c lies between A and B.

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Re: gmatprep - number line [#permalink]  27 Jun 2008, 15:56
On the number line, the distance between point A and C is 5 and the distance between point B and point C is 20. Does point C lie between point A and point B?

a. The distance between point A and point B is 25
b.Point A lies to the left of point B.

My choice is C. I will wait for you to concur. Thanks

Statement 2 is clearly insufficient on its own.

Statement 1: Draw the points A and B on the number line. It won't matter which is on the left; you can relabel them however you want. According to Statement 1, A and B are 25 apart. Now, C must be 5 away from A. You have two choices: put it on the left of A, or on the right of A. If you put C between A and B, the distance BC will be 20. If you don't, the distance will be 30. The only way for the distance AB to be 25, the distance AC to be 5, and the distance BC to be 20 is if C is between A and B. The information is sufficient.

The question is equivalent to the following:

If |a-c| = 5, and |b-c| = 20, does c lie between a and b on the number line?

1) |a-b| = 25
2) a < b

Again, the answer is A to the above.
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Re: gmatprep - number line [#permalink]  27 Jun 2008, 17:20
draw C=0,
AC = 5 -> two options: A1 = -5 and A2 = 5
BC = 20 -> two options B1 = -20 and B2 = 20

1) AB = 25 -> A=A1, B = B2 (C is between A1 and B2) or A=A2, B = B1 (C is between A2 and B1) -> sufficient
2) A1, B1 -> C is not between A and B; A1, B2 -> C is between A and B -> insufficient

Re: gmatprep - number line   [#permalink] 27 Jun 2008, 17:20
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