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What is the distance between a and b on the number line?

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Re: What is the distance between a and b on the number line? [#permalink] New post 01 Apr 2012, 00:51
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What is the distance between a and b on the number line?

We are asked to find the value of |a-b|.

(1) |a| – |b| = 6 --> if a=7 and b=1 then |a-b|=6 but if a=7 and b=-1 then |a-b|=8. Not sufficient.

(2) ab > 0 --> just says that a and b have the same sign. Not sufficient:

(1)+(2) If both a and b are positive then |a|-|b|=a-b=6 and |a-b|=6. If both a and b are negative then |a|-|b|=-a-(-b)=b-a=6, and |a-b|=6. So, in any case |a-b|=6. Sufficient.

Answer: C.
[Reveal] Spoiler: OA

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What is the distance between a and b on the number line? [#permalink] New post 27 Mar 2013, 01:10
What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0
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Re: What is the distance between a and b on the number line? [#permalink] New post 27 Mar 2013, 01:45
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mun23 wrote:
What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0


From F.S 1, let's pick values keeping |a| – |b| = 6. For a=-12; b=6, we have |a-b| = 18, however, for a=12;b=6 we have |a-b| = 6. Insufficient.

From F.S 2, we just know that a and b are of the same sign. Insufficient.

With both taken together, either a,b>0 in which case, |a| – |b| = 6 --> a– b = 6 .

or

a,b<0 in which case, b-a = 6. Thus, the distance between the points a and b, |a-b| is the same in either case. Sufficient.

C.
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Re: What is the distance between a and b on the number line? [#permalink] New post 27 Mar 2013, 03:25
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Re: What is the distance between a and b on the number line? [#permalink] New post 26 Jun 2013, 13:42
What is the distance between a and b on the number line?

(1) |a| – |b| = 6
(2) ab > 0

(1) |a| – |b| = 6

I made a stupid mistake here. I assumed that because we are dealing with absolute values here, we're dealing with just a positive number - a positive number (for example 12-6 = 6, 8-2 = 6, etc). Of course, we're looking for the distance of a and b, not the difference between |a| and |b|. For example, the difference between |-12| and |6| is (12-6=6) but on the number line they are actually 18 places apart. Therefore, we cannot determine what the distance between a and b is on the number line with #1.
INSUFFICIENT

(2) ab > 0

This tells us nothing about the placement of a and b on the number line, only that a and b are both positive or negative.

1+2) If a and b are both positive or both negative and that |a| – |b| = 6 then we can conclude the distance is always going to be 6.
SUFFICIENT

(C)
Re: What is the distance between a and b on the number line?   [#permalink] 26 Jun 2013, 13:42
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