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]

01 Apr 2012, 01:51

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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]

27 Mar 2013, 02:10

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]

27 Mar 2013, 02:45

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]

27 Mar 2013, 04:25

mun23 wrote:

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

(1) |a| – |b| = 6
(2) ab > 0

Merging similar topics.
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Re: What is the distance between a and b on the number line? [#permalink] 27 Mar 2013, 04:25

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