## Between A and B

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### Between A and B

by adi » Fri Mar 14, 2008 7:48 pm
If a and b are nonzero numbers on the number line, is 0 between a and b?

(1) The distance between 0 and a is greater than the distance between 0 and b.
(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum of a + b.

Answer should be "Statement (2) alone is sufficient.

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by simplyjat » Fri Mar 14, 2008 10:28 pm
Don't say "Answer should be", its confusing. Its better to say "my answer" and "official answer"...

Coming back to the question, when dealing with number line and distances, always think absolute values.
1) |a| > |b|
2) |a| + |b| > |a + b|

Here the second statement is true only when a and b have different sign, because with same signs |a| + |b| = |a + b|.
So we have two numbers with different signs 0 will always be in between...
simplyjat

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by kaf » Mon Apr 13, 2009 3:06 pm
Can someone please elaborate on this solution

thanks

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by vittalgmat » Mon Apr 13, 2009 3:37 pm
kaf wrote:Can someone please elaborate on this solution

thanks
Simplyjat has done excellent job in explaining..
I will try add my 2c.

Try plugging numbers to the absolute equation mentioned above.
But whenever u plug in numbers assume they are numbers on a numberline.
And whenever u see a absolute mentioned, immediately think of as a distance of that number from the origin.

Actually, u can see Stewart/Ian's comments on a previous Absolute!!! problem.

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by gmat740 » Tue Apr 14, 2009 8:28 pm
It is a good idea to draw a number line:

two cases are possible:

a..........b.........0

or a.........0........b

(I) this one talks about a.........0........b
but what about a..........b.........0

distance between 0 and a> distance between 0 and b

so Insuff

(II)clearly speaks of this:
a.........0........b

the other case will not be satisfied

So (II) Suff

Hence B

Hope this helps

Karan

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by bhumika.k.shah » Sun Apr 04, 2010 12:30 pm
karan,
I did the same thing. though can u explain it with #s?

I'm guessing that would make it quicker and simpler.
gmat740 wrote:It is a good idea to draw a number line:

two cases are possible:

a..........b.........0

or a.........0........b

(I) this one talks about a.........0........b
but what about a..........b.........0

distance between 0 and a> distance between 0 and b

so Insuff

(II)clearly speaks of this:
a.........0........b

the other case will not be satisfied

So (II) Suff

Hence B

Hope this helps

Karan

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by bhumika.k.shah » Sun Apr 04, 2010 12:31 pm
Also what would be the difficulty level of this Q? and how much time should one spend on this Q?
Can someone break down the second statement, please?

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by blee0810 » Sat Dec 04, 2010 5:39 pm
https://www.beatthegmat.com/a-and-b-on-t ... 37331.html

This thread has a good explanation for the answer

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by diebeatsthegmat » Mon Dec 06, 2010 11:08 am
adi wrote:If a and b are nonzero numbers on the number line, is 0 between a and b?

(1) The distance between 0 and a is greater than the distance between 0 and b.
(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum of a + b.

Answer should be "Statement (2) alone is sufficient.
ohh my answer is B too,
what is the OA? " answer should be statement 2 alone is sufficient" is your answer or OA?

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by GMATGuruNY » Mon Dec 06, 2010 12:30 pm
adi wrote:If a and b are nonzero numbers on the number line, is 0 between a and b?

(1) The distance between 0 and a is greater than the distance between 0 and b.
(2) The sum of the distances between 0 and a and between 0 and b is greater than the distance between 0 and the sum of a + b.

Answer should be "Statement (2) alone is sufficient.
Absolute value means distance from 0.

Statement 1: |a| > |b|
Plug in a=3, b=2.
This works, because |3| > |2|.
Is 0 between 3 and 2? No.

Plug in a= -3, b=2.
This works, because |-3| > |2|.
Is 0 between -3 and 2? Yes.

Since the answer can be both No and Yes, insufficient.

Statement 2: |a| + |b| > |a+b|
Plug in a=3, b=2.
|3| + |2| > |3+2|. Doesn't work, because |3| + |2| = |3+2|.
This shows us that a and b cannot both be positive.

Plug in a = -3, b = -2.
|-3| + |-2| > |-3 + (-2)|. Doesn't work, because |-3| + |-2| = |-3 + (-2)|.
This shows us that a and b cannot both be negative.

Since a and b cannot both be positive -- nor can they both be negative -- 0 must be between them. Sufficient.

The correct answer is B.

For example:
Plug in a=-3, b=2.
This works, because |-3| + |2| > |-3+2|.
Is 0 between -3 and 2? Yes.

Plug in a=3, b=-2.
This works, becuase |3| + |-2| > |3+(-2)|.
Is 0 between 3 and -2? Yes.

Since the answer is consistently Yes, sufficient.
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