please explain: absolute value

[ejager]

What is the distance between "a" and "b" on the number line?
1. absolute value of a - absolute value of b = 6
2. ab>0

I understand why each statement alone is not sufficient, but do not understand why together they are sufficient. Do not understand the MGMAT solution explanation.

Thanks

[GMATGuruNY]

What is the distance between "a" and "b" on the number line?
1. |a| - |b| = 6
2. ab > 0

Distance between a and b = |a-b|.

Statement 1: |a| = |b| + 6.
Let b=1, implying that |a| = 7.
If a=7, then |a-b| = |7-1| = 6.
If a=-7, then |a-b| = |-7-1| = 8.
Since |a-b| can be different values, INSUFFICIENT.

Statement 2: ab > 0
If a=1 and b=1, then |a-b| = |1-1| = 0.
If a=2 and b=1, then |a-b| = |2-1| = 1.
Since |a-b| can be different values, INSUFFICIENT.

Statements combined:
Both statements are satisfied by a=7 and b=1, in which case |a-b| = |7-1| = 6.
Both statements are satisfied by a=-10 and b=-4, in which case |a-b| = |-10 - (-4)| = 6.
Both statements are satisfied by a=6.5 and b=0.5, in which case |a-b| = |6.5 - 0.5| = 6.
In every case, |a-b| = 6.
SUFFICIENT.

The correct answer is C.

[GMATGuruNY]

What is the distance between "a" and "b" on the number line?
1. |a| = |b| + 6
2. ab > 0

Here is why the two statements combined are SUFFICIENT.

ab > 0 implies that a and b have the SAME SIGN and thus lie to THE SAME SIDE OF 0.

|b| = |b-0) = the distance between b and 0.
|a| = |a-0| = the distance between a and 0.
Thus:
|a| = |b| + 6 implies that the distance between a and 0 is 6 more than the distance between b and 0.

As a result, the number line must look like one of the following options:
.,.....................................0...........b<---6--->a...........
......a<---6--->b...........0.............................................

In each case, a lies 6 more places from 0 than does b.
In case case, the distance between a and b is equal to 6.

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Hi ejager,

When dealing with 'absolute value' questions, there are several different ways that you can deal with the 'math' involved. In this particular prompt, TESTing VALUES will work well, but you have to pay careful attention to the question that is ASKED...

We're asked for the distance between A and B on a number line.

Fact 1: |A| - |B| = 6

Since we're dealing with absolute values, we should keep negative values in mind (beyond anything else that we might choose to TEST).

IF....
A = 6
B = 0
The distance between A and B is 6

IF....
A = 7
B = -1
The distance between A and B is 8
Fact 1 is INSUFFICIENT

Fact 2: AB > 0

This Fact tells us that the two variables have the SAME SIGN (so they're either both positive or both negative). We don't know the actual values of the variables though...

IF....
A = 1
B = 2
The answer to the question is 1

IF...
A = -2
B = -4
The answer to the question is 2
Fact 2 is INSUFFICIENT

Combined, we know....
|A| - |B| = 6
A and B have the SAME SIGN

You can quickly list out a variety of options for A and B....
A = 7, B = 1
A = 8, B = 2
A = 9.5, B = 3.5

A = -7, B = -1
A = -10, B = -4
Etc.
In ALL cases, the distance between A and B is 6
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich