a and b are non zero integers. if |a| +|b| = 8, what is the value of

|a| + |b| = 8

stmt-1: |a/b| = 3 ---->> |-6/2| = 3 or |6/2| = 3.
|a| +|b| = 8 --->> |-6| + |2| = 8 or |6| + |2| = 8

hence a/b could be 3 or -3. insuff.

stmt-2: |a + b| = 8 ----->> |6 + 2| = 8 OR |4 + 4| = 8
|a| +|b| = 8 -->> |6| +|2| = 8 or |4| +|4| = 8

hence a/b could be 3 or 1. insuff.

stmt-1 + stmt-2:
a and b has to be positive for |a + b| = 8. a/b will be 3 when a=6 and b=2. a/b=3. suff.

Answer is C.
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a and b has to be positive for |a + b| = 8

as per s2, a & b can be negative & still have |a+b| = 8
so, it can be |(-2)+(-6)|=8 or |2+6|=8
hence we dont have a def value of a/b

Where am I doing it wrong?

definitly stmt-2 is insuff in itself.

its more appropriate to say that a and b should have same sign. with a=-6 & b=-2 OR a=6 & b=2. this way a/b=3
as |a/b| = 3 we cannot exchange values of a and b. otherwise |a/b| will be 1/3. so we can take values which are inline with followings (considering stmt-1+2):

|a| +|b| = 8
|a/b| = 3
|a + b| = 8

only a=-6 & b=-2 OR a=6 & b=2 can be taken and we get a/b=3. definite value. sufficient. C.
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|a| +|b| = 8

There are multiple possibilities
|-6| +|2| = 8

or, |-6| +|-2| = 8
or, |6| +|2| = 8

(1) |a/b| = 3

a/b can be +3 or -3

(2) |a + b| = 8
multiple possibilities

|-6 - 2| = 8
|-5 -3| = 8 and so on

Combining both statements
|a + b| = 8
|a| +|b| = 8

that means:-
|a + b|= |a| +|b|
both a and b have same sign, hence a/b will be +ve or 3

C is the answer
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Your fundamental mistake is that you aren't going all the way back to answer the question in the stem. Sure, there are two possibilities: a is -6 and b is -2, or a is 6 and b is 2. But both of those possibilities yield the same answer to the question, which means that the question only has one answer. That answer is -6/-2 = 6/2 = 3.

This is why it's important to note whether a problem is a 'combo' problem or not. A combo DS problem asks you to solve, not for one variable, but for a function of a variable ('what is the absolute value of x?') or a combination of two variables ('what is a/b?') The whole reason they put combo problems on the test, is because a lot of the time, you can solve a combo problem without actually knowing the values of the variables for certain. That means that even if you get multiple different values for a and b, or if you can't find their values at all, you might still have just one answer to the question.

Here's a much simpler example, just to illustrate the point:

What is x + y?

(1) x = 5
(2) 3x + 3y = 27

1 is insufficient. 2 doesn't let you solve for x and y - for instance, you could have x=0 and y=9, or x=3 and y=6 - but it does let you answer the question in exactly one way (the answer to 'what is x+y' is always 9.) So, the answer would be B.
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a and b are non zero but we don't know whether they are positive or negative. |a| + |b| = 8

What is \(\frac{a}{b}\)?

(1) |a/b| = 3

If \(|\frac{a}{b}| = 3\), \(\frac{a}{b}\) could be 3 or -3. Not sufficient alone.

(2) |a + b| = 8
Since |a+b| = |a| + |b| and a and b are non-zero, a and b have the same sign. They are either both positive or both negative. So \(\frac{a}{b}\) must be positive. We have no concrete value for \(\frac{a}{b}\) so not sufficient.

Using both statements, \(\frac{a}{b} = 3\). Sufficient.

Answer (C)

Check out these posts for absolute value properties:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html/2014/02 ... -the-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html/2014/02 ... t-part-ii/
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Here the question is represented in red color lines and asking us to find the point (i.e . unique solution) so that we can compute a/b.
Only if both statements are correct - when green line intersects the red lines ... i.e. when the slope is positive and from (2) when the point lies in first quadrant.
So the point lies in first quadrant and which is a unique point.
so answer is C

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