Statement 1: |a/b|=3
This tells us that a/b = 3 or -3
So a = 3b or a = -3b
You can quickly see without having to do much math really that given |a| + |b| = 8 and a = 3b or a = -3b, a = 6 or -6, and b = 2 or -2. Any combination of 6 or -6 and 2 or -2 would work.
So a/b could be 3 or -3.
Insufficient.
Statement 2: |a + b|= 8
Combining this with the information given in the question we have the following.
From the question, the absolute values of a and b add up to 8. Absolute value is the distance from 0. So the total distance from 0 of the two numbers = 8.
From Statement 2, the values of a and b combined add up to 8 or -8.
So Statement 2 adds to the information in the question, because Statement 2 tells us that not only does the total distance from 0 add up to 8 but also both numbers are on the same side of 0.
Either they are both negative and work together create a total distance from 0 in the negative direction, or they are both positive and work together to create a total distance from 0 of 8 in a positive direction.
Using this information we can tell that a and b must have the same sign. However it does not tell us what their values are. Any of the following would fit.
a = 1 and b = 7 a/b = 1/7
a = -2 and b = -6 a/b = 2/3
a = 5 and b = 3 a/b = 5/3
Insufficient.
Combining the statements we can tell from Statement 1 that a/b = 3 or -3, and from Statement 2 we know that a and b must have the same signs.
If a and b have the same signs, a/b must be positive. So a/b = 3, and combined the statements are sufficient.
The correct answer is C.
