Data sufficiency with modulus

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Data sufficiency with modulus

by uniyal01 » Fri Jan 29, 2016 10:01 am
a and b are non-zero integers.
If |a|+|b|= 8, what is the value of a/b?

1) |a/b|=3

2) |a+b|=8

I think the answer may be C- both sufficient together. Please help!

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by MartyMurray » Fri Jan 29, 2016 4:13 pm
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.


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


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.
Marty Murray
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by Brent@GMATPrepNow » Fri Jan 29, 2016 9:02 pm
ASIDE: Some people will incorrectly choose E as their answer if they don't pay attention to the target question here.
If we make the mistake of trying to determine the individual values of a and b, then we can see that the combined statements yield two possibilities:
case a: a = 6 and b = 2
case b: a = -6 and b = -2

HOWEVER, the target question doesn't ask for the individual values of a and b. It asks is to determine the value of a/b, in which case BOTH possible cases yield the same answer: a/b = 3

Brent Hanneson - Creator of