Quanatitative Comparison Question - Please Help

[tdave1999]

The answer to this problem is B, but I'm not sure why. Please help.

2. The question below is a quantitative
comparison question.

|4x +24| = 96
|4x| = 120

Column A = X

Column B = 18

A.Quantity A is greater.
B.Quantity B is greater.
C.The two quantities are equal.
D.The relationship cannot be
determined from the information
given.

[n00bpron00bpron00b]

|4x + 24| = 96

Solving the above equation gives us two cases -

a) 4x + 24 = +96
4x = 72
x = 18

b) 4x + 24 = -96
4x = -120
x = -30

Now,
|4x| = 120 - given

Substitute the value of "x" in the above equation
x = +18 or -30
if x = +18
|4(+18)| = 120
|72|=120
72 = 120 - invalid condition 72 is not equal to 120

if x = -30
|4(-30|=120
|-120|=120
120=120 - True !

So the value of x has to be -30

column A = x = -30
column B = 18

"B" greater

[tommywallach]

Great explanation from Noob, as usual. Remember, absolute value equations usually have two solutions, but there are ways around it (for example, in this case, we have TWO equations that can only be true simultaneously with one value), so always make sure you go to the trouble of solving things out.

-t