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Absolute Values

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ekattur
 Post subject: Absolute Values
 Post Posted: Sat Nov 15, 2008 12:39 pm 
When there is an absolute sign, when do we test both the positve and negetive scenarios. For example in a previous string :

One of the Manhattan GMAT practice test questions (Question name - "Work Your Abs") had this equation

3|x^2 – 4| = y – 2

The answer explanation for this equation came to the following conclusion - "absolute value expression |x^2 – 4| must be greater than or equal to 0."

Now one scenario is

|x^2 – 4| > 0

But is the other scenario not:

|x^2 – 4| <0

Thanks for your help!
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esledge
 Post subject:
 Post Posted: Sun Dec 07, 2008 5:26 pm 
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ManhattanGMAT Staff


Posts: 901
Location: St. Louis, MO
In the future, please post the entire question text, even if you only have a question about a part of it. Here it is, for reference:

What is the value of y?

(1) 3|x2 – 4| = y – 2

(2) |3 – y| = 11

Quote:
One of the Manhattan GMAT practice test questions (Question name - "Work Your Abs") had this equation

3|x^2 – 4| = y – 2

The answer explanation for this equation came to the following conclusion - "absolute value expression |x^2 – 4| must be greater than or equal to 0."

Now one scenario is

|x^2 – 4| > 0

But is the other scenario not:

|x^2 – 4| <0

Absolute value does indicate two scenarios (pos & neg) for what is inside the absolute value bars, but only one scenario (pos) for the entire absolute value.

Therefore, |x^2 – 4| < 0 (from your question above) is NOT possible, though (x^2 – 4) < 0 IS possible.

Finally, think about the purpose of this question. The question asks for the value of y, not that of x. So for statement (1) we aren't really concerned about the left side of the equation; setting up pos and neg scenarios for (x^2 - 4) wouldn't help us solve for y. We only use the absolute value expression to make a sign inference, narrowing down the possible values for the y found on the right side of the equation.

_________________
Emily Sledge
Instructor
ManhattanGMAT
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