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Help on DS Absolute Value Problem

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by cghan » Fri Jun 06, 2014 3:33 pm
What is the value of |x|?
1) |x^2 + 16| -5 = 27
2) x^2 = 8x - 16

My only question here is regarding statement 1. The solution to this problem does not put forth two ways to write the equation as you're supposed to do with absolute value equations.

The first version would be x^2 + 16 -5 = 27. Would the second version not be x^2 +16 -5 = -27 ?

The solution to the problem does not even set up the second equation for the case of -27.
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Source: — Data Sufficiency |

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by [email protected] » Fri Jun 06, 2014 4:10 pm
Hi cghan,

This DS question "overlaps" the Number Property rules, which means that there is NO second equation. Here's why:

Fact 1 gives us |X^2 + 16| - 5 = 27

Simplifying, we get...

|X^2 + 16| = 32

Normally, we'd be looking for two "types" of answers: usually 1 positive and 1 negative.

Here though, since X^2 CANNOT be negative, there's no way for X^2 + 16 to give us a negative result. We have ONLY a positive result to work with.

By extension, X can be either +4 or -4, but since the question asks for |X|, we end up with 4 either way. Fact 1 is SUFFICIENT.

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by theCodeToGMAT » Fri Jun 06, 2014 10:26 pm
To find: |X|

Statement 1:
|x^2 + 16| -5 = 27
|x^2 + 16| = 32
x^2 cannot be negative..
x^2 = 16 ==> |X| = 6
SUFFICIENT


Statement 2:
x^2 = 8x - 16
x^2 - 8x + 16 = 0
x = 4
SUFFICIENT

[spoiler]{D}?[/spoiler]
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by cghan » Sat Jun 07, 2014 4:47 am
Super, thanks so much for the explanation. I suppose I relied more on my 'automatic' processes (i.e. automatically making two versions of the equation rather than looking at the problem and seeing if it made sense.
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