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manhattan gmat absolutes

by resilient » Mon Mar 24, 2008 1:21 pm
What is X?

1. Absolute value x < 2
2. Absolute value x = 3x-2

statement 1 insuf
statement 2 yields x=1 or 1/2 . how can it be sufficient. I understand that absolutes have pos and neg outcomes yet statement tell otherwise!



qa obviously B
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by rey.fernandez » Mon Mar 24, 2008 1:54 pm
What sets this problem apart from the more basic absolute value equations is that the absolute value of x equals an expression in terms of x.

This is significant because after you solve the equation, you must check your solutions to ensure that the expression on the other side of the absolute value is in fact a positive value.

In this case:

|x| = 3x - 2

x = 3x - 2
2 = 2x
x = 1

This is a solution -- substitute into the original equation to see that. Now, the "other half" of the process is:

x = -3x + 2
4x = 2
x = 1/2

Now, if you plug this into the right-hand side of the original equation, you get a negative number. This is not a solution, therefore, because |x| must yield a positive number. So (2) is in fact sufficient.

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by maihuna » Wed Apr 15, 2009 10:25 am
Hi Ian,
I know trick here is to put back and check your answer, will the distance on number line approach will allow me with this trap? how?
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by vittalgmat » Wed Apr 15, 2009 11:19 am
I will IM Ian to help us solve this problem using the distance method.

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by Ian Stewart » Wed Apr 15, 2009 1:00 pm
vittalgmat wrote:I will IM Ian to help us solve this problem using the distance method.

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It's not straightforward to interpret the right side of the equation:

|x| = 3x - 2

as a distance. However, you might notice that if x were negative, the right side of the equation would be negative, and that's certainly impossible, since the left side of the equation can't be negative. So x must be positive or zero, and |x| = x. Since it's clear we could solve the equation x = 3x - 2 for x, the statement is sufficient.
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by vittalgmat » Wed Apr 15, 2009 1:11 pm
Thanks Ian
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