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GMAT Prep Question

by giatch » Fri Dec 26, 2008 10:25 pm
Is |K| = 2?

1) k^2 = 4

2) k = |-2|

I answered A, but the OA is D.

I'm a bit confused about the property of inequality rules here...

I understand k=+/- 2 for statement 1..

But what exactly do you do with the second statement? What do the rules say for that?
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by cramya » Fri Dec 26, 2008 10:29 pm
|x| is always positive in both cases below.

Case 1: If x is positive by definition |x| = x
Case 2: If x is negative by definition |x| = -x

Stmt II

k = |-2|

Applying case 2:

|-2| = - (-2) = 2 (since x is -2 , -(x) = - (-2) = 2)

Since k =2 |k| =2

Stmt I

I am sure u got it.

Here u will get k=2 or -2 and in both cases |k| = 2


Hope this helps! Hence D)
Last edited by cramya on Sat Dec 27, 2008 9:56 am, edited 2 times in total.
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Still confused?

by giatch » Fri Dec 26, 2008 10:38 pm
thanks for the help..but i'm still not completely understanding this statement.


|-2| = - (-2) = 2 (since x is -2 , -(x) =- (-2) = 2)

it says that k equals the absolute value of -2, which equals 2..now, why are you putting -(-2) = 2?

i understand that absolute values usually refer to distance...what exactly does the absolute value of -2 referring to here?
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by cramya » Fri Dec 26, 2008 10:43 pm
|-2| = - (-2) = 2 (since x is -2 , -(x) =- (-2) = 2)

it says that k equals the absolute value of -2, which equals 2..now, why are you putting -(-2) = 2?

I am literally applying the definition from case 2. Here x = -2 is negative by defnition |negative number| = - (negative number) = - (-2) = 2 -> still positive.

k = |-2| means k is 2 units away from 0.
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