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What is the value of |x| ?

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What is the value of |x| ?

by siddhans » Mon Oct 24, 2011 1:25 am
How to solve this algebrically?


What is the value of |x| ?
(1) x = -|x|
(2) x^2 = 4


OA B


Whats wrong with this method ?


) x = -|x|

this x = - (-x) or x = - (+x)

since |x| can be +ve pr -ve

thus

x = x or x = -x


x - x = 0 or x + x = 0

0=0 or 2x = 0

x =0....



st 2 says x = +/- 2

but |x| is always +ve so x = 2

thus it is D


but OA is B
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Source: — Data Sufficiency |
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by neelgandham » Mon Oct 24, 2011 2:32 am
What is the value of |x| ?

(1) x = -|x|

i.e. (x <= 0), Why ? see below !

Let x >0 and x=8 then Is x = -|x| ? 8 = -8 ? No!
Let x =0 then x = -|x| ? => 0=-0 => 0 =-1*0? => 0=0? Yes !
Let x <0 and x=-8 then Is x = -|x| ? -8 = -|-8| => -8 =-8 ? Yes !

Hence X<=0 Insufficient!

(2) x^2 = 4

x = + or -2 => |x| = 2 Sufficient

Option B
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by saketk » Mon Oct 24, 2011 12:37 pm
siddhans wrote:How to solve this algebrically?


What is the value of |x| ?
(1) x = -|x|
(2) x^2 = 4


OA B


Whats wrong with this method ?


) x = -|x|

this x = - (-x) or x = - (+x)

since |x| can be +ve pr -ve

thus

x = x or x = -x


x - x = 0 or x + x = 0

0=0 or 2x = 0

x =0....



st 2 says x = +/- 2

but |x| is always +ve so x = 2

thus it is D


but OA is B
Simply because you can fit infinite values in the statement 1. Remember, we need to find one and only 1 value from the statement.

For example

Let, X = -10
|-10| = 10 but -|-10| = -10

this fits in statement 1. Here, we can replace -10 by -1,-2,-3, or any number

Therefore, statement 1 is insufficient .
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by factor26 » Mon Oct 24, 2011 2:12 pm
Look at what the question is asking. They are asking for the value of x. Thus we need an actual number for x to answer the question.

Statement 1 says the negative absolute value of x is equal to x... This still doesn't give us a value for x. To reinforce, let's plug in values of x in the absolute value brackets for x.... Say the number in the absolute value of x bracket is -3 ... Then the absolute value of x is 3.... Multiply that by -1 we get x = -3
Plug in a second value for the statement ... Say the x value in the absolute value bracket equals 4 multiply that by -1 we get x =-4 .... We can not find the exact value for x so it's not sufficient. Eliminate answer choice a.

Statement 2 says x^2 equals 4 .... So x can be either + or - 2 ... Since we are looking for the absolute value for x .... The absolute value of 2 or -2 is still 2. We have only one value possible for x. Statement 2 by itself is sufficient. The answer is b.
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