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
What is the value of |x| ?
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- neelgandham
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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
(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
Anil Gandham
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Simply because you can fit infinite values in the statement 1. Remember, we need to find one and only 1 value from the statement.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
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 .
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.
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.