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Inequality

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Source: — Data Sufficiency |
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by shekhar.kataria » Mon Dec 26, 2011 1:36 am
IMO B

St 1 :- NOT sufficent

x-4 =2 ---> x = 6 , |x-2|= 4
-x+4=2 ----> x=2 , |x-2|= 0


St: 2 SUFFICIENT

2-x=4 ----> x=-2 , |x-2| = 4
-2+x=4 -----> x=6 , |x-2| = 4
karthikpandian19 wrote:What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4
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by pemdas » Mon Dec 26, 2011 2:54 am
st(1) x-4=2 and x-4=-2

x=6 and x=2 Not Sufficient as |6-2|=4 and |2-2|=0
st(2) 2-x=4 and 2-x=-4

x=-2 and x=6 Sufficient as |-2-2|=4 and |6-2|=4

b
karthikpandian19 wrote:What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4
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by karthikpandian19 » Tue Dec 27, 2011 9:47 pm
OA is B
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by santhoshsram » Wed Dec 28, 2011 5:00 pm
Another way without having to actually solve,

(1) |x-4| = 2 => distance betweek x and 4 is two => can is 2 or 6

(2) |2-x| = 4 => distance between 2 and x is 4, but distance between 2 and x is same as distance between x and 2 |x-2|. (2) is sufficient
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by harsh8686 » Thu Nov 29, 2018 7:28 am
best way to solve modulus question is by making graphs. This one is pretty straight forward question, but for hard questions, learn graphing technique from this guy https://www.youtube.com/user/misterwootube . His videos are awesome.
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by fskilnik@GMATH » Thu Nov 29, 2018 7:43 am
karthikpandian19 wrote:What is the value of |x−2|?

(1) |x−4|=2

(2) |2−x|=4
$$? = \left| {x - 2} \right|$$

$$\left( 1 \right)\,\,\,{\rm{dist}}\left( {x,4} \right) = \left| {x - 4} \right| = 2\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
\,x = 6\,\,\,\, \Rightarrow \,\,\,\,? = 4 \hfill \cr
\,x = 2\,\,\,\, \Rightarrow \,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.$$

$$\left( 2 \right)\,\,\,4 = \,\,\left| {2 - x} \right|\,\,{\rm{ = }}\,\,\left| {x - 2} \right|\,\,\,{\rm{ = }}\,\,\,{\rm{?}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$


This solution follows the notations and rationale taught in the GMATH method.

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by [email protected] » Thu Nov 29, 2018 2:24 pm
Hi All,

We're asked for the value of |X - 2|. This question comes down to a specific math concept (Absolute Value), some basic arithmetic and thoroughness on your part - meaning that you have to make sure that you answer the question that is ASKED.

1) |X - 4| = 2

Since we're dealing with an Absolute Value (and Absolute Value symbols turn negative 'results' into positive results), we have to consider TWO possibilities in this equation:
|X - 4| = |+2|
|X - 4| = |-2|

In the first equation, X = 6 and the answer to the question is |6 - 2| = |4| = 4
In the second equation, X = 2 and the answer to the question is |2 - 2| = |0| = 0
Fact 1 is INSUFFICIENT

2) |2 - X| = 4

Again, since we're dealing with an Absolute Value, we have to consider TWO possibilities in this equation:
|2 - X| = |+4|
|2 - X| = |-4|

In the first equation, X = -2 and the answer to the question is |-2 - 2| = |-4| = 4
In the second equation, X = 6 and the answer to the question is |6 - 2| = |4| = 4
The answer is ALWAYS 4.
Fact 2 is SUFFICIENT

Final Answer: B

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