Inequality

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Dec 26, 2011 1:09 am

What is the value of |xâˆ’2|?

(1) |xâˆ’4|=2

(2) |2âˆ’x|=4

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 26, 2011 1:09 am

shekhar.kataria: Master | Next Rank: 500 Posts; Posts: 268; Joined: Mon Mar 15, 2010 12:10 am; Thanked: 13 times

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 |xâˆ’2|?

(1) |xâˆ’4|=2

(2) |2âˆ’x|=4

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

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 |xâˆ’2|?

(1) |xâˆ’4|=2

(2) |2âˆ’x|=4

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Dec 27, 2011 9:47 pm

OA is B

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santhoshsram: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Wed Oct 26, 2011 2:30 pm; Thanked: 7 times

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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harsh8686: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Thu Aug 30, 2018 11:13 pm

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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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Thu Nov 29, 2018 7:43 am

karthikpandian19 wrote:What is the value of |xâˆ’2|?

(1) |xâˆ’4|=2

(2) |2âˆ’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.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

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