Is |x - 10| |x - 30|? (1) x 10 (2) x 25

Question

Is |x - 10| > |x - 30|?

(1) x > 10
(2) x > 25

IanStewart · Accepted Answer

|a - b| always means "the distance between a and b on the number line". So the inequality

|x - 10| > |x - 30|

means, in words "the distance between x and 10 is greater than the distance between x and 30", or in other words, "x is closer to 30 than it is to 10". For that to be true, x needs to be greater than the midpoint of 10 and 30, so x needs to be greater than 20. So that's the question: Is x > 20? Statement 2 establishes that conclusively, while Statement 1 does not, so B is the answer.

KaranB1 · Answer

For |x-10| to be greater than |x-30|, value of X has to be greater than the average of 10 and 30 i.e. 20.

Option B is sufficient.

aj3001 · Answer

Can someone please elaborate about the part wherein we ascertain x>20..?

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keshavmishra · Answer

|x - 10| > |x - 30| ???

essentially question means distance b/w a point x and 10 is greater than distance b/w x and 30. => x is closer to 30 than it is to 10. For that to be true, x needs to be greater than the midpoint of 10 and 30, so x needs to be greater than 20. 
So question can be inferred as is x > 20? 
statement 1 - x can be less that 20 & greater than 20. Not sufficient (cancel DA)
Statement 2 states x>25. in all cases sufficient

Answer B

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embaiii · Answer

Is |x-10| > |x-30|

Here's mathematical try
Square both side (since both sides are positive)
(x-10)^2 > (x-30)^2
(x^2+100-20x)>(x^2+900-60x)
(60x-20x)>(900-100)
40x>800
x>20

Hence, only St. 2 satisfy i.e x>25

a191291r · Answer

Draw a number line and mark the points   0  ,   10   and   30   on the number line. 
 Pick any arbitrary point on the number line and mark it as   x  . 
 The distance of this point   x   from point   10   would be   |x - 10|   and distance of this point   x   from point   30   would be   |x - 30|  .  
Check Statement 1:
 x>10 
 
 The arbitrary point   x   can be anywhere on right side of the   10   
 If point   x   lies between   10   and the midpoint of   10   and   30   (i.e.,   20  ), we can confidently say |x-10| < |10-30| 
 If point   x   lies anywhere on the right side of this midpoint (i.e,   20  ), we can confidently say |x-10| > |10-30|  
Therefore, insufficient.

Check Statement 2:
 x>25 
 
 The arbitrary point   x   lies anywhere on right side of the   25   
 Earlier, we have deduced that for all points on right side of   20  , |x-10| > |x-30|  
Therefore, sufficient.

AnuK2222 · Answer

Great explaination, I tend to struggle whenever ineuqalities and modulus are together in any question. this is neat approach

a191291r · Answer

Same! I struggle a lot with moduli and inequalities as well. Youtube playlists of  Khan Academy  and  PatrickJMT  on Linear inequalities helped me a lot. Just type it in the search box on Youtube. I could share the links, but I am new to this forum so I am not allowed to post urls.

sayan640 · Answer

Easiest approach:-

Whenever you see |a|=|b| ,
either a=b or a=-b ;
Apply this here ,
Either x -10 > x-30 ( ignore as -10 is always greater than-30)
or x -10 > - (x-30)
x -10 > -x + 30
x> 20 
Hence the question asks 
is x >20 ?

Option A does not give a definite answer as x can be 15 or 25 .
Option B does give a definite answer as x is greater than 25 means it will obviously be greater than 20.
B is the answer.

Posted from my mobile device

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Is |x - 10| > |x - 30|? (1) x > 10 (2) x > 25

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Is |x - 10| > |x - 30|? (1) x > 10 (2) x > 25

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