GRE Weekly Challenge #3

Question

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This week's question:

A	B
\|x – 5\| – \|a – b\|	\|b – a\| – \|5 – x\|

Compare Quantity A and Quantity B using the information given above, and select one of the following answer choices:
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Please post your answer, along with the explanation, below. Get cracking!

Edit: This challenge is now closed

The winner of this Week's Challenge is... (drum roll).... m2l2. Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide

Details of next week's competition will be posted in the Weekly Challenge Master thread... Stay tuned!

This challenge is now closed The winner of this Week's Challenge is... (drum roll).... m2l2 . Congratulations! Please send me a pm with your shipping address, and choice of Manhattan GRE Guide Details of next week's competition will be posted in the Weekly Challenge Master thread ... Stay tuned!

GyanOne · Answer

Should be (B)

nvgroshar · Answer

Answer B. The difference between B-A= 2|b-a| -2|x-5|>,0 since |b-a|>5 and |x-5|<5. In details, b>5, a<0, b-a>5; x<10; x-5<5.

AngelinaOllon · Answer

Answer B - Quantity B is greater.‎
‎|x – 5|=|5 – x|;‎
‎|a – b|=|b – a|;‎
As 5<x<10, then 0<|x – 5|<5 and 0<|5 – x|<5;‎
As a<0, b>0, then |a – b|=|b – a|=|a|+|b|;‎
‎|a|>0 and 5<|b|<10, then (|a|+|b|)>5;‎
Therefore, |x – 5| < |a – b|, (|x – 5| – |a – b|) < 0 and ‎
‎(|b – a| – |5 – x|) > 0, which means that‎
‎(|x – 5| – |a – b|) < (|b – a| – |5 – x|) for all a, b, x.‎

m2l2 · Answer

Quantity B is greater.  
A=|x-5|-|a-b|
 = (x-5)-(-(a-b)

since x>5, so the mod will always open positive.
since a<b, |a-b| will always open negetive.

so  A= x-5+a-b   ............(i)

B=|b-a|-|5-x|
 = (b-a)-(-(5-x)
same logic as above.

so  B= b-a+5-x   ...............(ii)

so  A= -(B)   ............... from (i) and (ii)
now,
numerical value of b-a is greater than 5 since 0 and 5 lies between a and b.
numerical value of 5-x is less than 5 since x lies between 5 and 10.
so, B is a positive quantity or A is a negetive quantity.

therefore,   B>A

dreambeliever · Answer

Ans B Let |x-5| = |5-x| = c --> 0 5

ramvemula · Answer

Ans: D

The intervals is not equal so we can not determine !!

Anonymous · Answer

The correct answer is: B)Quantity B is greater.

Quantity A:

0 < |x-5| < 5

|a-b| > b ==> |a-b| > 5

==>
|x – 5| – |a – b| = (0 < |x-5| < 5) - (|a-b| > 5) <=== This expression is clearly smaller than 0

Quantity B:

|b – a| = b+|a| > 5

|5 – x| < 5 (since 5 < x < 10 )

==>
|b – a| – |5 – x| = ( b+|a| > 5) - (|5 – x| < 5) <=== This expression is clearly greater than 0

So quantity B is greater than quantity A.

arjungn · Answer

Quantity B

|5-x|-->X varies from 5 to 10 therefore |5-x| varies from 0 to 5
|b-a|--> B varies from 5 to 10 and is greater then X ..and A is less than 0.Therefore |b-a| is either greater then 10 or greater than 5.Which means greater than 5 covers the entire range.
Hence ,|b-a|-|5-x| is always positive...(1)

Quantity A
Since x > 0 , |x-5| is the same range as |5-x| varying from 0 to 5
|a-b| again as |b-a| varies from 5 to 10
Hence . |b-a|-|5-x| is < 0 ....(2)

Therefore Clearly , Quantity B is greater then Quantity A.

viraa · Answer

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