GRE Weekly Challenge #3

Question

GMAT Club invites you to test your GRE knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GRE Strategy guide. What are you waiting for? Get out their scrap paper and start solving! Click here to view contest & prize details

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!

Moderator Note: 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

ready to participage....

GRE Weekly Challenge #3

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards