Last visit was: 24 Jul 2024, 06:02 It is currently 24 Jul 2024, 06:02
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
CEO
CEO
Joined: 26 Feb 2016
Posts: 2863
Own Kudos [?]: 5334 [6]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11485
Own Kudos [?]: 34578 [0]
Given Kudos: 325
Send PM
Current Student
Joined: 13 Apr 2015
Posts: 1426
Own Kudos [?]: 4603 [0]
Given Kudos: 1228
Location: India
Send PM
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1558 [0]
Given Kudos: 54
Location: India
GPA: 3.82
Send PM
Is x > 0? [#permalink]
ashikaverma13 wrote:
Is x > 0?

1) |3 - x| < |x+5|
2) |3-2x| < x - 1


Statement 1: \(|3-x|<|x+5|\), square both sides to get

\(9+x^2-6x<x^2+25+10x\)

\(=>16x>-16 =>x>-1\). Hence \(x>0\) or \(x<0\). Insufficient

Statement 2: implies \(-(x-1)<3-2x<x-1\)

\(=>3-2x<x-1 =>3x>4 =>x>\frac{4}{3}\)

and \(3-2x>1-x =>x<2\)

So range \(\frac{4}{3}<x<2\). Clearly \(x>0\). Sufficient

Option B
SVP
SVP
Joined: 26 Mar 2013
Posts: 2456
Own Kudos [?]: 1369 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 [#permalink]
pushpitkc wrote:
Is x > 0?

(1) |3 - x| < |x + 5|
(2) |3 - 2x| < x - 1

Source: Experts Global



Another approach

(1) |3 - x| < |x + 5|

I spotted quickly the following:

Let x = 0 ......|3| < |5|..Answer is No

Let x =1 .......|2| < |6|..Answer is Yes

Insufficient

|3 - 2x| < x - 1

|3 - 2x| is equal or greater than zero.......x-1 is also equal or greater than zero

x -1 > 0...x >1>0

Sufficient

Answer: B
Intern
Intern
Joined: 03 Nov 2017
Posts: 12
Own Kudos [?]: 14 [0]
Given Kudos: 93
GMAT 1: 590 Q48 V23
Send PM
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 [#permalink]
For statement 1, how do we know that we need to square both side ? I was trying to solve it and could not get the answer.
any tips on identifying this.
Retired Moderator
Joined: 25 Feb 2013
Posts: 893
Own Kudos [?]: 1558 [2]
Given Kudos: 54
Location: India
GPA: 3.82
Send PM
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 [#permalink]
2
Kudos
adityanahan wrote:
For statement 1, how do we know that we need to square both side ? I was trying to solve it and could not get the answer.
any tips on identifying this.


Hi adityanahan

by squaring a mod function you can get rid of the mod and then it becomes a simple equation which is easier to work with.
when you remove the mod function, then you need to be careful that you test both the positive and negative values. but by squaring, you can turn the function to a positive value as square is always positive or 0
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34061
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: Is x > 0? (1) |3 - x| < |x + 5| (2) |3 - 2x| < x - 1 [#permalink]
Moderator:
Math Expert
94605 posts