BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Confusion when root of a number is to be taken!

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Quantitative Reasoning |
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Sun Sep 08, 2013 2:01 am
Assuming the question is Is x > 12?

Then statement 1

x^1/2 > 4
√x > 4
|x| > 16 (squaring both sides)
|x| > 16 or -16

Does not make sense. Not sufficient

Statement 2

x > 144^1/2

x > √144

x > 12 Sufficient

What is the source? And the question appears odd!
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 9
Joined: Sun Aug 04, 2013 12:36 am
Thanked: 1 times

by apurva.jalit » Sun Sep 08, 2013 2:07 am
when you say √x > 4, on squaring √x, we are always going to get a +ve number right? so shouldn't we directly assume x > 16?

I am confused over the way you have used second statement.
statement : x > √144
can't we say here that x > 12 or x > -12, if we have the second case, we can't be sure that x >12?
Also my question is whether taking -ve root acceptable here? if not, why so?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Sun Sep 08, 2013 2:36 am
apurva.jalit wrote:when you say √x > 4, on squaring √x, we are always going to get a +ve number right? so shouldn't we directly assume x > 16?

I am confused over the way you have used second statement.
statement : x > √144
can't we say here that x > 12 or x > -12, if we have the second case, we can't be sure that x >12?
Also my question is whether taking -ve root acceptable here? if not, why so?
Hi,

There are 2 different scenarios

See square of a number, say -4 or 4 is always 16, but √ of a number is usually taken as positive, such as √16 is 4.

Both the cases we need to find the value of x, so in statement 1 we don't have a direct equation mentioning the value of x, so we have to find a solution for x, so it is like this √x is nothing but x ^1/2 so squaring results in (x^1/2)^2, so we get x.

Also we cannot square root a negative number.It is convention that is followed, symbols need to have 1 value.

So for your query:

1. No you cannot assume that a solution for a square of a number is always positive, it can be negative or positive. You have to find the solution.

2. Square root of a number(Usually symbols have one value only) has to be positive, that's a convention followed to remove ambiguity.
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Sun Sep 08, 2013 6:22 am
apurva.jalit wrote:is x > 12?

i) √x > 4
ii) x > √144
Target question: Is x > 12?

Statement 1: √x > 4
NOTE: This implies that x must be positive. If x were negative, then √x would be undefined, and an undefined value cannot be greater than 4
Since 4 = √16, we can take √x > 4 and rewrite it as √x > √16
From here, we can conclude that x > 16, which means x is definitely greater than 12
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x > √144
Since √144 = 12, this statement tells us that x is definitely greater than 12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1