GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Apr 2019, 21:18

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

If √x=x , then which of the following must be true ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Intern
Intern
avatar
Joined: 22 Aug 2014
Posts: 1
If √x=x , then which of the following must be true ?  [#permalink]

Show Tags

New post 26 Oct 2014, 04:35
7
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

58% (00:55) correct 42% (00:54) wrong based on 226 sessions

HideShow timer Statistics

If \(\sqrt{x}=x\) , then which of the following must be true ?

A. \(x\) is positive
B. \(x = 1\)
C. \(x^2 > x\)
D. \(x\) is nonnegative
E. None of the above
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 274
Re: If √x=x , then which of the following must be true ?  [#permalink]

Show Tags

New post 26 Oct 2014, 06:01
1
amitabc wrote:
Q : if √x=x , then which of the following must be true

a) x is positive
b) x=1
c) square(x)>x
d) x is nonnegative
e) none of the above


√x=x; squaring both sides we have
x=x^2
x(x-1)=0
x=0 or 1

lets look in to the each option

a) x can be zero as well, which is neutral (neither positive nor negative) hence out
b) x can be zero as well
c) clearly out
d) this must be true. as non negative, satisfies both x=0 and x=1

hence D
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1813
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If √x=x , then which of the following must be true ?  [#permalink]

Show Tags

New post 26 Oct 2014, 06:08
1
3
amitabc wrote:
Q : if √x=x , then which of the following must be true

a) x is positive
b) x=1
c) square(x)>x
d) x is nonnegative
e) none of the above


We require to find what must be true rather than what can be true?

Testing all options:

a) x is positive >> Not necessary >> \(\sqrt{0} = 0\)

b) x=1 >> Not necessary >> x can be zero \(\sqrt{0} = 0\)

c) square(x)>x >> Not necessary >> For x=1 or x = 0, \(x^2 = x\)

d) x is nonnegative >> That's correct >> x has to be non-negative because square root of a negative integer cannot be the same integer

\(\sqrt{-1}\neq{1}\)

e) none of the above >> D hold true

Answer = D
_________________
Kindly press "+1 Kudos" to appreciate :)
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13958
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If √x=x , then which of the following must be true ?  [#permalink]

Show Tags

New post 16 Feb 2018, 18:43
Hi All,

This question is really more about the 'thoroughness' of your thinking than anything else. Most Test Takers would look at this question and think "Oh, the answer is obviously X=1....", but is that really the ONLY answer???

The numbers -1, 0 and 1 have all sorts of interesting 'impacts' on how various math rules 'work', so it's important to keep them in mind as you work through the Quant section of the GMAT.

Here, we're asked what MUST be true based on the equation √x = x. You should be able to determine the 2 solutions to this equation (whether you do the formal algebra or not). Those solutions are 0 and 1. Using those answers as reference, only one of the 5 answers choices is correct...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Manager
User avatar
S
Joined: 12 Sep 2017
Posts: 221
If √x=x , then which of the following must be true ?  [#permalink]

Show Tags

New post 17 Mar 2019, 16:22
\(\sqrt{x}=x\)

\(\sqrt{x}^2=x^2\)

\(x = x^2\)

\(0 = \frac{x^2}{x}\)

\(0 =x\)

Nonnegative

D
GMAT Club Bot
If √x=x , then which of the following must be true ?   [#permalink] 17 Mar 2019, 16:22
Display posts from previous: Sort by

If √x=x , then which of the following must be true ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.