GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 11 Jul 2020, 07:11

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

x^2-4x<0 Inequalities

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 10 Nov 2018
Posts: 9
x^2-4x<0 Inequalities  [#permalink]

Show Tags

New post 29 May 2020, 01:58
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Can someone please assist? Thanks.
Manager
Manager
avatar
G
Joined: 01 Nov 2017
Posts: 106
Location: India
Concentration: Finance, Leadership
Schools: ISB '21
GMAT 1: 690 Q49 V36
GPA: 4
WE: Web Development (Consulting)
GMAT ToolKit User Premium Member
Re: x^2-4x<0 Inequalities  [#permalink]

Show Tags

New post 29 May 2020, 02:28
happyapple123 wrote:
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Can someone please assist? Thanks.



Hi happyapple123,

\(x^2 - 4x <0 => x (x - 4) < 0\)

This means either \(x < 0\) or \((x - 4) < 0\) but not both, because if both are negative then multiplication of two negative numbers is positive so the equation will not be true.

Now, if
\(x < 0\) then \((x - 4)\) is also less than 0, which makes both negative, so this cannot be true.

for example,

if \(x = -1\), then \((x - 4) => (-1 - 4) = -5 < 0\)
=> so, \((-1) * (-5) = 5 > 0\), so equation doesn't agree.

Hence, only \((x - 4) < 0\) but \(x > 0\) which means

\(0 < x < 4\)
Intern
Intern
avatar
B
Joined: 10 Nov 2018
Posts: 9
Re: x^2-4x<0 Inequalities  [#permalink]

Show Tags

New post 29 May 2020, 03:44
Thanks Codebug4it!
VP
VP
User avatar
V
Joined: 11 Feb 2015
Posts: 1177
Re: x^2-4x<0 Inequalities  [#permalink]

Show Tags

New post 29 May 2020, 04:44
happyapple123 wrote:
What is the range for the inequality x^2 - 4x <0?

The solution is 0<x<4.

But I think the solution should be x<0 x>4.

Can someone please assist? Thanks.


If you think x<0 x>4. then the inequality must hold true for x= 1 and x = 5 and Not for x=2, right?

Plugin the value yourself, calculate and see for yourself what happens?

Whenever in doubt, you can test by plugging the values of x and consider various scenarios. You will get the answer yourself.
_________________
Manish
GMAT Club Bot
Re: x^2-4x<0 Inequalities   [#permalink] 29 May 2020, 04:44

x^2-4x<0 Inequalities

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





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