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

It is currently 18 Jan 2019, 10:01

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
Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

Lily has only red and blue balls in a jar. If she removes three balls,

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

Hide Tags

 
SC Moderator
User avatar
V
Joined: 23 Sep 2015
Posts: 1614
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 10 Jun 2018, 06:21
1
5
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:17) correct 69% (02:40) wrong based on 97 sessions

HideShow timer Statistics

Lily has only red and blue balls in a jar. If she removes three balls, is the probability of getting all red balls greater than the probability of getting at least one blue ball?

(1) The number of red balls is more than three times the number of blue balls.
(2) Less than (1)/(4) th of the balls in the jar are blue.

Source: Expert Global

_________________

Thanks!
Do give some kudos.

Simple strategy:
“Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.”

Want to improve your Score:
GMAT Ninja YouTube! Series 1| GMAT Ninja YouTube! Series 2 | How to Improve GMAT Quant from Q49 to a Perfect Q51

My Notes:
Reading comprehension | Critical Reasoning | Absolute Phrases | Subjunctive Mood

Manager
Manager
avatar
B
Joined: 19 Feb 2017
Posts: 137
Location: India
GMAT 1: 690 Q50 V31
GMAT ToolKit User
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 10 Jun 2018, 07:50
Answer should be E. Eg: Take there are 4 red balls and 1 blue ball. Then P(RRR)= 2/5 and P(atleast 1B) = 3/5. So 2nd expression is smaller.

Then take there are 7 red balls and 1 blue ball. Then P(RRR)= 5/8 and P(atleast 1B) = 3/8. So 1st expression is smaller.

This example will work for both the statements. Therefore, no sufficiency in any. Hence, E.
Intern
Intern
avatar
B
Joined: 03 Sep 2015
Posts: 18
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 28 Aug 2018, 09:13
Hi. How did you get 3/5 for blue balls?
Intern
Intern
avatar
Joined: 09 Aug 2018
Posts: 3
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 29 Aug 2018, 04:37
1
Hi
I find the resource helpful, you can also try this probability lecture.
Intern
Intern
avatar
B
Joined: 03 Sep 2015
Posts: 18
Re: Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 29 Aug 2018, 04:48
Thanks so much for this

Posted from my mobile device
GMATH Teacher
User avatar
G
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 616
Lily has only red and blue balls in a jar. If she removes three balls,  [#permalink]

Show Tags

New post 29 Aug 2018, 05:57
1
Quote:
Lily has only red and blue balls in a jar. If she gets three balls randomly, is the probability of getting all red balls greater than the probability of getting at least one blue ball?

(1) The number of red balls is more than three times the number of blue balls.
(2) Less than (1)/(4) of the balls in the jar are blue.

Source: Expert Global


Nice problem!

\(\operatorname{P} \left( {{\text{all}}\,\,3\,\,{\text{red}}} \right)\,\,\,\,\mathop > \limits^? \,\,\,\operatorname{P} \left( {{\text{not}}\,\,{\text{all}}\,\,3\,\,{\text{red}}} \right)\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\operatorname{P} \left( {{\text{all}}\,\,3\,\,{\text{red}}} \right) = \boxed{\frac{{C\left( {r,3} \right)}}{{C\left( {r + b,3} \right)}}\,\,\,\,\mathop > \limits^? \,\,\,\frac{1}{2}}\)

\(\left( {1 + 2} \right)\,\,\)

\(Take\,\,\left( {r,b} \right) = \left( {4,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {4,3} \right)}}{{C\left( {5,3} \right)}} = \,\frac{1}{{10}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle\)

\(Take\,\,\left( {r,b} \right) = \left( {5,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {5,3} \right)}}{{C\left( {6,3} \right)}} = \,\frac{{10}}{{20}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,{\text{but}}\,\,\,{\text{increasing}}\,\,...\)

\(Take\,\,\left( {r,b} \right) = \left( {6,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\frac{{C\left( {6,3} \right)}}{{C\left( {7,3} \right)}} = \,\frac{4}{7}\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\)

(Keeping the number of blue balls fixed and increasing the number of red ones, we know the probability of getting 3 reds must increase...)

The answer is (E), because we were able to BIFURCATE (1+2)!

The above follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

GMAT Club Bot
Lily has only red and blue balls in a jar. If she removes three balls, &nbs [#permalink] 29 Aug 2018, 05:57
Display posts from previous: Sort by

Lily has only red and blue balls in a jar. If she removes three balls,

  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®.