It is currently 24 Feb 2018, 10:20

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

Events & Promotions in June
Open Detailed Calendar

M32-04

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
M32-04 [#permalink]

Show Tags

New post 13 Jun 2016, 05:40
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

46% (00:37) correct 54% (00:50) wrong based on 71 sessions

HideShow timer Statistics

A bag contains only blue and red balls. What is the probability that the second ball we pick will be blue, if the first ball we picked was red?



(1) Initially, the number of red balls was one more than the number of blue balls.

(2) Initially, the number of red balls was 7.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re M32-04 [#permalink]

Show Tags

New post 13 Jun 2016, 05:40
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Official Solution:


A bag contains only blue and red balls. What is the probability that the second ball we pick will be blue, if the first ball we picked was red?

Say, initially there were \(b\) blue balls and \(r\) red balls. The probability that the second ball we pick will be blue, if the first ball we picked was red will therefore be \(\frac{b}{b+r-1}\)

(1) Initially, the number of red balls was one more than the number of blue balls. This implies that \(r=b+1\), hence the probability is \(\frac{b}{b+r-1}=\frac{b}{b+(b+1)-1}=\frac{b}{2b}=\frac{1}{2}\). Sufficient.

(2) Initially, the number of red balls was 7. Clearly insufficient.


Answer: A
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 30 Mar 2016
Posts: 1
Premium Member
Re M32-04 [#permalink]

Show Tags

New post 17 Jun 2016, 20:12
I think this is a poor-quality question and I don't agree with the explanation. I chose answer E because the question doesn't mention whether or not the first ball picked was put back in the bag.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: M32-04 [#permalink]

Show Tags

New post 19 Jun 2016, 09:24
edgargee wrote:
I think this is a poor-quality question and I don't agree with the explanation. I chose answer E because the question doesn't mention whether or not the first ball picked was put back in the bag.


If it were with replacement it would have been explicitly mentioned.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
B
Joined: 10 Aug 2013
Posts: 43
Location: United Kingdom
Concentration: Strategy, Marketing
GMAT 1: 710 Q49 V38
GMAT 2: 730 Q49 V40
GPA: 3
WE: Consulting (Consulting)
M32-04 [#permalink]

Show Tags

New post 22 Aug 2016, 20:34
This probability defined for picking blue given that first red doesnt seem right to me as its a conditional probability and should not be straight up b/(r+b-1). I might be wrong but would be good to confirm this.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: M32-04 [#permalink]

Show Tags

New post 24 Aug 2016, 03:57
sharmaanurag wrote:
This probability defined for picking blue given that first red doesnt seem right to me as its a conditional probability and should not be straight up b/(r+b-1). I might be wrong but would be good to confirm this.


No, it's right. When you pick 1 red you are left with b blue balls and r red balls. The probability that the second ball we pick will be blue, if the first ball we picked was red will therefore be \(\frac{b}{b+(r-1)}\)
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 06 May 2016
Posts: 14
Re: M32-04 [#permalink]

Show Tags

New post 06 Sep 2016, 10:23
Bunuel,

I think I am missing something here. I tried with an example:

Lets blue balls be 3 and red balls be 4 :

4/7 * 3/6 = 2/7

but if

B=5 and R=6 then it will be 3/11

How you are getting 1/2 as the answer?
1 KUDOS received
Intern
Intern
avatar
Joined: 22 Aug 2016
Posts: 1
M32-04 [#permalink]

Show Tags

New post 07 Sep 2016, 07:12
1
This post received
KUDOS
gmatravi wrote:
Bunuel,

I think I am missing something here. I tried with an example:

Lets blue balls be 3 and red balls be 4 :

4/7 * 3/6 = 2/7

but if

B=5 and R=6 then it will be 3/11

How you are getting 1/2 as the answer?


What you've calculated here is conditional probability.

3/11 would've been correct if we were asked to calculate the probability of getting the FIRST ball red and THEN picking the second ball blue.

But here we're given that the FIRST has already been picked and it was red. That event has already happened, so we don't need to worry about that.

In mathematical terms,

P[first ball red] = 1 , as there is no other possible outcome other than what already came

Using your example,
Let blue balls be 3 and red balls be 4 :

1/1 * 3/6 = 1/2

Hence, it's correct.
3 KUDOS received
Intern
Intern
User avatar
B
Joined: 18 Jun 2015
Posts: 41
Reviews Badge
Re: M32-04 [#permalink]

Show Tags

New post 11 Sep 2016, 04:00
3
This post received
KUDOS
We can solve this question while reading the question ...
Given one red ball was picked.

condition 1 > red ball was one more than the blue ball.
as we have picked one red ball now so red balls equals blue ball.

So the probability of picking the blue ball is half.
Hence condition 1 is sufficient.

condition 2 > not sufficient.
Intern
Intern
avatar
B
Joined: 17 Feb 2016
Posts: 2
Re: M32-04 [#permalink]

Show Tags

New post 22 Mar 2017, 03:42
Hi Bunuel. I don't agree with the explanation,

Statement (1): What's up if there are zero blue balls and only one red ball in the bag? The probability of getting a blue ball would be zero (because there are no blue balls in the bag!) - I agree that for any other case, the P is 1/2.

So we need statement (2) to solve.

Please correct me.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43896
Re: M32-04 [#permalink]

Show Tags

New post 22 Mar 2017, 04:08
jcriedel wrote:
Hi Bunuel. I don't agree with the explanation,

Statement (1): What's up if there are zero blue balls and only one red ball in the bag? The probability of getting a blue ball would be zero (because there are no blue balls in the bag!) - I agree that for any other case, the P is 1/2.

So we need statement (2) to solve.

Please correct me.


Since we are told that "A bag contains only blue and red balls", then I think it's safe to assume that the number of blue balls is more than 0. If it were otherwise then we could say that the bag contains 0 number of any other color balls.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: M32-04   [#permalink] 22 Mar 2017, 04:08
Display posts from previous: Sort by

M32-04

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

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.