GMAT Changed on April 16th - Read about the latest changes here

It is currently 25 Apr 2018, 11:02

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

M23-02

  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: 44655
M23-02 [#permalink]

Show Tags

New post 16 Sep 2014, 01:18
Expert's post
33
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (00:42) correct 55% (00:44) wrong based on 206 sessions

HideShow timer Statistics

If Event \(A\) and Event \(B\) are independent, is the probability that both Event \(A\) and Event \(B\) will happen greater than 0.3?


(1) Probability that \(A\) will happen is 0.25

(2) Probability that \(B\) will NOT happen is 0.71
[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: 44655
Re M23-02 [#permalink]

Show Tags

New post 16 Sep 2014, 01:18
1
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
Official Solution:


Notice that since events \(A\) and \(B\) are independent, then the probability that both occur, equals to the product of their individual probability, so \(P(A \text { and } B)=P(A)*P(B)\). Also notice that \(0 \le P(A) \le 1\) and \(0 \le P(B) \le1\).

(1) Probability that \(A\) will happen is 0.25. Now, since \(P(A)=0.25\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.25 \lt 0.3\). Sufficient. Or consider the following: how can the probability that both Event \(A\) and Event \(B\) will happen be more than individual probability of each happening? So, the probability that both happen cannot be more than 0.25.

(2) Probability that B will NOT happen is 0.71. The same here: since \(P(B)=1-0.71=0.29\), then \(P(A \text { and } B)=P(A)*P(B) \le 0.29 \lt 0.3\). Sufficient.


Answer: D
_________________

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

Current Student
avatar
Joined: 10 Nov 2013
Posts: 19
Location: United States
Concentration: Healthcare, Strategy
WE: Information Technology (Health Care)
GMAT ToolKit User Premium Member Reviews Badge
Re: M23-02 [#permalink]

Show Tags

New post 03 Dec 2014, 22:13
Could you please explain this scenario.

1. Statement A provides only the probabilty of A - 0.25.
If the probability of B is zero, then P(A) * P(B) = 0.
If the probabilty of B is non-zero, then P(A and B) cannot be greater than 0.25

2. Statement B provides the probability of B
If the probability of A is zero, then P(A) * P(B) = 0.

The same scenario will hold true if the probability of either one of the event is 1.
6 KUDOS received
Manager
Manager
User avatar
Joined: 08 Jul 2012
Posts: 50
Re: M23-02 [#permalink]

Show Tags

New post 10 Dec 2014, 21:18
6
This post received
KUDOS
3
This post was
BOOKMARKED
coolparthi wrote:
Could you please explain this scenario.

1. Statement A provides only the probabilty of A - 0.25.
If the probability of B is zero, then P(A) * P(B) = 0.
If the probabilty of B is non-zero, then P(A and B) cannot be greater than 0.25

2. Statement B provides the probability of B
If the probability of A is zero, then P(A) * P(B) = 0.

The same scenario will hold true if the probability of either one of the event is 1.



I believe the question stem is asking the probability of A&B is >0.3 ?
"If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3?"
1) provides P(A)=0.25 now P(B) can be maximum 1, in this case P(A)*P(B)=0.25*1=0.25 <0.3
min value of P(B) can be 0, in this case P(A)*P(B)=0.25*0=0 <0.3
in either case the combined probability is < 0.3, hence sufficient

2) same reasoning as 1)

Ans. D)
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

1 KUDOS received
Current Student
avatar
Joined: 10 Nov 2013
Posts: 19
Location: United States
Concentration: Healthcare, Strategy
WE: Information Technology (Health Care)
GMAT ToolKit User Premium Member Reviews Badge
Re: M23-02 [#permalink]

Show Tags

New post 10 Dec 2014, 23:31
1
This post received
KUDOS
JJo wrote:
coolparthi wrote:
Could you please explain this scenario.

1. Statement A provides only the probabilty of A - 0.25.
If the probability of B is zero, then P(A) * P(B) = 0.
If the probabilty of B is non-zero, then P(A and B) cannot be greater than 0.25

2. Statement B provides the probability of B
If the probability of A is zero, then P(A) * P(B) = 0.

The same scenario will hold true if the probability of either one of the event is 1.



I believe the question stem is asking the probability of A&B is >0.3 ?
"If Event A and Event B are independent, is the probability that both Event A and Event B will happen greater than 0.3?"
1) provides P(A)=0.25 now P(B) can be maximum 1, in this case P(A)*P(B)=0.25*1=0.25 <0.3
min value of P(B) can be 0, in this case P(A)*P(B)=0.25*0=0 <0.3
in either case the combined probability is < 0.3, hence sufficient

2) same reasoning as 1)

Ans. D)


Thanks. Did not realize that!!
1 KUDOS received
Intern
Intern
avatar
Joined: 09 Aug 2014
Posts: 13
Re M23-02 [#permalink]

Show Tags

New post 18 Mar 2015, 10:08
1
This post received
KUDOS
I think this question is good and helpful.
Manager
Manager
avatar
B
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 249
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32
GMAT 2: 680 Q47 V35
GMAT ToolKit User Reviews Badge
Re: M23-02 [#permalink]

Show Tags

New post 19 Aug 2015, 20:02
Beautiful question!
When i first attempted it, i thought it was sub-600 level. And i got it wrong!
After seeing the solution i realized i had all the knowledge that was required to solve this question. But, this was a classic example that shows how GMAT doesn't care about what i 'know' but the way I comprehend the given info and apply what I know.
_________________

One Kudos for an everlasting piece of knowledge is not a bad deal at all... :thanks

------------------------------------------------------------------------------------------------------------------------
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover.
-Mark Twain

Current Student
User avatar
Joined: 12 Aug 2015
Posts: 292
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
M23-02 [#permalink]

Show Tags

New post 02 Nov 2015, 23:30
1
This post was
BOOKMARKED
As long as the events are independent we use general case formula P(A and B)=P(A)*P(B) where ocurrence of event A does not influence occurence of event B. We also remember that probability cannot exceed 1 for any single event or combination of the events. So the question asks whether:

P(A) * P(B) > 0.3

(1) P(A) = 0.25. Let us try to apply the formula here: under what circumstances the "and" probability of the 2 independent events can be at least equal to 0.3? Given probability of A we can build the formula and see what probability we would need for the event B for the whole formula become equal to 0.3.

0.25 * P(B) = 0.3

P(B) = 0.3/0.25 = 1.2 - hold on this cant be true, the probability of event cannot exceed 1. Hence the "and" probability of A and B just never can be 0.3 and/or greater than that. SUFFICIENT.

(2) P(not B) = 0.71 -> P(B)=0.29. Same logic - P(A) would exceed 1 which is not possible, hence SUFFICIENT to anwser the question conclusively.
_________________

KUDO me plenty

Manager
Manager
User avatar
Joined: 11 Oct 2013
Posts: 115
Concentration: Marketing, General Management
GMAT 1: 600 Q41 V31
GMAT ToolKit User
Re M23-02 [#permalink]

Show Tags

New post 18 Dec 2015, 06:02
I think this is a high-quality question and I agree with explanation.
_________________

Its not over..

Intern
Intern
avatar
Joined: 23 Sep 2015
Posts: 39
Re M23-02 [#permalink]

Show Tags

New post 02 Mar 2016, 07:17
I think this the explanation isn't clear enough, please elaborate. and can you please provide a link from where i can understand probability and combinatorics
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44655
Re: M23-02 [#permalink]

Show Tags

New post 03 Mar 2016, 07:30
Expert's post
6
This post was
BOOKMARKED
nishantdoshi wrote:
I think this the explanation isn't clear enough, please elaborate. and can you please provide a link from where i can understand probability and combinatorics


Probability Made Easy!
Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions

Combinatorics Made Easy!

Theory on Combinations

DS questions on Combinations
PS questions on Combinations
_________________

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 Jun 2016
Posts: 1
Re M23-02 [#permalink]

Show Tags

New post 30 Jun 2016, 06:18
The question reads that P(A and B)>0.3, but the explanation read that P(A and B) < 0.3.

What am I missing?
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44655
M23-02 [#permalink]

Show Tags

New post 30 Jun 2016, 08:30
gentlestrength wrote:
The question reads that P(A and B)>0.3, but the explanation read that P(A and B) < 0.3.

What am I missing?


Not true. The question ASKS is the probability of the event greater than 0.3. From both statements we get NO answer to the question, the probability of that even is less than 0.3.
_________________

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

Senior Manager
Senior Manager
User avatar
Joined: 31 Mar 2016
Posts: 404
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)
GMAT ToolKit User Premium Member
Re M23-02 [#permalink]

Show Tags

New post 09 Jul 2016, 04:14
I think this is a high-quality question and I agree with explanation.
Intern
Intern
User avatar
B
Joined: 15 Sep 2017
Posts: 23
Location: United States
Concentration: Entrepreneurship, Technology
GPA: 3.8
WE: Real Estate (Real Estate)
Re: M23-02 [#permalink]

Show Tags

New post 20 Nov 2017, 12:08
Great Question!!
_________________

"Revenge is a dish best served cold"

Intern
Intern
avatar
S
Joined: 20 Sep 2012
Posts: 6
Concentration: Finance, General Management
GMAT ToolKit User Reviews Badge
Re M23-02 [#permalink]

Show Tags

New post 14 Apr 2018, 04:01
I think this is a high-quality question and I agree with explanation.
Re M23-02   [#permalink] 14 Apr 2018, 04:01
Display posts from previous: Sort by

M23-02

  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®.