|
Author |
Message |
|
TAGS:
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[1] , given: 828
|
A certain club has 10 members, including Harry. One of the [#permalink]
 25 Jun 2012, 02:31
1
This post received
KUDOS
Question Stats:
48% (02:12) correct
51% (01:47) wrong based on 7 sessions
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectA certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer? (A) 1/720 (B) 1/80 (C) 1/10 (D) 1/9 (E) 1/5 Diagnostic Test
Question: 7
Page: 21
Difficulty: 650 GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! _________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
|
|
Senior Manager
Joined: 29 Mar 2012
Posts: 250
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 10
Kudos [?]:
52
[2] , given: 20
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
25 Jun 2012, 04:35
2
This post received
KUDOS
Hi, Difficulty level = 650 Probability = (Favorable cases)/(total cases) Case 1: When Harry is chosen as secretary probability = 9/10 * 1/9 * 8/8 = 1/10 (9 available for post of president out of 10, then Harry has to be chosen out of 9, and finally out of 8 anyone can be treasurer) Case 2: When Harry is chosen as treasurer probability = 9/10 * 8/9 * 1/8 = 1/10 (9 available for post of president out of 10, then out of 8 anyone can be secretary, and finally Harry has to be treasurer) probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer = 1/10 + 1/10 =1/5 Answer (E), Regards,
_________________
My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules
My story: 640 What a blunder!
My page:
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[1] , given: 828
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
25 Jun 2012, 02:31
1
This post received
KUDOS
SOLUTIONA certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?(A) 1/720 (B) 1/80 (C) 1/10 (D) 1/9 (E) 1/5 This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10. Answer: E. Similar questions to practice: a-certain-team-has-12-members-including-joey-a-three-131321.htmla-certain-television-show-has-15-sponsors-including-company-127423.htmla-medical-researcher-must-choose-one-of-14-patients-to-127396.htmla-certain-class-consists-of-8-students-including-kim-127730.html
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[0], given: 828
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
29 Jun 2012, 02:43
SOLUTIONA certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?(A) 1/720 (B) 1/80 (C) 1/10 (D) 1/9 (E) 1/5 This question is much easier than it appears. Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/10 and the probability that Harry will be selected to be the treasurer is also 1/10. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/10+1/10=2/10. Answer: E. Similar questions to practice: a-certain-team-has-12-members-including-joey-a-three-131321.htmla-certain-television-show-has-15-sponsors-including-company-127423.htmla-medical-researcher-must-choose-one-of-14-patients-to-127396.htmla-certain-class-consists-of-8-students-including-kim-127730.html
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 12 Feb 2012
Posts: 63
Followers: 1
Kudos [?]:
3
[0], given: 23
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
09 Sep 2012, 17:18
Hey Bunuel,
This the qay I did it:
P(secretary)=P(not Harry)*P(Harry)*P(not Harry)=(9/10)(1/9)(8/8)=1/10
P(treasurer)=P(not Harry)*P(not Harry)*P(Harry)=(9/10)(8/9)(1/8)=1/10
P(secretary OR treasurer)=P(secretary)+P(treasurer)=(1/10)+(1/10)=1/5
But I am confused since:
P(secretary OR treasurer)=P(secretary)+P(treasurer)-P(secretary and treasurer)+ P(Neither secretary nor treasurer)
Now since the two events are mutually exclusive and Harry can neither be both secretary and treasurer, P(secretary and treasurer)=0.
P(Neither secretary nor treasurer)=(9/10)(8/9)(7/8).
What am I doing wrong?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11610
Followers: 1800
Kudos [?]:
9593
[0], given: 828
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
11 Sep 2012, 02:53
alphabeta1234 wrote: Hey Bunuel,
This the qay I did it:
P(secretary)=P(not Harry)*P(Harry)*P(not Harry)=(9/10)(1/9)(8/8)=1/10
P(treasurer)=P(not Harry)*P(not Harry)*P(Harry)=(9/10)(8/9)(1/8)=1/10
P(secretary OR treasurer)=P(secretary)+P(treasurer)=(1/10)+(1/10)=1/5
But I am confused since:
P(secretary OR treasurer)=P(secretary)+P(treasurer)-P(secretary and treasurer)+ P(Neither secretary nor treasurer)
Now since the two events are mutually exclusive and Harry can neither be both secretary and treasurer, P(secretary and treasurer)=0.
P(Neither secretary nor treasurer)=(9/10)(8/9)(7/8).
What am I doing wrong? If you want to do this way then: P(secretary or treasurer)=P(not Harry)*P(Harry)*P(any)+P(not Harry)*P(not Harry)*P(Harry)=9/10*1/9*1+9/10*8/9*1/8=2/10. In the red, you are calculating the probability that Harry will be secretary OR treasurer OR neither and we don't need neither. Hope it's clear.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Intern
Joined: 28 Dec 2012
Posts: 46
Followers: 1
Kudos [?]:
11
[0], given: 53
|
A certain club has 10 members, including Harry. One of the [#permalink]
06 Jan 2013, 13:49
E.
[ 9C2 * ( 3! - 2!) ] / 10C3
= 1/5
|
|
|
|
|
|
Intern
Joined: 09 Jan 2013
Posts: 13
Concentration: Entrepreneurship, Sustainability
GMAT 1: 650 Q45 V34
GRE 1: 1440 Q790 V650
GPA: 3.76
WE: Other (Pharmaceuticals and Biotech)
Followers: 1
Kudos [?]:
0
[0], given: 9
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
26 Jan 2013, 22:59
sagarsingh wrote: E.
[ 9C2 * ( 3! - 2!) ] / 10C3
= 1/5 Hi Sagar, I tried to solve this problem in a similar way, but couldn't get it right. Please explain the significance of (3! - 2!).
|
|
|
|
|
|
Intern
Joined: 08 Feb 2013
Posts: 2
Followers: 0
Kudos [?]:
0
[0], given: 0
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
12 Feb 2013, 03:02
Can you do this with the formula Favorables/Total? Tried but cant get the right result.
|
|
|
|
|
|
Manager
Joined: 24 Sep 2012
Posts: 90
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Followers: 1
Kudos [?]:
36
[0], given: 3
|
Re: A certain club has 10 members, including Harry. One of the [#permalink]
16 Feb 2013, 12:58
Favorable method: Total options=10*9*8 // since any of the ten members can become President, any one of the nine can become secretary and any one of the remaining eight can become treasurer Favorable options are the ones which include Harry as Treasurer or the secretary Now consider the number of options in which harry is chosen as the secretary. Since we know that there is only one option for secretary, that position already has one person fixed. Hence, the president must be chosen out of the remaining nine people and the secretary from the remaining eight. Hence, ways in which Harry can become secretary are 9*1*8=72 Similarly, ways in which Harry can become treasurer are 9*8*1=72 Since the probability asks for "or" we must add both the favorable outputs=72+72=144 Now, (favorable results/total results) = (144/720)=1/5 Hence the answer is E. Let me know if any other clarifications are required. Victorlp89 wrote: Can you do this with the formula Favorables/Total? Tried but cant get the right result.
_________________
Thanks
Kris
Instructor at Aspire4GMAT
Visit us at http://www.aspire4gmat.com
Post your queries
Join our free GMAT course
New blog: How to get that 700+
New blog: Data Sufficiency Tricks
Press Kudos if this helps!
|
|
|
|
|
|
|
Re: A certain club has 10 members, including Harry. One of the
[#permalink]
16 Feb 2013, 12:58
|
|
|
|
|
|
|
|
|
|
|
close
