Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Aug 2015, 05:41
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Anthony and Michael sit on the six-member board of directors

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
Intern
Intern
avatar
Joined: 19 Sep 2010
Posts: 26
Followers: 0

Kudos [?]: 46 [2] , given: 0

Anthony and Michael sit on the six-member board of directors [#permalink] New post 01 Oct 2010, 07:39
2
This post received
KUDOS
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

49% (01:00) correct 51% (01:28) wrong based on 241 sessions
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%
[Reveal] Spoiler: OA
Expert Post
12 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49623 [12] , given: 7400

Re: Probability - MGMAT Test [#permalink] New post 01 Oct 2010, 07:42
12
This post received
KUDOS
Expert's post
13
This post was
BOOKMARKED
Barkatis wrote:
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%


First approach:
Let's take the group with Michael: there is a place for two other members and one of them should be taken by Anthony, as there are total of 5 people left, hence there is probability of 2/5=40%.

Second approach:
Again in Michael's group 2 places are left, # of selections of 2 out of 5 5C2=10 - total # of outcomes.
Select Anthony - 1C1=1, select any third member out of 4 - 4C1=4, total # =1C1*4C1=4 - total # of winning outcomes.
P=# of winning outcomes/# of outcomes=4/10=40%

Third approach:
Michael's group:
Select Anthony as a second member out of 5 - 1/5 and any other as a third one out of 4 left 4/4, total=1/5*4/4=1/5;
Select any member but Anthony as second member out of 5 - 4/5 and Anthony as a third out of 4 left 1/4, total=4/5*1/4=1/5;
Sum=1/5+1/5=2/5=40%

Fourth approach:
Total # of splitting group of 6 into two groups of 3: 6C3*3C3/2!=10
# of groups with Michael and Anthony: 1C1*1C1*4C1=4
P=4/10=40%

Answer: C.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 19 Sep 2010
Posts: 26
Followers: 0

Kudos [?]: 46 [0], given: 0

Re: Probability - MGMAT Test [#permalink] New post 01 Oct 2010, 08:05
Thanks.
Just a question: I noticed that you responded very quickly to my posts. Which I thank you for. But I am wondering if it's ok that I post questions that have been obviously posted before. If it's a problem then please tell me how can I check whether a question is already on the forum or not. Thanks.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49623 [1] , given: 7400

Re: Probability - MGMAT Test [#permalink] New post 01 Oct 2010, 08:26
1
This post received
KUDOS
Expert's post
Barkatis wrote:
Thanks.
Just a question: I noticed that you responded very quickly to my posts. Which I thank you for. But I am wondering if it's ok that I post questions that have been obviously posted before. If it's a problem then please tell me how can I check whether a question is already on the forum or not. Thanks.


Generally it's a good idea to do the search before posting, for example I would search in PS subforum (there is a search field above the topics) for the word "Anthony", don't think that there are many questions with this name. Though it's not a probelm to post a question that was posted before: if moderators find previous discussions they will merge the topics, copy the solution from there or give a link to it.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 19 Sep 2010
Posts: 26
Followers: 0

Kudos [?]: 46 [0], given: 0

Re: Probability - MGMAT Test [#permalink] New post 04 Oct 2010, 11:56
Bunuel, A question just came to my mind concerning the second approach of the solution that you proposed:

total # of winning outcomes
Select Anthony: 1C1=1, select any third member out of 4: 4C1=4, total # =1C1*4C1=4

If we say 1C1*4C1 don't we assume that the winning can be either (Anthony,Third member) or (Third member, Anthony) but not both ?
shouldn't we multiply 1C1*4C1 by 2 to get the total number of possible combinations ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49623 [0], given: 7400

Re: Probability - MGMAT Test [#permalink] New post 04 Oct 2010, 12:12
Expert's post
Barkatis wrote:
Bunuel, A question just came to my mind concerning the second approach of the solution that you proposed:

total # of winning outcomes
Select Anthony: 1C1=1, select any third member out of 4: 4C1=4, total # =1C1*4C1=4

If we say 1C1*4C1 don't we assume that the winning can be either (Anthony,Third member) or (Third member, Anthony) but not both ?
shouldn't we multiply 1C1*4C1 by 2 to get the total number of possible combinations ?


We are counting # of committees with Anthony and Michael:

{M,A,1};
{M,A,2};
{M,A,3};
{M,A,4}.

Here {M,A,1} is the same committee as {M,1,A}.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 06 Nov 2010
Posts: 22
Followers: 0

Kudos [?]: 15 [0], given: 16

GMAT ToolKit User
Re: Probability - MGMAT Test [#permalink] New post 21 Jan 2011, 15:54
Bunuel, can you advise why do we have to divide 6C3 * 3C3 by 2!, in the fourth approach ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49623 [0], given: 7400

Re: Probability - MGMAT Test [#permalink] New post 21 Jan 2011, 16:14
Expert's post
1
This post was
BOOKMARKED
praveenvino wrote:
Bunuel, can you advise why do we have to divide 6C3 * 3C3 by 2!, in the fourth approach ?


We are dividing by 2! (factorial of the # of groups) because the order of the groups is not important (we don't have the group #1 and the group #2) and we need to get rid of the duplications.

Dividing a group into subgroups:
combinations-problems-95344.html
split-the-group-101813.html
9-people-and-combinatorics-101722.html
ways-to-divide-99053.html
combination-and-selection-into-team-106277.html
ways-to-split-a-group-of-6-boys-into-two-groups-of-3-boys-ea-105381.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 18

Kudos [?]: 293 [0], given: 11

GMAT ToolKit User
Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 28 Dec 2012, 01:39
Barkatis wrote:
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%


Here is my approach:

I first counted the possible creation of 2 subcommittees without restriction: \(\frac{6!}{3!3!}* \frac{3!}{3!}= 20\)
Then, I now proceed to counting the number of ways to create committee with Michael and Anthony together.

M A _ + _ _ _ = \(\frac{4!}{1!3!} * \frac{1!}{1!} = 4\)

MA could be in group#1 or group#2. Thus, \(=4*2 = 8\)

Final calculation: \(8/20 = 4/10 = 40%\)

Answer: C
_________________

Impossible is nothing to God.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6091
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 20 Jan 2014, 09:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6091
Followers: 340

Kudos [?]: 68 [0], given: 0

Premium Member
Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 26 Mar 2015, 08:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 25 May 2014
Posts: 24
GPA: 3.55
Followers: 0

Kudos [?]: 1 [0], given: 13

Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 08 Jun 2015, 08:24
Bunuel wrote:
Barkatis wrote:
Anthony and Michael sit on the six-member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?

A. 20%
B. 30%
C. 40%
D. 50%
E. 60%


First approach:
Let's take the group with Michael: there is a place for two other members and one of them should be taken by Anthony, as there are total of 5 people left, hence there is probability of 2/5=40%.

Second approach:
Again in Michael's group 2 places are left, # of selections of 2 out of 5 5C2=10 - total # of outcomes.
Select Anthony - 1C1=1, select any third member out of 4 - 4C1=4, total # =1C1*4C1=4 - total # of winning outcomes.
P=# of winning outcomes/# of outcomes=4/10=40%

Third approach:
Michael's group:
Select Anthony as a second member out of 5 - 1/5 and any other as a third one out of 4 left 4/4, total=1/5*4/4=1/5;
Select any member but Anthony as second member out of 5 - 4/5 and Anthony as a third out of 4 left 1/4, total=4/5*1/4=1/5;
Sum=1/5+1/5=2/5=40%

Fourth approach:
Total # of splitting group of 6 into two groups of 3: 6C3*3C3/2!=10
# of groups with Michael and Anthony: 1C1*1C1*4C1=4
P=4/10=40%

Answer: C.

Hope it helps.



Bunuel, my question is for your fourth approach: Why don't we have to divide "# of groups with Michael and Anthony: 1C1*1C1*4C1=4" by 2! anymore?



To expound.

For total # of groups:
6C3 to choose 3 people for first group.
3C3 to choose 3 people for second group.

(6C3)(3C3)/2! divide by 2! as order is not important.

For # groups with Michael and Anthony:

1C1 to choose 1st person for group 1, 1C1 to choose 2nd person for group 1, 4C1 to choose 3rd person for group 1 = 4
3C3 to choose 3 people for second group.

(1C1)(1C1)(4C1)(3C3) <-- how come we no longer need to divide this by 2! ?
Intern
Intern
avatar
Joined: 18 Oct 2014
Posts: 26
Followers: 0

Kudos [?]: 5 [0], given: 6

GMAT ToolKit User CAT Tests
Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 08 Jun 2015, 18:43
Hi!

Just a question here.

Number of ways to Divide 3 people out of 6 are- 6C3= 20 Ways
Number of ways by which 1st member is Michal, 2nd is Anthony and 3rd is anyone from remaining four are- 1X1X4= 4 ways
So probability= number of desired events/number of total events *100= 4/20*100= 20%
This is the probability of Michal and Anthony being present in group 1. Group 2 will also have the same probability of 20%. So total probability is 20+20=40%

Please suggest if I am wrong anywhere.
Thanks
Manager
Manager
User avatar
Joined: 14 Mar 2014
Posts: 130
Followers: 0

Kudos [?]: 61 [0], given: 90

Lampard and Terry sit on the six member board [#permalink] New post 10 Aug 2015, 07:33
Lampard and Terry sit on the six member board of directors for company X. If the board is to be split up into 2 three - person subcommittees, what percent of all the possible subcommittees that include Terry also include Lampard?

a. 20
b. 30
c. 40
d. 50
e. 60
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ :-)

Manager
Manager
User avatar
Joined: 14 Mar 2014
Posts: 130
Followers: 0

Kudos [?]: 61 [0], given: 90

Re: Lampard and Terry sit on the six member board [#permalink] New post 10 Aug 2015, 07:37
VenoMfTw wrote:
Lampard and Terry sit on the six member board of directors for company X. If the board is to be split up into 2 three - person subcommittees, what percent of all the possible subcommittees that include Terry also include Lampard?

a. 20
b. 30
c. 40
d. 50
e. 60



All Possible Subcommittees that has terry in it = T _ _ --> 5c2 = 10
Possible subcommittees that include Terry also include Lampard --> T L _ --> 4c1 = 4

Percentage = ( 4 /10 ) * 100 = 40

Option C
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos
¯\_(ツ)_/¯ :-)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29100
Followers: 4722

Kudos [?]: 49623 [0], given: 7400

Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 10 Aug 2015, 07:47
Expert's post
VenoMfTw wrote:
Lampard and Terry sit on the six member board of directors for company X. If the board is to be split up into 2 three - person subcommittees, what percent of all the possible subcommittees that include Terry also include Lampard?

a. 20
b. 30
c. 40
d. 50
e. 60


PLEASE SEARCH BEFORE POSTING A QUESTION.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 26 Jul 2015
Posts: 21
Followers: 0

Kudos [?]: 0 [0], given: 12

GMAT ToolKit User
Re: Anthony and Michael sit on the six-member board of directors [#permalink] New post 11 Aug 2015, 21:16
Bunuel, some day you should take this test and DEMOLISH it.
http://www.matrix67.com/iqtest/

Cheers!

Jawad
Re: Anthony and Michael sit on the six-member board of directors   [#permalink] 11 Aug 2015, 21:16
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Anthony and Michael sit on the six member board od directors srivas 11 27 Sep 2009, 01:51
24 Experts publish their posts in the topic Anthony and Michael sit on the six-member board of directors arora2m 11 04 Nov 2009, 16:28
33 Experts publish their posts in the topic Anthony and Michael sit on the six member board of directors kamilaak 43 23 Jan 2008, 06:12
13 Experts publish their posts in the topic Anthony and Michael sit on the six-member board of directors aliensoybean 21 02 Jan 2008, 13:50
5 Experts publish their posts in the topic Anthony and Michael sit on the six-member board of directors cool_jonny009 12 05 Feb 2006, 21:35
Display posts from previous: Sort by

Anthony and Michael sit on the six-member board of directors

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.