Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 29 Mar 2017, 16:01

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# An engagement team consists of a project manager, team leade

Author Message
TAGS:

### Hide Tags

VP
Joined: 22 Nov 2007
Posts: 1090
Followers: 8

Kudos [?]: 531 [3] , given: 0

### Show Tags

31 Jan 2008, 22:09
3
KUDOS
29
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:56) correct 32% (02:07) wrong based on 666 sessions

### HideShow timer Statistics

An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Feb 2014, 00:07, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
CEO
Joined: 29 Mar 2007
Posts: 2575
Followers: 20

Kudos [?]: 436 [1] , given: 0

### Show Tags

31 Jan 2008, 22:47
1
KUDOS
1
This post was
BOOKMARKED
marcodonzelli wrote:
An engagement team consists of a project manager, team leader and four consultants. There are 2 candidates for the position of proj.manager, 3 for the position of team leader and 7 for 4 consultants slots. If 2 of the 7 consultants refuse to be on the same team, how many different team are possible?

25
35
150
210
300

I get C. If I see this on the test, id prolly get to 210 and then guess A B or C.

OK so for the first position we have only 2 possiblities ( proj manager) 3 for the team leader so and 7!/3!4! for the consultants

2*3*35 --> 210

Now I dunno how to figure out the constraints quickly but I eventually figured it out. Obvs. we want to figure out the total ways in which the two ARE on the same team.

I did it by AB are the two and XYZFN are the rest

ABXO (O stands for the other 4) So the first is ABXY, Z,F,N 4 possible choices

The next is

ABYO (but notice we already had YX so there are only 3 possible choices)
ABZO
ABFO
ABNO No possible here we used them all up

So 4+3+2+1 = 10

SO now its 2*3*10 =60

So 210-60 = 150
Director
Joined: 01 May 2007
Posts: 793
Followers: 1

Kudos [?]: 313 [0], given: 0

### Show Tags

01 Feb 2008, 10:15
1
This post was
BOOKMARKED
Following you up till the constraint part...Looking for a combo master to teach us how to do it by calculation and not by hand
Director
Joined: 01 Jan 2008
Posts: 626
Followers: 5

Kudos [?]: 180 [1] , given: 1

### Show Tags

01 Feb 2008, 10:25
1
KUDOS
3
This post was
BOOKMARKED
marcodonzelli wrote:
An engagement team consists of a project manager, team leader and four consultants. There are 2 candidates for the position of proj.manager, 3 for the position of team leader and 7 for 4 consultants slots. If 2 of the 7 consultants refuse to be on the same team, how many different team are possible?

25
35
150
210
300

2C1*3C1*(5C4+5C3*2C1)=2*3*(5+10*2)=6*25=150 -> C
Director
Joined: 01 May 2007
Posts: 793
Followers: 1

Kudos [?]: 313 [0], given: 0

### Show Tags

01 Feb 2008, 10:27
Can you explain this part is words:

(5C4+5C3*2C1)
Manager
Joined: 01 Jan 2008
Posts: 225
Schools: Booth, Stern, Haas
Followers: 2

Kudos [?]: 58 [1] , given: 2

### Show Tags

01 Feb 2008, 10:35
1
KUDOS
jimmyjamesdonkey wrote:
Can you explain this part is words:

(5C4+5C3*2C1)

yes, can you explain?
Director
Joined: 01 Jan 2008
Posts: 626
Followers: 5

Kudos [?]: 180 [6] , given: 1

### Show Tags

01 Feb 2008, 10:42
6
KUDOS
3
This post was
BOOKMARKED
jimmyjamesdonkey wrote:
Can you explain this part is words:

(5C4+5C3*2C1)

We can either choose 4 consultants from a group of 5 (5C4) who are willing to work with everyone or choose 3 from that group (5C3) and one person from the other group of 2 consultants (2C1) who don't want to work with each other.
Director
Joined: 01 May 2007
Posts: 793
Followers: 1

Kudos [?]: 313 [0], given: 0

### Show Tags

01 Feb 2008, 10:55
Very cool. Thanks. +1
Manager
Joined: 02 Jan 2008
Posts: 158
Followers: 2

Kudos [?]: 118 [9] , given: 0

### Show Tags

02 Feb 2008, 06:20
9
KUDOS
12
This post was
BOOKMARKED
To get the number of ways you can select 4 consultants, you can do this:

A. Total number of ways 4 can be selected out of 7 = 7C4 = 35
B. Total number of ways in which these two snobbish consultants are together (two are already there, so you just need to select rest two out of 5) = 5C2 = 10

A (minus) B results in 25 which can then be multiplied with (2C1*3C1) to result in 150
Senior Manager
Joined: 20 Dec 2004
Posts: 255
Followers: 6

Kudos [?]: 107 [1] , given: 0

### Show Tags

02 Feb 2008, 12:20
1
KUDOS
2C1*3C1*7C4 - 2C1*3C1*5C2 = 6[35-10] = 150.
_________________

Stay Hungry, Stay Foolish

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14559
Followers: 609

Kudos [?]: 175 [0], given: 0

Re: An engagement team consists of a project manager, team [#permalink]

### Show Tags

18 Feb 2014, 04:33
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.
_________________
Senior Manager
Joined: 17 Dec 2012
Posts: 446
Location: India
Followers: 27

Kudos [?]: 413 [2] , given: 14

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

10 Mar 2014, 23:34
2
KUDOS
3
This post was
BOOKMARKED
Answer= Total number combinations - Total number of combinations with constraints

Total number of combinations = 2C1*3C1*7C4= 210
Total number of combinations with constraints = 2C1*3C1*5C2=60

_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom and Online Coaching

Intern
Joined: 23 Apr 2014
Posts: 9
Followers: 0

Kudos [?]: 7 [2] , given: 2

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

14 May 2014, 03:46
2
KUDOS
2
This post was
BOOKMARKED
a) No of ways to select 1 Manager = 2c1 = 2
b) No of ways to select 1 Team leader = 3c1 = 3
c) No of ways to select 4 Consultants = 7c4 = 35
Therefore, possible teams without any constraint = 2x3x35 = 210

No of ways to select 4 Consultants out of 7 when 2 of them are always together = 6c4 x2! = 60

Therefore, possible teams with given constraint = 210 - 60 = 150

Hope its clear.
Intern
Joined: 02 May 2013
Posts: 24
Followers: 0

Kudos [?]: 18 [6] , given: 76

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

17 May 2014, 02:25
6
KUDOS
Well, probably the quickest way to do this problem is to

1) eliminate D & E, because we are pretty sure it is less than 210 (we know max is 2*3*35).
2) eliminate A & B, because we know 25 and 35 are not multiple of 6 (we know the combination will be an integer).
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14559
Followers: 609

Kudos [?]: 175 [2] , given: 0

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

29 Jun 2015, 11:24
2
KUDOS
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.
_________________
Senior Manager
Joined: 10 Mar 2013
Posts: 290
GMAT 1: 620 Q44 V31
GMAT 2: 690 Q47 V37
GMAT 3: 610 Q47 V28
GMAT 4: 700 Q50 V34
GMAT 5: 700 Q49 V36
GMAT 6: 690 Q48 V35
GMAT 7: 750 Q49 V42
GMAT 8: 730 Q50 V39
Followers: 10

Kudos [?]: 102 [1] , given: 2405

### Show Tags

21 Nov 2015, 12:21
1
KUDOS
srp wrote:
To get the number of ways you can select 4 consultants, you can do this:

A. Total number of ways 4 can be selected out of 7 = 7C4 = 35
B. Total number of ways in which these two snobbish consultants are together (two are already there, so you just need to select rest two out of 5) = 5C2 = 10

A (minus) B results in 25 which can then be multiplied with (2C1*3C1) to result in 150

Simple and straightforward! (Also, I used this method as well! )

2C2 * 5C2 = 1 * 10 = 10
We have 2C2, because we have already chosen the consultants in the group.
Intern
Joined: 19 Feb 2013
Posts: 3
Location: India
GMAT 1: 610 Q43 V31
Followers: 0

Kudos [?]: 5 [0], given: 81

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

13 Jul 2016, 05:05
marcodonzelli wrote:
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300

This is how I solved this question and got the answer incorrect.

Total Combinations - (the number of combinations in which A and B are always together) = Number of ways in which A and B won't work together

Assuming that A and B are the two consultants who don't want to work together.

Number of ways to choose 1 PM out of 2 candidates x Number of ways to choose 1 TL out of 3 candidates x Number of ways to choose 4 Consultants out of 7 candidates = Total

2 ways x 3 ways x 35 ways(7!/4!.3!) = 210 ways.

I got this right. However, somewhere in the next steps is where I made a mistake.

Number of ways in which A and B will work together and the rest two positions can be filled with the remaining 5 candidates.

2 x 3 x 1 x 1 x 5 x 4

So I subtracted 120 from 210.

However after following the answers here, I understood that for the remaining two positions, instead of doing a 5C2, I chose to fill them in 5 ways and 4 ways.

I would like to understand: 1) what sort of an error am I committing. 2When should I follow the approach I used above and when should I do a 5C2 logic.

Suggestions welcome. Thanks!

Regards,
Arvind.
Manager
Joined: 29 May 2016
Posts: 110
Followers: 0

Kudos [?]: 8 [0], given: 211

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

13 Jul 2016, 23:42
total teams 2c1 * 3c1* 7c4 = 210
let both be on same team and always selected so now we have to choose 2 out of remaining 5
total team when both candidates on same team will be 2c1 * 3c1* 5c2 = 60
210-60 = 150
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 8777
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 413

Kudos [?]: 2663 [1] , given: 168

### Show Tags

14 Jul 2016, 08:02
1
KUDOS
Expert's post
Hi All,

The answer choices to this question provide us with an interesting 'shortcut' that we can use to avoid some of the math involved.

Since there are 2 possible project managers and 3 potential team leaders, then the final answer MUST be a multiple of (2)(3) = 6.

Since we're choosing 4 of 7 possible consultants, we can use the Combination Formula:

7!/(4!3!) = 35 possible groups of 4 consultants.

IF there were no additional restrictions, then there would be (6)(35) = 210 possible groups. HOWEVER, we know that certain consultants won't work with other consultants, so the number of possible groups must be LESS than 210. Based on the answer choices, there's only one option that is a multiple of 6 and is less than 210...

[Reveal] Spoiler:
C

GMAT assassins aren't born, they're made,
Rich
_________________

Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

# Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 23 Sep 2016
Posts: 31
Followers: 0

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

Re: An engagement team consists of a project manager, team leade [#permalink]

### Show Tags

22 Dec 2016, 01:34
marcodonzelli wrote:
An engagement team consists of a project manager, team leader, and four consultants. There are 2 candidates for the position of project manager, 3 candidates for the position of team leader, and 7 candidates for the 4 consultant slots. If 2 out of 7 consultants refuse to be on the same team, how many different teams are possible?

A. 25
B. 35
C. 150
D. 210
E. 300

i did this question in this way
2c1 * 3c1* 5c4+5c3*2c1= 2*3*(5+5*4*2/2)=6*25=150
Re: An engagement team consists of a project manager, team leade   [#permalink] 22 Dec 2016, 01:34
Similar topics Replies Last post
Similar
Topics:
A basketball team’s current roster consists of g guards and f forwards 1 07 Mar 2017, 02:02
1 An "integrated" team consists of 2 members from the engineering team 2 06 Jun 2016, 05:13
A research team is to consist of 3 scientists from Company A 1 08 Oct 2014, 04:09
3 The school soccer team consists entirely of freshmen and s 4 12 Mar 2013, 01:16
There are 12 co-workers who work on projects in teams each month. Each 4 16 Dec 2010, 01:40
Display posts from previous: Sort by