An engagement team consists of a project manager, team

Expert replies

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Thu Sep 27, 2018 1:55 pm

Timer

00:00

Answers

Stats

Difficulty—

Source: Manhattan Prep

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

The OA is C.

Like this post

Source: Beat The GMAT — Problem Solving | Thu Sep 27, 2018 1:55 pm

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Sep 27, 2018 5:43 pm

BTGmoderatorLU wrote:Source: Manhattan Prep

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

The OA is C.

For this question, let's first ignore the restriction regarding the two consultants who refuse to work together and find the total number of different teams.
Then we'll determine how many of those teams break the rule about the two consultants.

In other words, # of "good" teams = Total number of teams (ignoring the restriction) - # of "bad" teams (that break the rule)

Total number of teams (ignoring the restriction)
Take the task of building teams and break it into stages.

Stage 1: Select a project manager
There are 2 candidates for this position, so we can complete stage 1 in 2 ways

Stage 2: Select a team leader
There are 3 candidates for this position, so we can complete stage 2 in 3 ways

Stage 3: Select the four consultants
Since the order in which we select the consultants does not matter, we can use combinations.
We can select 4 consultants from 7 consultants in 7C4 ways (35 ways)

If anyone is interested, we have a video on calculating combinations (like 7C4) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus build our team) in (2)(3)(35) ways ( = 210 ways)

# of "bad" teams (that break the rule)
Take the task of building "bad" teams and break it into stages.

Stage 1: Select a project manager
There are 2 candidates for this position, so we can complete stage 1 in 2 ways

Stage 2: Select a team leader
There are 3 candidates for this position, so we can complete stage 2 in 3 ways

Stage 3: Select four consultants
Here, we want to break the rule. So, let's place the two bickering consultants on the team.
So, for this stage, we need only select two other consultants to join them.
Since the order in which we select the 2 remaining consultants does not matter, we can use combinations.
We can select 2 consultants from the remaining 5 consultants in 5C2 ways (10 ways)

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus build our "bad" team) in (2)(3)(10) ways ( = 60 ways)

So, # of "good" teams = 210 - 60
= 150
= C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Tue Oct 09, 2018 9:43 am

BTGmoderatorLU wrote:Source: Manhattan Prep

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

We can select the project manager in 2 ways and the team leader in 3 ways. For the consultants, there are 7 candidates for 4 positions, but 2 of the 7 cannot be together.

We can use the following equation:

# of ways to select the consultants = # of ways with the 2 together + # of ways with the 2 not together.

The total number of ways to select the consultants is 7C4 = 7!/[4!(7-4)!] = 7!/(4!3!) = (7 x 6 x 5 x 4)/4! = 7 x 6 x 5 x 4)/(4 x 3 x 2) = 35.

The number of ways to select the consultants when the 2 are together can be found by choosing 2 people for the remaining slots from the 5 remaining candidates, which is given by 5C2 = (5 x 4)/2 = 10.

Thus, the number of ways to select the consultants when the 2 are not together is 35 - 10 = 25.

So, the total number of ways to select the teams is 2 x 3 x 25 = 150.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review