Allison and Barbara are part of an 8-member dance troupe.

Expert replies

Previous Topic Next Topic

swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Jun 27, 2018 9:31 am

Timer

00:00

Answers

Stats

Difficulty—

Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

The OA is B.

Please, can anyone explain this PS question? I can't get the correct answer. I need help. Thanks.

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 27, 2018 9:31 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Jun 27, 2018 10:14 am

Hi swerve,

We're told that Allison and Barbara are part of an 8-member dance troupe and that the troupe will be divided into two 4-person ensembles (with each ensemble performing a specialized dance). We're asked for the fraction of all the possible ensembles that include Allison AND Barbara. This question is a 'Combination Formula' question with a 'twist.'

Since there are 8 members and we're forming groups of 4, there will be 8!/4!(8-4)! = (8)(7)(6)(5)/(4)(3)(2)(1) = 70 possible groups of 4 for the 1st group.

The 'twist' is that once you have your 1st group of 4, the other 4 people will also form a DIFFERENT group of 4. In simple terms, Allison could be in the 1st group OR the 2nd group, so we have to consider both options.

Allison will take 1 of the 4 spots in a group, and if Barbara takes one of the other spots, then there would be 2 spots left for the 6 remaining dancers. The number of ways in which that could occur is 6!/2!(4!) = (6)(5)/(2)(1) = 15 groups of 4 with Allison AND Barbara.

Thus, the probability that Allison and Barbara would be on the 1st group is 15/70 = 3/14. However, since there are TWO groups (the 1st group and the 2nd group), the overall probability of Allison and Barbara being on the SAME group (regardless of which one it is) is (2)(3/14) = 6/14 = 3/7.

Final Answer: B

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

Contact Rich at [email protected]

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Jun 27, 2018 11:34 am

swerve wrote:Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

There are 7 people besides Allison.
From this pool of 7 people, 3 must be selected to join Allison's 4-person ensemble.
Thus -- from the pool of 7 people -- the probability that Barbara is among the 3 people selected = 3/7.

The correct answer is B.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

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 » Wed Jun 27, 2018 12:10 pm

swerve wrote:Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

The OA is B.

Please, can anyone explain this PS question? I can't get the correct answer. I need help. Thanks.

Asking,"What fraction of all the possible ensembles that include Allison will also include Barbara?" is the same as asking, "What is the probability that Allison are Barbara are in the same troupe?

Step 1: Place Allison in one of the troupes.

Step 2: Choose the 3 remaining people to be in Allison's troupe.
Ask, "What is the probability that Barbara is one of the 3 chosen?"
There are 7 people who can fill the remaining 3 spots in Allison's troupe.
So, Barbara has a 3/7 chance of being in Allison's troupe.

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Mon Jul 02, 2018 9:07 am

swerve wrote:Allison and Barbara are part of an 8-member dance troupe. For the upcoming spring recital, the troupe will be divided into two 4-person ensembles and each ensemble will perform a specialized dance. What fraction of all the possible ensembles that include Allison will also include Barbara?

A. 1/4
B. 3/7
C. 1/2
D. 3/4
E. 6/7

Let's first determine the number of ensembles that include Allison. Suppose that Allison has been chosen for one of the ensembles. The three remaining people in the ensemble can be chosen in 7C3 = (7 x 6 x 5)/(3 x 2) = 35 different ways.

Now, let's determine the number of ensembles that include both Allison and Barbara. Suppose that they are both chosen as members in one of the ensembles. The remaining two people can be chosen in 6C2 = (6 x 5)/(2 x 1) = 15 different ways.

Thus, 15/35 = 3/7 of all the possible ensembles that include Allison also include Barbara.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[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