BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2499
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members

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

by swerve » Wed Jun 27, 2018 9:31 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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.
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
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]
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
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
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
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
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

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]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1