A dance team with 5 members will perform, 2 dancers at a

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri May 10, 2019 5:55 pm

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Source: Princeton Review

A dance team with 5 members will perform, 2 dancers at a time, until all the possible combinations of dancers have performed. If each combination dances for 5 minutes, and there are no breaks or interruptions, what is the total running time of the performance?

A. 80 minutes
B. 75 minutes
C. 60 minutes
D. 50 minutes
E. 45 minutes

The OA is D

Source: Beat The GMAT — Problem Solving | Fri May 10, 2019 5:55 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sat May 11, 2019 5:34 pm

Total combinations 5c2 = 10
and each set performs for 5 minutes
So, total time ; 10*5 = 50.

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by Scott@TargetTestPrep » Tue May 14, 2019 6:24 pm

BTGmoderatorLU wrote:Source: Princeton Review

A dance team with 5 members will perform, 2 dancers at a time, until all the possible combinations of dancers have performed. If each combination dances for 5 minutes, and there are no breaks or interruptions, what is the total running time of the performance?

A. 80 minutes
B. 75 minutes
C. 60 minutes
D. 50 minutes
E. 45 minutes

The OA is D

The number of combinations of dancers is 5C2 = (5 x 4)/2! = 10 and therefore the total running time of the performance is 10 x 5 = 50 minutes.

Answer: D

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Fri May 17, 2019 5:00 am

5 members with 2 dancers at a time;
$$Possible\ combination=5_{C_2}=\frac{5\cdot4}{2\cdot1}=\frac{20}{2}=10 ways$$
$$The\ the\ total\ runtime\ of\ 5\ \min utes\ per\ 10\ ways\ =\ 5\cdot10=50\ \min utes\ \ \ \ \ \left(option\ D\right)$$

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