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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 06, 2011 12:57 pm

A director is deciding how to cast a play from a pool of 50 available actors and actresses. There are m male roles and n female roles. If each male actor can play any male part, and each female actress can play any female part, how many ways are there to cast the play?

(1) 60% of the acting pool is female.

(2) There are 116,280 ways to cast the male parts.

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 06, 2011 12:57 pm

edge: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jun 26, 2011 5:45 pm; Thanked: 2 times

by edge » Sat Aug 06, 2011 1:11 pm

What is the OA? Can you please post it along with your questions using spoiler tags?

My answer is E.

St1 just tells us that there are 20 male and 30 female actors available in the pool. Insufficient.
St2 tells us that if there are 'M' male actors and 'm' parts, MCm = 116280. Maybe m can be calculated here? Insufficient.

Taken together, they still don't provide any way to calculate the number of female parts available. Hence, total number of ways to cast the play (m x n) cannot be calculated.

Last edited by edge on Sat Aug 06, 2011 1:14 pm, edited 1 time in total.

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sat Aug 06, 2011 1:13 pm

E:
1. says 30 female actor and 20 male actor

2, says male can be cast in 116280 ways : so 30Cm = 116280 => !30/!m*!30-m = 116280
so one can find out how mant male roles are there.

but female roles can not be ascertain even after combining so E.

GmatKiss wrote:A director is deciding how to cast a play from a pool of 50 available actors and actresses. There are m male roles and n female roles. If each male actor can play any male part, and each female actress can play any female part, how many ways are there to cast the play?

(1) 60% of the acting pool is female.

(2) There are 116,280 ways to cast the male parts.

Charged up again to beat the beast

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sat Aug 06, 2011 1:18 pm

IMO:E

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goalevan: Master | Next Rank: 500 Posts; Posts: 111; Joined: Tue Dec 30, 2008 1:25 pm; Location: USA; Thanked: 28 times; GMAT Score:770

by goalevan » Sat Aug 06, 2011 5:14 pm

"What is M!/(M - m)! * F!/(F - m)! ?" or "What is MPm * FPf?"

To evaluate this quantity, the values of M (the number of males), m (the number of male roles), F (the number of females), and f (the number of female roles) must be known.

Statement 1) F = 60% * 50 = 30, so M = 50 - 30 = 20.

M and F are known, but m and f are still unknown. Insufficient.

Statement 2) M!/(M - m)! = 116,280

Both M and m could be calculated, and F could be calculated as 50 - M, but f would remain unknown. Insufficient.

Combined) f, the number of female roles, still remains unknown even with both statements.

116,280 * 30/(30 - 2)! gives a different result than
116,280 * 30/(30 - 10)!

Insufficient, E

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gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Sun Aug 07, 2011 11:03 pm

This doesn't change the answer, but I just wanted to comment that the GMAT will NEVER use a combinations/permutations question with a number like 116,280 involved. Especially when, to find m, you would need to solve:

116,280 = 20!/(20-m)!

Even though you don't actually need to find m to determine that the answer is E, every GMAT question has variables that can be reasonably solved for. This one does not. So, don't worry if the "calculations" on this question throw you off. You will never need to do them.

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czarczar: Master | Next Rank: 500 Posts; Posts: 106; Joined: Fri Feb 05, 2010 9:39 amFollowed by: 1 member; Thanked: 4 times

by czarczar » Mon Aug 08, 2011 8:49 am

E:

You still do not have value of F.

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navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Tue Aug 09, 2011 4:54 am

Interesting question
IMO E

This time no looking back!!!
Navami

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