Percentages

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Fri Dec 12, 2008 2:59 pm

A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?

(A) 10
(B) 20
(C) 40
(D) 60
(E) 80

OA is C

Abdulla

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Source: Beat The GMAT — Problem Solving | Fri Dec 12, 2008 2:59 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Fri Dec 12, 2008 3:33 pm

15% of 160 is women = 24

Let x represent people who left the room(30% of these are women + 10% of 160-x are women and these both must add up to the original number of women we found above i.e. 24)

.30x + .10(160-x) = 24

x=40

C)

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Abdulla: Master | Next Rank: 500 Posts; Posts: 328; Joined: Thu Aug 07, 2008 5:25 pm; Location: Philadelphia; Thanked: 4 times; GMAT Score:550

by Abdulla » Fri Dec 12, 2008 3:44 pm

always your approach is better than the Official Explantion..

Thanks

Abdulla

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canuckclint: Master | Next Rank: 500 Posts; Posts: 154; Joined: Tue Aug 26, 2008 12:59 pm; Location: Canada; Thanked: 4 times

by canuckclint » Fri Dec 12, 2008 6:24 pm

Found a good way to solve this algebraically.

Let x be people who left the room, y of which are women.
y/x = 30/100 --30% who left the room are women
(24-y)/(160-x) = 10/100 --people left in the room 10% are women

2400 - 100y = 1600 - 10x
800 = 100y - 10x
800 = 100(x*30/100) - 10x
800 = 20x
x = 40

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