Fraction w/no absolute numbers

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Zanardi: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Feb 21, 2011 10:35 am

by Zanardi » Mon Feb 21, 2011 10:44 am

I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

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Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Mon Feb 21, 2011 11:04 am

1st classrom --> # seats n, occupied n/2
2nd classroom --> # seats 2n, occupied 6n/4
3rd classroom --> # seats (n+2n), occupied (n/2 + 6n/4)
ratio --> (n/2 + 6n/4)/3n=2n/3n=2/3

IOM [spoiler]2/3[/spoiler]

Zanardi wrote:I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

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gmatmachoman: Legendary Member; Posts: 2326; Joined: Mon Jul 28, 2008 3:54 amFollowed by: 2 members; Thanked: 173 times; GMAT Score:710

by gmatmachoman » Mon Feb 21, 2011 11:04 am

X= number of seats in a room.

Room 1 : X

Occupied X/2

Room 2 : 2X

Occupied : 3/4 * 2X = 3/2 X

Combined seating capacity ( Room 3) = Total capacity of Room 1 +Total capacity of Room 2
= X+2X
= 3X

Occupied seats : X/2 + 3/2 X
: 2X

Question asks for fraction of seats occupied over total capacity:

= 2X/ 3X
= 2/3
= 66.6%

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ikaplan: Master | Next Rank: 500 Posts; Posts: 181; Joined: Fri Sep 04, 2009 12:06 pmFollowed by: 1 member; Thanked: 17 times

by ikaplan » Mon Feb 21, 2011 11:09 am

I would use picking numbers for this one.

First classroom: capacity --> 6, occupied--> 1/2*6= 3
Second classroom: capacity --> 12, occupied --> 3/4*12=9
Third classroom: capacity --> 6+12=18, occupied --> 9+3=12

ratio=12/18=2/3

IMO [spoiler]2/3[/spoiler]

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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 » Mon Feb 21, 2011 12:43 pm

Zanardi wrote:I am currently stuck on this single problem:

In one classroom exactly 1/2 of the seats are occupied. In another classroom with double the seating capacity of the first, exactly 3/4 of the seats are occupied. If the students from both classrooms are transferred into a third empty classroom that has a seating capacity exactly equal to the first two combined, what fraction of the seats in the third classroom are occupied?

Thank you for any assistance.

We can plug in values that satisfy the conditions given. Let A = smaller classroom and B = larger classroom.

Plug in A = 2 seats.
Number of seats occupied in A = 1/2 * 2 = 1.
Since B is twice as big as A, B = 2*2 = 4 seats.
Number of seats occupied in B = 3/4 * 4 = 3.
Total seats occupied = 1+3 = 4.
Total seats combined = A+B = 2+4 = 6.
Total occupied/Total seats = 4/6 = 2/3.

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Zanardi: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon Feb 21, 2011 10:35 am

by Zanardi » Mon Feb 21, 2011 12:56 pm

Thanks for all the replies!

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