ECONOMY CARS? (PRINCETON)

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu May 07, 2009 4:11 am

ONE WEEK A CERTAIN CAR RENTAL RENTED 4/5 OF ITS CARS, INCLUDING 3/4 OF ITS ECONOMY CARS. IF 2/3 OF ITS CARS ARE ECONOMY CARS, WHAT % OF THE CARS THAT WERE NOT RENTED WERE ECONOMY CARS? (PRINCETON)
A: 33 1/3%
B: 50%
C: 66 2/3%
D: 75%
E: 83 1/3%

The sender called it a PRINCETON question with no answer, and IMO E

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Source: Beat The GMAT — Problem Solving | Thu May 07, 2009 4:11 am

Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

Re: ECONOMY CARS? (PRINCETON)

by Vemuri » Thu May 07, 2009 4:31 am

IMO E.

Lets assume there are 120 cars.
Economy cars are = 2/3*120 = 80
Rented cars = 4/5*120 = 96 (this also includes the 3/4 * 80 = 60 economy cars)

Not rented cars = 120-96 = 24
Not rented economy cars = 80-60 = 20

x% * 24 = 20 ==> x% = 20/24 ==> x% = 5/6 (i.e. 83.3%)

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Thu May 07, 2009 4:38 am

i get E as well.

becomes easier to visualize with a matrix.

let the total number of cars be 60 (5*4*2), so that we have easier integral numbers to work with

Rented cars=4/5*60=48
=>Non Rented cars=12
Eco cars= 2/3*60=40
=> Non Eco cars=20
Eco+Rented cars=3/4*40=30
=>Eco+Non Rent cars=40-30=10

or 10/12=83.3%, hence E

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