PS-2

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sparsh.21: Master | Next Rank: 500 Posts; Posts: 129; Joined: Tue Jul 22, 2008 3:53 am; Thanked: 2 times

by sparsh.21 » Sat Jan 03, 2009 10:53 am

Laura can paint 1/x of a certain room in 20 minutes. What
fraction of the same room can Joseph paint in 20 minutes if the two
of them can paint the room in an hour, working together at their
respective rates?

A. 1/3x
B. 3x/(x – 3)
C. (x – 3)/3x
D. x/(x – 3)
E. (x – 3)/x

OA

C

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Source: Beat The GMAT — Problem Solving | Sat Jan 03, 2009 10:53 am

amitabhprasad: Master | Next Rank: 500 Posts; Posts: 259; Joined: Thu Jan 18, 2007 8:30 pm; Thanked: 16 times

by amitabhprasad » Sat Jan 03, 2009 11:15 am

L -->1/x in 20 min ==> x/3 hrs to paint the room ==> she can paint 3/x part of room in 1 hrs
Say J can paint the room in y hrs ==> in 1 hrs J can paint 1/y par of room
Together
J+L can paint the room completely.
3/x+1/y => 3y+x = xy ==> y = x/x-3
in 1 hrs J will paint x-3/x thus in 20 min he will paint
(x-3)/3x

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bsandhyav: Master | Next Rank: 500 Posts; Posts: 116; Joined: Fri Aug 29, 2008 10:22 am; Location: Mumbai,India; Thanked: 1 times

Re: PS-2

by bsandhyav » Sat Jan 03, 2009 11:21 am

sparsh.21 wrote:Laura can paint 1/x of a certain room in 20 minutes. What
fraction of the same room can Joseph paint in 20 minutes if the two
of them can paint the room in an hour, working together at their
respective rates?

A. 1/3x
B. 3x/(x – 3)
C. (x – 3)/3x
D. x/(x – 3)
E. (x – 3)/x

OA

C

The basic formula that needs to be used here is : rate* time= work

rate(Laura) + rate(Joseph) = rate of both working together

rate of both working together = 1/60 ( i.e work/time)

Therefore (1/x)/20 + rate (Joseph) = 1/60
rate(Joseph) = (x-3)/(60*x)

so work(joseph)= rate*time
=(x-3)*20/(60*x)
= (x-3)/3x

Hence C

This is a purely algebric approach. Any body with a better solution?

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

by cramya » Sat Jan 03, 2009 11:32 pm

This is a purely algebric approach. Any body with a better solution

The one Amit/u did would be the safest, IMO. Plus its not time consuming by any means.. Solvable well within 2 minutes..

Regards,
CR

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Mozartain: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Tue Nov 11, 2008 8:38 pm; Thanked: 3 times; GMAT Score:740

by Mozartain » Sun Jan 04, 2009 4:23 am

I'd strive to avoid unnecessary calculations.

since both of them working together take an hour to paint the whole room, in 20 minutes they together can paint 1/3 of the room.

since Laura paints 1/x of it, Joseph does the rest, which is 1/3 - 1/x

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