secretaries

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pmFollowed by: 1 member; Thanked: 15 times; GMAT Score:690

by crackgmat007 » Sat Nov 07, 2009 4:07 pm

Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?

1 hour and 34 minutes
1 hour and 45 minutes
2 hours and 24 minutes
3 hours and 15 minutes
3 hours and 25 minutes

OA D

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

Re: secretaries

by Testluv » Sat Nov 07, 2009 4:52 pm

crackgmat007 wrote:Three secretaries working together can type 36 pages of text in half an hour. If the typing speeds of the secretaries are in a 4:3:2 ratio, how long will it take the slowest-typing secretary working alone to type 52 pages of text?

1 hour and 34 minutes
1 hour and 45 minutes
2 hours and 24 minutes
3 hours and 15 minutes
3 hours and 25 minutes

OA D

Hi crackgmat007,

Their speeds are in a 4:3:2 ratio. So, if we split the job into 9 (4+3+2) parts, the fastest secretary will have contribued 4/9 towards the job, the middle one 3/9, and the slowest secretary contributed 2/9 towards the job.

So, the slowest secretary manages 2/9 of 36 pages in a half an hour: 2/9 * 36 = 8 pages in a half an hour. Then, her rate per hour is 16 pages per hour.

It will take her 52/16 = 3.25 hours, or three hours and fifteen minutes to type 52 pages. Choose D.

Kaplan Teacher in Toronto

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vivek.kapoor83: Legendary Member; Posts: 833; Joined: Mon Aug 04, 2008 1:56 am; Thanked: 13 times

by vivek.kapoor83 » Mon Nov 09, 2009 4:10 am

let total x no. of pages
in 1 hr they will type
4x+3x+2x = 72 pages
x = 8
1st type = 4*8 = 32 pages/hr
2nd type = 24 pages/hr
3rd type = 2*8 = 16 pages/hr
So, for typing 52 pages
3 will take
3hr = 48 pages
and for 4 pages = 1/4hr = 15min
hence 3 hrs 15 min
Ans is D/

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