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# Four staff members at a certain company worked on a project.

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Intern
Joined: 10 Aug 2007
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Four staff members at a certain company worked on a project. [#permalink]  16 Oct 2007, 09:17
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Four staff members at a certain company worked on a project. The amounts of tiem that the four staff members worked on the project were in the ratio 2 : 3 : 5 : 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project

A. 80
B. 96
C. 160
D. 192
E. 240

Manager
Joined: 02 Aug 2007
Posts: 146
Followers: 1

Kudos [?]: 14 [1] , given: 0

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KUDOS
Try plugging in 30 hours for each of the 4 staff members. Starting with the staff member working the least (2) = 30/2 = 15. Next multiply 15 with the remaining ratios and add to get total hours.

2: (2*15)+(3*15)+(5*15)+(6*15) = 240 hours
3: (3*10)+(2*10)+(5*10)+(6*10) = 160 hours
5: (5*6)+(2*6)+(3*6)+(6*6) = 96 hours
6: (6*5)+(2*5)+(3*5)+(5*5) = 80 hours

So by process of elimination = D. 192 cannot be a possibility
VP
Joined: 09 Jul 2007
Posts: 1108
Location: London
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Re: PS - Work Problem [#permalink]  16 Oct 2007, 11:28
alohagirl wrote:
Four staff members at a certain company worked on a project. The amounts of tiem that the four staff members worked on the project were in the ratio 2 : 3 : 5 : 6. If one of the four staff members worked on the project for 30 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project

A. 80
B. 96
C. 160
D. 192
E. 240

x=common factor

2x+3x+5x+6x=Y
16x=Y

so one of the answer choices is not Y, which is not multiple of 16

it is D. 192
Intern
Joined: 16 Apr 2007
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I don't its the right way, 192 is a multiple of 16, 192/16 = 12. So even that can be the answer.

Thanks
Mohan
Director
Joined: 09 Aug 2006
Posts: 766
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mohansb wrote:
I don't its the right way, 192 is a multiple of 16, 192/16 = 12. So even that can be the answer.

Thanks
Mohan

Though 192 is a multiple of 16, none of the ratios, 2, 3, 5, 6 yield a 30 when multiplied by 192/16=12. That is why 192 is the answer.
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