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

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Senior Manager
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Four staff members at a certain company worked on a project. [#permalink] New post 09 Aug 2006, 08:51
Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 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

Guys, is there an easier way of solving this problem aside from plugging in? I recall solving a similar problem wherein you just add all of the ratios and see if the answer choices are divisible by the sum. In the case all are divisible. Is that the correct way of going about it?
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 [#permalink] New post 09 Aug 2006, 09:10
one of the members works for 30 hours.
total number of hours can be found as

2x+3x+5x+6x=T

if one person works for 30 hours then x can be either 15, 10, 6 or 5.

take 15 , 10 or 5 so the sum of all will either have 5 or 0 in the units place.

Now take 6. the Total will be 12+18+30+36 = 96

Hence, the Answer is D.
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 [#permalink] New post 09 Aug 2006, 09:26
Answer: D

If one of the workers worked for 30 hrs, multiples of the ratios are 15, 10, 6, 5

A. 80/16 = 5
B. 96/16 = 6
C. 160/16 = 10
D. 192/16 = 12
E. 240/16 =15

Of these only D is not a multiple.
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 [#permalink] New post 09 Aug 2006, 09:32
We only need the ratio.

Ratio = 2:3:5:6
For any member the number of hours worked will be = Ratio * Total hours/(2+3+5+6 = 16)
One of the person worked for 30 hours.

So 1/16 for all choices is
A- 5 - Possible for 6*5
B - 6 - Possible for 5*6
C - 10 - Possible for 3
D - 12 - Not possible for anybody: ANSWER
E - 15 - Possible for 15*2
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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 [#permalink] New post 09 Aug 2006, 21:33
Thanks guys,

Learned something new again :-D
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 [#permalink] New post 10 Aug 2006, 03:23
D

Let 30 hrs is spent by the first worker
Hence total number of hrs = 30*16/2 = 240

Similarily
when second worker spends 30hr
Total number =30*16/3 = 160

When 3rd person spends 30 hrs
total = 30*16/5 = 96

When 4th person spends 30 hrs
total = 30*16/6 = 80

hence 192 is the only number of hrs that cannot be spent by all the workers.
  [#permalink] 10 Aug 2006, 03:23
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