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Four staff members at a certain company worked on a project [#permalink]

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27 Feb 2012, 10:03

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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?

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

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240; If 3x = 30 then 16x = 160; If 5x = 30 then 16x = 96; If 6x = 30 then 16x = 80;

Re: Four staff members at a certain company worked on a project [#permalink]

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21 Mar 2012, 00:16

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well 192 is a multiple of 16, where x=12. since for x=12, no person in the company can have worked 30 hrs, hence 192 cannot be the total hours... that is my understanding... am i correct???

well 192 is a multiple of 16, where x=12. since for x=12, no person in the company can have worked 30 hrs, hence 192 cannot be the total hours... that is my understanding... am i correct???

That's correct. Another approach is given in my previous post.
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Re: Four staff members at a certain company worked on a project [#permalink]

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12 Sep 2013, 09:41

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Re: Four staff members at a certain company worked on a project [#permalink]

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13 Nov 2014, 08:35

Bunuel wrote:

BANON wrote:

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

A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.

If 2x = 30 then 16x = 240; If 3x = 30 then 16x = 160; If 5x = 30 then 16x = 96; If 6x = 30 then 16x = 80;

Only answer choices which is not obtained is 192.

Answer: D.

Thanks Brunel

Just a thought, I used the same concept but only used the last digits

If 2x = 30 then 16x = 240; (eliminate 240,160 and 80) If 3x = 30 then 16x = 160; If 5x = 30 then 16x = 96; (Eliminate 96) If 6x = 30 then 16x = 80;

Re: Four staff members at a certain company worked on a project [#permalink]

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12 Apr 2016, 23:03

Hello from the GMAT Club BumpBot!

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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

Solution:

We are given that the amounts of time that the four members worked on the project were in the ratio 2 to 3 to 5 to 6. A straightforward approach is to create a ratio with x multipliers. The ratio becomes: 2x : 3x : 5x : 6x, where 2x was person 1’s time, 3x was person 2’s time, 5x was person 3’s time, and 6x was person 4’s time.

From this information, we can determine that the total time worked by all the members is the sum of our ratios: 2x + 3x + 5x + 6x = 16x.

We are also given that one of the members worked for 30 hours. Thus, we can create 4 different equations to get 4 different possible x values.

Option 1) If Person 1 was the individual who worked 30 hours, then 2x = 30 and x = 15

Option 2) If Person 2 was the individual who worked 30 hours, then 3x = 30 and x = 10

Option 3) If Person 3 was the individual who worked 30 hours, then 5x = 30 and x = 6

Option 4) If Person 4 was the individual who worked 30 hours, then 6x = 30 and x = 5

The above results show the 4 different options for the total number of hours an individual staff member worked.

Now, remember that the entire group worked for 16x hours. We substitute each of the 4 possible values for x into this expression:

Option 1: 16x = (16) (15) = 240 hours

Option 2: 16x = (16) (10) = 160 hours

Option 3: 16x = (16) (6) = 96 hours

Option 4: 16x = (16) (5) = 80 hours

The only value that we did not get was 192 hours, so D is the correct answer.
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Re: Four staff members at a certain company worked on a project [#permalink]

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03 Jun 2016, 21:50

2:3:5:6 is the ratio of hours that the four employees worked. This means that: 1 employee worked 2/16 of the total hours 1 employee worked 3/16 of the total hours 1 employee worked 5/16 of the total hours 1 employee worked 6/16 of the total hours

Knowing this, we can divide 30 by the answer choices to make sure it matches up with one of the above. Essentially I plugged in to find the solution to this problem.

A.) 30 hours/ 80 total hours = 6/16 which is good B.) 30 hours/ 96 total hours = 5/16 which is good C.) 30 hours/160 total hours = 3/16 which is good

At this point I know the answer is either C or D, and I do not like the idea of plugging in D.) so I skip straight to E.) E.) 30 hours/240 total hours = 2/16 which is good ---> the answer is D.)

Concentration: International Business, General Management

Re: Four staff members at a certain company worked on a project [#permalink]

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03 Jun 2017, 00:57

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Brute Force: You know the ratio is 2x:3x:5x:6x =16x Now you can set 16x equal to all the answer options and see which one when you calculate through the options yields 30. So each option except one does contain one member that worked 30 hours. For A) x yields 5 so 6*5=30 -->wrong B) x yields 6 5*6= 30 -->wrong C) x yields 10 3*10=30 --> wrong D) x yields 12 when you calculate through you see nothing yields 30 --> bingo E) x yields 15 2*15 =30 -->wrong The moment you figured out D does not yield a 30 you can stop working

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