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

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

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27 Feb 2012, 09:03
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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?

A. 80
B. 96
C. 160
D. 192
E. 240
[Reveal] Spoiler: OA

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

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27 Feb 2012, 12:31
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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.

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

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20 Mar 2012, 23:16
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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???

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

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20 Mar 2012, 23:29
monalimishra wrote:
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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13 Nov 2014, 07:35
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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.

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;

You can then deduce the answer quicker

Cheers

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

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13 Nov 2014, 21:25

Ratio = 2x:3x:5x:6x > Total = 16x

Any one has worked for 30 Hrs. We have to check condition for all 4.

So, multiple 30 * 16 = 480

The given OA should divide 480 properly; the result should come up anything of 2, 3, 5, 6

only 192 is unable to divide
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Four staff members at a certain company worked on a project. The [#permalink]

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11 Apr 2015, 07:33
According to the question
2:3:5:6 [Dividing by 2]
1:3:5:3 [now dividing by 3]
1:1:5:1

Now adding the ratios : 1+1+5+1 = 8
All the options is divisible by 8 except 192, Thus Answer is D. Please write I did wrong.
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Re: Four staff members at a certain company worked on a project [#permalink]

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02 May 2016, 08:03
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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

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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10 May 2016, 17:22
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Attached is a visual that should help.
Attachments

Screen Shot 2016-05-10 at 5.52.54 PM.png [ 56.16 KiB | Viewed 9062 times ]

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

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03 Jun 2016, 20:50
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.)

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

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02 Jun 2017, 23:57
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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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Re: Four staff members at a certain company worked on a project [#permalink]

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18 Dec 2017, 06:58
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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

Concept Involved

Take any Ratio: $$\frac{A}{B}$$ = $$\frac{3}{4}$$
Becomes $$\frac{A}{B}$$ = $$\frac{3x}{4x}$$

Since its a Ratio we do not know the total elements, values represent. But we do know this
Total = 3x +4x= 7x
It will be some multiple of 7

Using this concept as iteration we can
Total for entire staff as : 2x + 3x + 5x + 6x= 16x
Total will be some multiple of sixteen

Since we have total hours (30) for one of the staff members, we will get four different multipliers.
2x=30 : x=15
3x=30 : x=10
5x=30 : x=6
6x=30 : x=5

Using these multipliers By Trial and error you would quickly realise Answer is D

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

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26 Dec 2017, 05:56
niks18 Bunuel amanvermagmat

Quote:
If one of the four staff members worked on the project for 30 hours,

Is this statement in Q stem required to be given? LCM of 2,3,5 and 6 is 30. Can I leverage this info to arrive
at solution?
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Re: Four staff members at a certain company worked on a project [#permalink]

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26 Dec 2017, 07:34
niks18 Bunuel amanvermagmat

Quote:
If one of the four staff members worked on the project for 30 hours,

Is this statement in Q stem required to be given? LCM of 2,3,5 and 6 is 30. Can I leverage this info to arrive
at solution?

What was your reason for finding LCM? 2,3,5,& 6 are the ratio of time worked by each, finding LCM will not help here. Even if you find the LCM and it happens to be 30 here you cannot say that one of the staff worked for 30 hours and this info is required to calculate hours worked by others. In this question instead of 30 any other value can be used and options can be changed accordingly. In such a scenario, knowing that LCM is 30 will not help.

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Re: Four staff members at a certain company worked on a project   [#permalink] 26 Dec 2017, 07:34
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