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# The amount of time that three people worked on a special project was

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Math Expert
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The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 03:16
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The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Re: The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 03:36
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Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

Solution -

Time is in the ratio 2:3:5
Total time taken for the project = 110hrs

1st person time taken = (2/10)*110 = 22 hrs
2nd person = (3/10)*110 = 33 hrs
3rd person = (5/10)*110 = 55 hrs
How many more hours did the hardest working person work than the person who worked the least = 55 - 22 = 33 hours
ANS C
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Re: The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 04:07
Let the persons be A, B, C.

Hours worked:
A = 2*110/10 = 22 hours
B = 3*110/10 = 33 hours
C = 5*110/10 = 55 hours

C is the hardest worker and A worked for the least number of hours. So the difference is 55-22 = 33 hours.
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Re: The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 06:30
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Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

2+3+5=10--->110hours
So 1 unit (or x) of the ratio is 11 hours.

Hardest working - Least Working = 5x-2x=3x
x=11
Therefore, 3x=3*11=33

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The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 07:24
a LOT easier than I first thought, but that's what I suppose the question was testing, comprehension, etc. A simple ratio would solve the problem.

Time is given as a ratio: $$2x:3x:5x$$, sum $$10x$$
Work is given in hours: $$110$$ hours
Thus, each person works $$11$$ times their time ratio

Hardest working (most hours presumably) - person who has least amount of hours =
$$55 - 22 = 33$$

OR, differece of two ratios $$5-2 = 3$$. Ratio $$3x * 11 = 33$$. Since the integrity of the ratio is maintained, this method works too.

Thus, C.

Suppose back solving would be another approach, less efficient, mind you.
A. 55 hours, impossible since the range of the ratio limits the multiple to 3x
B. 44 hours, impossible since the range of the ratio limits the multiple to 3x
C. 33 hours, most correct answer
D. 22 hours, trick answer. If range is sought, then the range must not be less than 3x.
E. 11 hours, trick answer. If range is sought, then the range must not be less than 3x.

Thanks,
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Re: The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 08:55
1
KUDOS
Let x be common multiplier

So least hard working person worked for 2x hours
next person worked for 3x hours
most hard working person worked for 5x hours

In total the worked for 2x+3x+5x hours = 110
10x =110
x=11

So difference between least and most hard working person = 5(11) - 2(11) = 33

Ans C
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Re: The amount of time that three people worked on a special project was [#permalink]

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03 Jul 2015, 18:45
Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

Ratio of the Time taken by A:B:C = 2:3:5

i.e. If, A = 2x, then B = 3x and C = 5x

i.e. Total Time taken by all three of them together = 2x + 3x + 5x = 10x = 110 hours (Given)

i.e. x = 110/10 = 11

i.e. Time of A = 2x = 2*11 = 22 (Least Working Person)
i.e. Time of B = 3x = 3*11 = 33
i.e. Time of C = 5x = 5*11 = 55 (Hardest Working Person)

Extra No. of Hours worked by Hardest working Person more than Least Working Person = 55 - 22 = 33

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Re: The amount of time that three people worked on a special project was [#permalink]

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04 Jul 2015, 09:02
1
KUDOS
Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

Let the no of hours each employee worked be 2x,3x and 5x
Now, 2x+3x+5x=110
x=11
Therefore, difference betwen 2x and 5x=55-22=33 hours
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The amount of time that three people worked on a special project was [#permalink]

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04 Jul 2015, 09:10
Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

The ratios of time spent is 2:3:5. Thus, the times spent by each person is 2x, 3x and 5x, with the total being 10x

Given, 10x=110 >> x=11. The difference between the times spent by the hardest worker and the least worked worker = 5x-2x=3x= 3*11 = 33 hours. Thus C is the correct answer.

Bunuel, the language of this questions is vague. We need to assume that 'hardest' and 'least' work is directly proportional to the amount of time spent. A better way to phrase this question will be to ask what is the difference in the most time spent and the least time spent. The quantity or quality of work can not be determined by just relying on time spent.
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The amount of time that three people worked on a special project was [#permalink]

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04 Jul 2015, 10:10
C is correct
Time is in the ratio 2:3:5
Total time taken for the project = 110hrs

1st person time taken = (2/10)*110 = 22 hrs
2nd person = (3/10)*110 = 33 hrs
3rd person = (5/10)*110 = 55 hrs
Hours between hardest working person work than the person who worked the least = 55 - 22 = 33 hours
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Posts: 43785
Re: The amount of time that three people worked on a special project was [#permalink]

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06 Jul 2015, 05:25
Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

Kudos for a correct solution.

MANHATTAN GMAT OFFICIAL SOLUTION:

Use an equation with the Unknown Multiplier to represent the total hours put in by the three people:

2x + 3x + 5x= 110
10x = 110
x= 11

Therefore, the hardest working person put in 5(11) = 55 hours, and the person who worked the least put in 2(11) = 22 hours. This represents a difference of 55 - 22 = 33 hours.

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Re: The amount of time that three people worked on a special project was [#permalink]

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Re: The amount of time that three people worked on a special project was [#permalink]

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15 Mar 2017, 15:46
Bunuel wrote:
The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, how many more hours did the hardest working person work than the person who worked the least?

A. 55 hours
B. 44 hours
C. 33 hours
D. 22 hours
E. 11 hours

We are given that the amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. We can create the following ratio:

person working least : person working 2nd least : person working most = 2x : 3x : 5x

Since the project took a total of 110 hours, we can create the following equation:

2x + 3x + 5x = 110

10x = 110

x = 11

Thus, the person who worked the most number of hours worked for 5 * 11 = 55 hours and the person who worked the least worked for 2 * 11 = 22 hours. The difference between the two values is 55 - 22 = 33 hours.

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Re: The amount of time that three people worked on a special project was   [#permalink] 15 Mar 2017, 15:46
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