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The amounts of time that three secretaries worked on a

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fiendex
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The amounts of time that three secretaries worked on a [#permalink] New post   07 Feb 2012, 02:12
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The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?

A) 80
B) 70
C) 56
D) 16
E) 14
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B
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   07 Feb 2012, 02:28
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8x = 112
=> x = 14

Therefore the secretary who worked the longest spent 14 x 5 = 70 hours on the project

Option (B)
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   07 Feb 2012, 05:05
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fiendex wrote:
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longet spend on the project?

A) 80
B) 70
C) 56
D) 16
E) 14


Since, amounts of time that secretaries worked in the ratio of 1 to 2 to 5, then \(\frac{\frac{1x}{2x}}{5x}\), for some number x --> x+2x+5x=8x=112 --> x=14 --> the secretary who worked the longet spent 5x=70 hours.

Answer: B.
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   07 Feb 2012, 06:53
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All three secretaries worked 112h and with a ratio of 1to2to5

8x = 112h
x = 14h

5*14h = 50h --> B
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   23 May 2017, 02:48
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fiendex wrote:
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?

A) 80
B) 70
C) 56
D) 16
E) 14


Similar question: https://gmatclub.com/forum/the-amount-o ... 01139.html
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   25 May 2017, 15:48
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fiendex wrote:
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?

A) 80
B) 70
C) 56
D) 16
E) 14


The ratio of the amounts of time that the secretaries worked on the project is x : 2x : 5x or a total of 8x.

Since the total number of hours is 112:

8x = 112

x = 14

The secretary who worked the longest worked for 5x = 5(14) = 70 hours.

Answer: B
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The amounts of time that three secretaries worked on a [#permalink] New post   08 Dec 2017, 19:36
\(\frac{5}{8ths}\)of the time was spent by the longest working secretary. So the answer is more than 56. An eighth of
112 is 14. 56+14=70
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   09 Oct 2020, 05:08
OFFICIAL GMAT EXPLANATION

Since the ratio of hours worked by the secretaries on the project is 1 to 2 to 5, the third secretary spent the longest time on the project, that is, (5/8)(112) or 70 hours. The best answer is therefore B.
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The amounts of time that three secretaries worked on a [#permalink] New post   10 Dec 2020, 08:49
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fiendex wrote:
The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5. If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?

A) 80
B) 70
C) 56
D) 16
E) 14


The amounts of time that three secretaries worked on a special project are in the ratio of 1 to 2 to 5
1 + 2 + 5 = 8
So the above information is telling us that, for every 8 hours worked, the first secretary worked 1 hour, the second secretary worked 2 hours, and the third secretary worked 5 hours.
In other words, of the 3 secretaries contributed to 1/8, 2/8 and 5/8 of the job.

If they worked a combined total of 112 hours, how many hours did the secretary who worked the longest spend on the project?
The secretary who worked the longest is the one who contributed 5/8 of the job.
Since the job took a total of 112 hours, the number of hours that secretary worked = 5/8 of 112
= 5/8 x 112
= 70 hours

Answer: B
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Re: The amounts of time that three secretaries worked on a [#permalink] New post   18 May 2023, 01:33
Let's denote the amounts of time worked by the secretaries as x, 2x, and 5x, respectively. We are given that the combined total of their hours is 112.

Therefore, we have the equation:
x + 2x + 5x = 112

Combining like terms, we get:
8x = 112

Dividing both sides by 8, we find:
x = 14

So, the secretary who worked the longest spent 5x = 5 * 14 = 70 hours on the project.

Therefore, the correct answer is (B) 70.
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Re: The amounts of time that three secretaries worked on a [#permalink]
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