At a post office last week, 25 percent of the employees were part-time

Question

At a post office last week, 25 percent of the employees were part-time employees and the rest were full-time employees. Each of the part-time employees worked \(\frac{3}{5}\) as many hours as each of the full-time employees last week. The total number of hours worked by the part-time employees last week was what fraction of the total number of hours worked by all of the employees at the post office last week?

A. \(\frac{1}{15}\)
B. \(\frac{1}{9}\)
C. \(\frac{3}{20}\)
D. \(\frac{1}{6}\)
E. \(\frac{1}{5}\)

A.  \frac{1}{15} 
B.  \frac{1}{9} 
C.  \frac{3}{20} 
D.  \frac{1}{6} 
E.  \frac{1}{5}

ScottTargetTestPrep · Accepted Answer

Since each part time employee worked 3/5 as many hours as each full time employee, we can let the number of hours worked by each full-time employee be 5 and the number of hours of each part-time employee be 3.

Thus, the hours worked by the part-time employees is 1 x 3 = 3 and the total hours worked by all employees is 3 + (3 x 5) = 18.

So, the fracton of all hours worked by part-time employees is 3/18 = 1/6.

Answer: D

kayze · Answer

Here is the way I solved this.

Let p = part-time employees and f = full-time employees. We know that  p = \frac{f}{3}  because they are 25% of the total employees while f is 75%, thus  \frac{25%}{75%} = \frac{1}{3} .

Now, to find the part-time hours worked in relation to full-time hours worked, we multiply  \frac{1}{3}  by  \frac{3}{5}  and get  \frac{1}{5} .

Note that the answer is not  \frac{1}{5} , because it is asking for the fraction of part-time work out of the total number of work by ALL employees, not the ratio between part-time work and full-time work. Thus, we must add part-time work and full-time work. If part-time work is  \frac{1}{5}  of full-time work, that means the total work is  \frac{1}{5} + \frac{5}{5} = \frac{6}{5} .

Now we divide part-time work by total work:  \frac{1}{5} / \frac{6}{5} = \frac{1}{6}

This might be an unconventional or inefficient way to solve, so if anyone has a better way please share!

kayze · Answer

Seems like a good candidate for plugging in smart numbers, should have thought of this. Thanks!

ScottTargetTestPrep · Answer

Agree! It's a great place to use smart numbers:)

MartyMurray · Answer

At a post office last week, 25 percent of the employees were part-time employees and the rest were full-time employees. Each of the part-time employees worked \(\frac{3}{5}\) as many hours as each of the full-time employees last week. The total number of hours worked by the part-time employees last week was what fraction of the total number of hours worked by all of the employees at the post office last week?

A. \(\frac{1}{15}\)
B. \(\frac{1}{9}\)
C. \(\frac{3}{20}\)
D. \(\frac{1}{6}\)
E. \(\frac{1}{5}\)

Total Employees:  E

Hours Worked by Each Full-Time Employee:  H

Total hours worked by Part-Time Employees:

\frac{1}{4}E × \frac{3}{5}H

Total hours worked by Full-Time Employees:

\frac{3}{4}E × H

Fraction of Hours Worked by Part-Time Employees:

(\frac{1}{4}E × \frac{3}{5}H) / ((\frac{1}{4}E × \frac{3}{5}H ) + ( \frac{3}{4}E × H))

\frac{3}{20} / (\frac{3}{20} + \frac{3}{4})

\frac{3}{20} / \frac{18}{20}

1 / 6

A.  \frac{1}{15} 
B.  \frac{1}{9} 
C.  \frac{3}{20} 
D.  \frac{1}{6} 
E.  \frac{1}{5}

Correct answer:   D

weez · Answer

We're working with ratios, so say there are 100 employees total and x is the number of hours each full-time employee worked.

Type | Hours worked last week 
Part-time | 25 * (3x/5)= 15x 
Full time | 75x

Then, the fraction of the total number of hours worked by all of the employees is 15x / (15x + 75x) = 15/90 = 1/6

bot00078 · Answer

https://gmatclub.com/forum/download/file.php?id=86211 GMAT-Club-Forum-iet5qoz1.jpeg

At a post office last week, 25 percent of the employees were part-time

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At a post office last week, 25 percent of the employees were part-time

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