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Three factory employees work at constant rates to produce
[#permalink]
09 Dec 2017, 19:29

Expert Reply

1

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Question Stats:

Three factory employees work at constant rates to produce DVDs. Employee A produces y DVDs in \(\frac{2}{5}\) of an hour. Employee B produces y DVDs in \(\frac{3}{5}\) of an hour. Employee C produces y DVDs in \(\frac{5}{4}\) of an hour. Which of the following combinations of employees can produce at least 5y DVDs in 2 hours?

Indicate all such statements.

A. Employee A alone

B. Employee B alone

C. Employee C alone

D. Employees A and B together

E. Employees B and C together

F. Employees A, B, and C together

G. Even if all three employees work together, they will not finish the job

_________________

Indicate all such statements.

A. Employee A alone

B. Employee B alone

C. Employee C alone

D. Employees A and B together

E. Employees B and C together

F. Employees A, B, and C together

G. Even if all three employees work together, they will not finish the job

Show: :: OA

A, D, F

Drill 4

Question: 8

Page: 532

Question: 8

Page: 532

_________________

Sandy

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Re: Three factory employees work at constant rates to produce
[#permalink]
23 May 2021, 12:28

2

Expert Reply

sandy wrote:

Three factory employees work at constant rates to produce DVDs. Employee A produces y DVDs in \(\frac{2}{5}\) of an hour. Employee B produces y DVDs in \(\frac{3}{5}\) of an hour. Employee C produces y DVDs in \(\frac{5}{4}\) of an hour. Which of the following combinations of employees can produce at least 5y DVDs in 2 hours?

Indicate all such statements.

A. Employee A alone

B. Employee B alone

C. Employee C alone

D. Employees A and B together

E. Employees B and C together

F. Employees A, B, and C together

G. Even if all three employees work together, they will not finish the job

Indicate all such statements.

A. Employee A alone

B. Employee B alone

C. Employee C alone

D. Employees A and B together

E. Employees B and C together

F. Employees A, B, and C together

G. Even if all three employees work together, they will not finish the job

Show: :: OA

A, D, F

Drill 4

Question: 8

Page: 532

Question: 8

Page: 532

Output summary for each employee

Employee A produces y DVDs in 24 minutes

Employee B produces y DVDs in 36 minutes

Employee C produces y DVDs in 75 minutes

We want to determine which combination of employees can produce at least 5y DVDs in 120 minutes

A. Employee A alone

120/24 = 5

So there are 5 24-minute periods in 120 minutes

Since employee A produces y DVDs during every 24-minute period, we know that employee A can produce 5y DVDs in 120 minutes.

Answer choice A works.

Important: Employee A produces EXACTLY 5y DVDs in 120 minutes.

Since employee A is the fastest worker, we know that employees B and C will not be able to produce 5y DVDs in 120 minutes.

Eliminate answer choices B and C.

Also, since employee A can produce 5y DVDs in 120 minutes by himself/herself, any combination of workers that includes employee A will be able to produce at least 5y DVDs in 120 minutes

So, answer choices D and F work.

E. Employees B and C together

120/36 = 3 1/3

So there are 3 1/3 36-minute periods in 120 minutes

Since employee B produces y DVDs during every 36-minute period, we know that employee B can produce (3 1/3)y DVDs in 120 minutes.

120/75 = 1.6

So there are 1.6 75-minute periods in 120 minutes

Since employee C produces y DVDs during every 75-minute period, we know that employee C can produce 1.6y DVDs in 120 minutes.

So if employees B and C work together, the total number of DVDs they can produce = (3 1/3)y + 1.6y, Which is less than 5y.

Eliminate answer choice D.

G. Even if all three employees work together, they will not finish the job

We already concluded that employee A can produce 5y DVDs in 120 minutes by himself/herself

Eliminate answer choice G.

Answer: A, D and F

_________________

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Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

Re: Three factory employees work at constant rates to produce
[#permalink]
29 Dec 2017, 16:43

Expert Reply

Explanation

Plug in for y. If y = 30, then Employee A produces 30 DVDs in \(\frac{2}{5}\) of an hour, so using a Rate Pie you can figure out that his rate is 75 DVDs per hour. Employee B produces 30 DVDs in of \(\frac{3}{5}\) an hour, so his rate is 50 DVDs per hour. Employee C produces 30 DVDs \(\frac{5}{4}\) in of an hour, so his rate is 24 DVDs per hour.

5y = 150, so you need to find the combination of employees that can produce 150 DVDs in 2 hours. Employee A will produce exactly 150 DVDs in 2 hours, so choice (A) is a credited answer. If you know that Employee A alone can produce 5y DVDs in 2 hours, then choices (D) and (F) must also be correct answers, and choice (G) must be incorrect.

Employee B will only produce 100 DVDs in 2 hours, so you can eliminate choice (B). Employee C will only produce 48 DVDs in 2 hours, so you can also eliminate choice (C). If Employees B and C work together for 2 hours, they will produce 148 DVDs, so choice (E) is incorrect.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Plug in for y. If y = 30, then Employee A produces 30 DVDs in \(\frac{2}{5}\) of an hour, so using a Rate Pie you can figure out that his rate is 75 DVDs per hour. Employee B produces 30 DVDs in of \(\frac{3}{5}\) an hour, so his rate is 50 DVDs per hour. Employee C produces 30 DVDs \(\frac{5}{4}\) in of an hour, so his rate is 24 DVDs per hour.

5y = 150, so you need to find the combination of employees that can produce 150 DVDs in 2 hours. Employee A will produce exactly 150 DVDs in 2 hours, so choice (A) is a credited answer. If you know that Employee A alone can produce 5y DVDs in 2 hours, then choices (D) and (F) must also be correct answers, and choice (G) must be incorrect.

Employee B will only produce 100 DVDs in 2 hours, so you can eliminate choice (B). Employee C will only produce 48 DVDs in 2 hours, so you can also eliminate choice (C). If Employees B and C work together for 2 hours, they will produce 148 DVDs, so choice (E) is incorrect.

_________________

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Re: Three factory employees work at constant rates to produce
[#permalink]
23 May 2021, 01:30

Is there any other way to solve this question, apart from plug-in?

Re: Three factory employees work at constant rates to produce
[#permalink]
23 May 2021, 08:47

Expert Reply

Uhnil wrote:

Is there any other way to solve this question, apart from plug-in?

For sure yes.

However, plug in number is the fastest way. Set up an equation would become a nightmare.

Maybe GreenlightTestPrep knows how

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