AAPL wrote:Economist GMAT

A marzipan factory has two machines producing marzipan. Every day, the two machines operate constantly from 08:00 to 18:00, and produce together N kg of marzipan. What percent of the total amount of marzipan produced by machines W and D together was produced by machine W?

1) Working alone, it takes machine W twenty-five hours to produce (N/2) kg of marzipan.
2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

Statement 1:
Let N = 50 kg.
Since W and D produce the entire 50 kg over the 10 hours between 8:00 and 18:00, the combined rate for W and D = 50/10 = 5 kg per hour.
Since W takes 25 hours to produce N/2 = 25 kg, W's rate alone = w/t = 25/25 = 1 kg per hour.

Of every 5 kg produced each hour when W and D work together, W produces 1 kg.
Thus:
(W's hourly work)/(total hourly work) = 1/5 = 20%.
SUFFICIENT.

Statement 2:
Let N = 4 kg and D's time for N kg = 1 hour.
Thus, D's rate = (4 kg)/(1 hour) = 4 kg per hour.

Since W produces N/2 kg (2 kg) in twice D's time for N kg (2 hours), W's rate = (2 kg)/(2 hours) = 1 kg per hour.
Combined rate for W and D working together = 1+4 = 5 kg per hour.

Of every 5 kg produced each hour when W and D work together, W produces 1 kg.
Thus:
(W's hourly work)/(total hourly work) = 1/5 = 20%.
SUFFICIENT.

The correct answer is D.

Hi, I have a doubt.

2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

How is option B sufficient? it doesn't state anything about the time for either machine W or machine D; it only compares the work of two machines.

I feel the answer should be A.

swerve wrote:Hi, I have a doubt.

2) Machine W alone produces N/2 kg of marzipan in double the time it takes machine D alone to produce N kg of marzipan.

How is option B sufficient? it doesn't state anything about the time for either machine W or machine D; it only compares the work of two machines.

I feel the answer should be A.

The prompt states:
Every day, the two machines operate constantly from 08:00 to 18:00.
As shown in my post above, Statement 2 yields the following rate ratio:
(W alone) : (W and D together) = 1:5.
The rate ratio indicates that -- of every 5 kg produced when W and D work together from 8:00 to 18:00 -- W will produce 1 kg.
Thus:
(W's hourly work)/(total hourly work) = 1/5 = 20%.
SUFFICIENT.