Could someone explain the below?
Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
A) 2
B) 3
C) 4
D) 6
E) 8
From Official GMATPrep Software
OA is B
Machine Rate
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If 6 machines take 12 days to complete the job, then we can say that the job takes 72 "machine days" to complete (6 x 12 = 72)6 machines, each working at same constant rate, together can complete the job in 12 days. How many additional machines, each working at same constant rate, will be needed to complete job in 8 days?
A 3
B 4
C 5
D 6
E 2
To complete the job in 8 days would require 9 machines (72 machine days divided by 8 days)
So, we need an additional 3 machines.
Answer = A
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Approach 1: Plug in a rate for EACH MACHINESix machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?
2
3
4
6
8
Let the rate for each machine = 1 unit per day.
Rate for 6 machines = 6 units per day.
In 12 days, the amount of work produced by 6 machines = r*t = 6*12 = 72 units.
To produce 72 units in 8 days, the required amount of work per day = w/t = 72/8 = 9 units per day.
To increase the rate from 6 units per day to 9 units per day, 3 more machines are needed.
The correct answer is B.
Approach 2: Inverse proportion method
The number of machines is INVERSELY PROPORTIONAL to the number of days:
(machines)(days) = (machines)(days).
As the number of machines INCREASES, the number of days must DECREASE, so that in each case the SAME AMOUNT OF WORK is produced.
Since 6 machines take 12 days, and the job is to be completed in 8 days, we get:
6 * 12 = m * 8
72 = 8m
m = 9.
Since 9 machines are required, the original number of machines -- 6 -- must increase by 3.
The correct answer is B.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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