Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x=4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours ?
A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%
source .MGMAT
OA
E
Machine A currently takes x hours to complete a certain job
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Here's an approach that minimizes that calculations required.guerrero wrote:Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x=4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours ?
A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%
source .MGMAT
OA
E
First, let y = 1
In other words, Machine B takes 1 hour to complete the job.
If x = 4y, then x = 4(1) = 4
So, Machine A takes 4 hours to complete the job.
We want A and B, working together, to complete the job in 3y/8 hours.
Since y = 1, we want their time to be 3(1)/8 hours.
So, working together, they need to complete the job in 3/8 hours.
IMPORTANT
At the moment, x = 4 (Machine A takes 4 hours to complete the job.)
Let's see what happens if we decrease x by 75%. When we do this, we get 1
In other words, Machine A takes 1 hour to complete the job.
So, if Machine A takes 1 hour to complete the job, and Machine B takes 1 hour to complete the job, then working together, they will complete the job in 1/2 hour.
However, we need them to complete the job in 3/8 hours (we need them to complete the job even faster than 1/2 an hour)
So, we need to decrease the value of x by MORE THAN 75%
Since only answer choice E is greater than 75%, it must be the correct answer.
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Brent
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Time for Machine B:guerrero wrote:Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x=4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours ?
A. 15%
B. 25%
C. 30%
D. 62,5%
E. 85%
E
So that 3y/8 is an integer value, let y = 8 hours.
Time for Machine A:
x = 4y = 4*8 = 32 hours.
Let the job = the LCM of 8, 3 and 32 = 96 units.
Rate for B = w/y = 96/8 = 12 units per hour.
Rate for A = w/x = 96/32 = 3 units per hour.
To complete the job in 3y/8 = 3 hours, the required rate for A and B together = 96/3 = 32 units per hour.
Since B produces 12 units per hour. A must produce the balance:
32-12 = 20 units per hour.
Thus, A's new time = w/(new rate) = 96/20 = 48/10 = 4.8 hours.
Decrease in A's time = 32-4.8 = 27.2 hours.
Since 75% of 32 = 24 hours, A's time decreases by MORE THAN 75%.
The correct answer is E.
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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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