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%
How can we solve it by picking numbers?
OA E
Word problems,percenatge
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Here's an approach that minimizes that calculations required.tapanmittal 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%
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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Since the job must be completed in 3y/8 hours, let y = 8 hours, implying that x = 4y = 4*8 = 32 hours and that the shorter time = 3y/8 = (3*8)/8 = 3 hours.tapanmittal 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%
Let the job = the LCM of 8, 32 and 3 = 96 widgets.
Regular times:
Since A takes 32 hours to complete the job, A's rate = w/t = 96/32 = 3 widgets per hour.
Since B takes 8 hours to complete the job, B's rate = w/t = 96/8 = 12 widgets per hour.
Shorter time:
At a rate of 12 widgets per hour, the number of widgets produced by B in 3 hours = rt = 12*3 = 36 widgets.
Since B produces 36 of the 96 widgets, the number of widgets produced by A in 3 hours = 96-36 = 60 widgets.
At A's normal rate of 3 widgets per hour, the normal time for A to produce 60 widgets = w/r = 60/3 = 20 hours.
Percent decrease change in A's time to produce 60 widgets:
(normal time - faster time)/(normal time) = (20-3)/20 = 17/20 = 85/100 = 85%.
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].
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