Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
A:
x - y
------
x + y
B:
x
-----
y - x
C:
x + y
-----
xy
D:
y
-----
x - y
E:
y
----
x + y
OA is E
rate-work -any short method
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- eagleeye
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Hi hey_thr67:
The key to doing this fast is realizing that as long as A and B works at their constant rates, the fraction of work done by A and B in any given time is the same. With that in mind, let's do this one quickly.
Machine A can complete a certain job in x hours.
Hence, work done by A in one hour = 1/x.
Machine B can complete the same job in y hours.
Hence, work done by B in one hour = 1/y.
When they are working together work done by A and B in one hour = 1/x+1/y.
Now the work that B doesn't do, is the work that is done by A. Hence the correct fraction of work done by A
= (work done by A in one hour) / (Work done by A and B together in 1 hour)
= (1/x) / (1/x+1/y) = xy/( x*(x+y)) = y/(x+y). Hence E
Let me know if this helps
The key to doing this fast is realizing that as long as A and B works at their constant rates, the fraction of work done by A and B in any given time is the same. With that in mind, let's do this one quickly.
Machine A can complete a certain job in x hours.
Hence, work done by A in one hour = 1/x.
Machine B can complete the same job in y hours.
Hence, work done by B in one hour = 1/y.
When they are working together work done by A and B in one hour = 1/x+1/y.
Now the work that B doesn't do, is the work that is done by A. Hence the correct fraction of work done by A
= (work done by A in one hour) / (Work done by A and B together in 1 hour)
= (1/x) / (1/x+1/y) = xy/( x*(x+y)) = y/(x+y). Hence E
Let me know if this helps
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- Anurag@Gurome
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Fraction of the job that B will not have to complete = Fraction of the job that A will completehey_thr67 wrote:Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
Algebraic Approach:
In 1 hour, A completes 1/x of the job.
In 1 hour, B completes 1/y of the job.
In 1 hour, A and B together complete (1/x + 1/y) = (x + y)/xy of the job.
Hence, A and B together will complete the job in xy/(x + y) hours.
In xy/(x + y) hours A will do [xy/(x + y)]*(1/x) = y/(x + y) of the job.
The correct answer is E.
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Fraction of the job that B will not have to complete = Fraction of the job that A will completehey_thr67 wrote:Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
Tricky Approach:
Let us assume that A completes the job in zero hours, i.e. A completes the job alone and we don't need B to any part of the job. (This is not practically impossible but mathematics should hold for this situation also)
Hence, x = 0
We will put this value of x in the given options to see which of them is equal to 1.
- A. (x - y)/(x + y) = -y/y = -1 --> NO
B. x/(x + y) = 0 --> NO
C. (x + y)/(xy) = Not definite --> NO
D. y/(x - y) = -y/y = -1 --> NO
E. y/(x + y) = y/y = 1 --> YES
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Time and rate are RECIPROCALS.hey_thr67 wrote:Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
A:
x - y
------
x + y
B:
x
-----
y - x
C:
x + y
-----
xy
D:
y
-----
x - y
E:
y
----
x + y
OA is E
Let x = 2 hours and y = 5 hours.
Since the ratio of A's time to B's time = 2:5, the ratio of A's rate to B's rate = 5:2.
The ratio of the rates implies the following:
Of every 7 units produced, 5 will be produced by A and 2 will be produced by B, implying that the fraction not produced by B = 5/7. This is our target.
Now we plug x=2 and y=5 into the answers to which yields our target of 5/7.
A quick scan of the answer choices reveals that only E works:
y/(x+y) = 5/(2+5) = 5/7.
The correct answer is E.
Note that the same reasoning can be applied directly to the variables themselves.
Since the ratio of A's time to B's time = x:y, the ratio of A's rate to B's rate = y : x.
The ratio of the rates implies the following:
Of every (x+y) units produced, y will be produced by A, implying that the fraction not produced by B = y/(x+y).
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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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