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If A works a job alone, it takes x days, if B does it alone,

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If A works a job alone, it takes x days, if B does it alone,

by Max@Math Revolution » Sun Dec 08, 2019 10:40 pm
[GMAT math practice question]

If A works a job alone, it takes x days, if B does it alone, it takes y days, and if A and B work together, they can do 3/20 of the total job a day. A and B worked together for 5 days, and A worked alone for 3 days to finish the job. What is x + y?

A. 20
B. 21
C. 25
D. 27
E. 29
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by Max@Math Revolution » Tue Dec 10, 2019 11:34 pm
=>

Assume the total amount of work is 1.
We have an equation 1/x + 1/y = 3/20.
Then we have (1/x + 1/y)*5 + (1/x)*3 = 1 and 8/x + 5/y = 1
When we multiply both sides of 1/x + 1/y = 3/20 by 5, we have 5/x + 5/y = 3/4.
We subtract it from 8/x + 5/y = 1 to get (8/x + 5/y) - (5/x + 5/y) = 1 - 3/4, and we have 3/x = 1/4 or x = 12.
Then we have 1/12 + 1/y = 3/20, 1/y = 3/20 - 1/12, 1/y = 9/60 - 5/60, 1/y = 4/60, 1/y = 1/15, and y = 15.
Therefore x + y = 12 + 15 = 27.

Therefore, the answer is D.
Answer: D
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