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If A works a job alone, it takes x days. If B does it alone, it takes y days. If A and B work toget

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by Max@Math Revolution » Fri May 08, 2020 12:17 am

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[GMAT math practice question]

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

A. 20
B. 21
C. 25
D. 27
E. 29
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Re: If A works a job alone, it takes x days. If B does it alone, it takes y days. If A and B work toget

by Max@Math Revolution » Sun May 10, 2020 5:52 pm
=>

Assume 1 is the work amount of the job.
The work amount that machines A and B can do in a day is 1/x and 1/y, respectively.
Then we have 1/x + 1/y = 3/20.
And we have (1/x + 1/y)*5 + (1/x)*3 = 1.

(1/x + 1/y)*5 + (1/x)*3 = 1
⇔ (3/20)*5 + (1/x)*3 = 1, since 1/x + 1/y = 3/20
⇔ (3/4) + (1/x)*3 = 1
⇔ (1/x)*3 = 1/4
⇔ (1/x) = 1/12
⇔ x = 12

1/x + 1/y = 3/20
⇔ 1/12 + 1/y = 3/20, since x = 12
⇔ 1/y = 3/20 – 1/12 = 9/60 – 5/60 = 4/60 = 1/15
⇔ y = 15

Thus, we have x + y = 12 + 15 = 27.

Therefore, D is the answer.
Answer: D
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