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Can someone help with this one please?

Expert replies
by fambrini » Wed Oct 26, 2016 4:52 pm
Working alone, Sumio can mow a certain field in x hours. Yoko can mow 50% more field in the same time. When the two work together, they are paid m dollars each one. If Sumio decides to pay Yoko n dollars so they would have received the same compensation per field mowed, what is n in terms of m?

A) 1/2 m
B) 1/3 m
C) 1/4 m
D) 1/5 m
E) 1/6 m

OA: D

Thanks,
Fambrini
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Source: — Problem Solving |

by [email protected] » Wed Oct 26, 2016 7:52 pm
Hi fambrini,

What is the source of this question? I ask because it's a word-for-word "lift" of this question:

https://www.beatthegmat.com/work-problem-t74538.html

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by fiza gupta » Thu Oct 27, 2016 4:54 am
Sumio mow certain field in x hours be = y
Yoko mow 3/2y of the field in y hour
sumio gave y dollars to yoko = > m-n = m+n
compensations per field is same for both =>

m-n/y = m+n/3/2y
3m-3n = 2m-2n
m = 5n
n = 1/5
so D
Fiza Gupta
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by Matt@VeritasPrep » Thu Oct 27, 2016 11:27 pm
There's a much easier way of solving this.

Suppose that Sumio's rate = s. Then Yoko's rate = 1.5s.

When they work together, Yoko does 1.5s / (s + 1.5s) of the work, or 60%, but only gets 50% of the money.

To fix this, Sumio needs to give Yoko 10% of the money. Sumio has 50% of the money right now, so Sumio must pay Yoko 1/5 of his money (10% of the total / 50% of the total = 1/5).

Thus the answer is (1/5) * Sumio's money, or D.
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