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The grass in a field grows in a constant rate. If 240 sheep were to gr

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The grass in a field grows in a constant rate. If 240 sheep were to gr  [#permalink]

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New post 21 May 2019, 10:28
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Question Stats:

52% (02:31) correct 48% (02:17) wrong based on 23 sessions

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The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?

A. 9
B. 10
C. 12
D. 14
E. 15
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Re: The grass in a field grows in a constant rate. If 240 sheep were to gr  [#permalink]

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New post 21 May 2019, 19:07
nick1816 wrote:
The grass in a field grows in a constant rate. If 240 sheep were to graze on it, it will become bare in 5 weeks. If 200 sheep were to graze on it, it will become bare in 7 weeks. How many weeks would it take 170 sheep to graze, before the field becomes bare?

A. 9
B. 10
C. 12
D. 14
E. 15



I would try to solve it algebraically although not likely to be tested on GMAT.

So let initial land have x amount of grass, and every week v amount of grass grows.
Thus, if each sheep can graze a amount of grass per week, we can set up our equation as
240 sheeps in 5 weeks - x+5v=240*5a....(I)
200 sheeps in 7 weeks - x+7v=200*7a...(II)

Subtract I from II...
2v=200a......v=100a,. This tells us that what grows in a week can be fed to 100 sheeps in that week.
Let us substitute this value to get x...x+5*100a=1200a....x=700a.This tells us that what exists in the beginning can be fed to 700 sheeps in one week.

Now we can firm a similar equation for 170 sheeps..
x+zv=170*za, where z is the number of weeks..
Substitute x and v in terms of a...700a+100az=170az....70=7z...z=10 weeks..

So , B.

If it were ever to come in GMAT, it will be 700 level.
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Re: The grass in a field grows in a constant rate. If 240 sheep were to gr   [#permalink] 21 May 2019, 19:07
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