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21 May 2019, 10:28
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:49) correct
43%
(02:37)
wrong
based on 201
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
A. 9
B. 10
C. 12
D. 14
E. 15
21 Jun 2023, 04:22
Kudos
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Non Algebraic method - Using options
Let 240 sheep in 5 weeks eat 240x5 x g = 1200g (Amount of grass)
Let 200 sheep in 7 weeks eat 200 x 7 x g = 1400g
Therefore in two weeks 200g of extra grass has grown, i.e 100g grows per week (Since grass grows at a constant rate)
So 170 sheep in how many weeks will make the grass bare?
Lets look at the options..
If we consider 9 weeks, extra grass from 7th week onwards is 200g , so total grass = 1600g
But 170 x 9 not equal to 1600
If we consider 10 weeks, extra grass from 7th week onwards is 300g, so total grass = 1700g
170 x 10 = 1700.
Therefore correct answer = 10 weeks
Let 240 sheep in 5 weeks eat 240x5 x g = 1200g (Amount of grass)
Let 200 sheep in 7 weeks eat 200 x 7 x g = 1400g
Therefore in two weeks 200g of extra grass has grown, i.e 100g grows per week (Since grass grows at a constant rate)
So 170 sheep in how many weeks will make the grass bare?
Lets look at the options..
If we consider 9 weeks, extra grass from 7th week onwards is 200g , so total grass = 1600g
But 170 x 9 not equal to 1600
If we consider 10 weeks, extra grass from 7th week onwards is 300g, so total grass = 1700g
170 x 10 = 1700.
Therefore correct answer = 10 weeks
General Discussion
21 May 2019, 19:07
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nick1816
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.
