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# Grass in pasture grows equally thick and at a uniform rate. It takes 2

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Manager
Joined: 29 Nov 2018
Posts: 221
Concentration: Marketing, Strategy
Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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13 Jan 2019, 09:49
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00:00

Difficulty:

95% (hard)

Question Stats:

26% (02:12) correct 74% (02:37) wrong based on 46 sessions

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Grass in pasture grows equally thick and at a uniform rate. It takes 24 days for 70 cows to graze the pasture completely. However if there were only 30 cows, they could graze the entire pasture for 60 days. How many cows will graze the entire pasture in 96 days?

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4232
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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13 Jan 2019, 10:08
1
cfc198 wrote:
Grass in pasture grows equally thick and at a uniform rate. It takes 24 days for 70 cows to graze the pasture completely. However if there were only 30 cows, they could graze the entire pasture for 60 days. How many cows will graze the entire pasture in 96 days?

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32

cfc198
hi is the question posted correct?
I am getting answer as 18 ..
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Manager
Joined: 29 Nov 2018
Posts: 221
Concentration: Marketing, Strategy
Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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13 Jan 2019, 15:19
Archit3110 wrote:
cfc198 wrote:
Grass in pasture grows equally thick and at a uniform rate. It takes 24 days for 70 cows to graze the pasture completely. However if there were only 30 cows, they could graze the entire pasture for 60 days. How many cows will graze the entire pasture in 96 days?

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32

cfc198
hi is the question posted correct?
I am getting answer as 18 ..

when field is grazed in 24 days, we need 24 × 70 i.e. 1680 cow-days
when field is grazed in 60 days, we need 60 × 30 i.e. 1800 cow-days.

Thus, an increase of 36 days necessitated an additional 120 cow-days
If field has to last for 96 days, i.e. a further 36 days (from 60 days), a
further 120 cow-days would be needed. Thus, total cow-days needed for
the field to last 96 days is 1800 + 120 = 1920.

1920 cow-days, with days being 96 implies, the number of cows is

1920/ 96 = 20
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4232
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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13 Jan 2019, 23:04
1
cfc198

whats the source of the question..

cfc198 wrote:
Archit3110 wrote:
cfc198 wrote:
Grass in pasture grows equally thick and at a uniform rate. It takes 24 days for 70 cows to graze the pasture completely. However if there were only 30 cows, they could graze the entire pasture for 60 days. How many cows will graze the entire pasture in 96 days?

(A) 48
(B) 18
(C) 20
(D) 25
(E) 32

cfc198
hi is the question posted correct?
I am getting answer as 18 ..

when field is grazed in 24 days, we need 24 × 70 i.e. 1680 cow-days
when field is grazed in 60 days, we need 60 × 30 i.e. 1800 cow-days.

Thus, an increase of 36 days necessitated an additional 120 cow-days
If field has to last for 96 days, i.e. a further 36 days (from 60 days), a
further 120 cow-days would be needed. Thus, total cow-days needed for
the field to last 96 days is 1800 + 120 = 1920.

1920 cow-days, with days being 96 implies, the number of cows is

1920/ 96 = 20

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Senior Manager
Joined: 28 Jul 2016
Posts: 468
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)
Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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20 Jan 2019, 11:35
Bunuel can you please elaborate on the solution.
not very sure of the solution posted
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Manager
Joined: 02 Aug 2015
Posts: 153
Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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20 Jan 2019, 12:12
cfc198 wrote:

when field is grazed in 24 days, we need 24 × 70 i.e. 1680 cow-days
when field is grazed in 60 days, we need 60 × 30 i.e. 1800 cow-days.

Thus, an increase of 36 days necessitated an additional 120 cow-days
If field has to last for 96 days, i.e. a further 36 days (from 60 days), a
further 120 cow-days would be needed. Thus, total cow-days needed for
the field to last 96 days is 1800 + 120 = 1920.

1920 cow-days, with days being 96 implies, the number of cows is

1920/ 96 = 20

Hey cfc198

Not only an increase of 36 days, but also a decrease of 40 cows are responsible for the change of 120 cow-days, right?

It takes 24 days for 70 cows - So each cow takes 1/(24*70) days to graze the pasture.
if there were only 30 cows, they could graze the entire pasture for 60 days - Each cow takes 1/(60*30) days to graze the pasture.

The rate of work done by each cow varies in the two given scenarios. Is such variation possible or am I missing something?

Please let us know the source of the question.

Cheers!
Intern
Joined: 18 Dec 2018
Posts: 2
Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2  [#permalink]

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20 Jan 2019, 12:28
I'll attempt to answer this, the method could be completely wrong

We get given in the question that:
70 cows take 24 days
30 cows take 60 days

I solved this problem using ratios

So first I found the ratios of days:

$$\frac{60}{24} = 2.5 \\ \frac{96}{60} = 1.6$$

Now I will calculate the ratio of the cows:

$$\frac{70}{30} = \frac{7}{3} \\ \frac{30}{x} = y$$

Here $$x =$$ no. of cows & $$y =$$the ratio between the number of cows.

Here is where my method goes a little weird, so to find $$y$$ I worked out the ratio between the two day ratios and then multiplied this by the cow ratio. It's hard to explain but it's logically sound but I'm not amazing with explaining stuff.

$$\frac{1.6}{2.5} = \frac{16}{25} \approx \frac{2}{3}$$

Now multiple this value by the cow ratio:

$$\frac{2}{3} * \frac{7}{3} = \frac{14}{9} \approx 1.5 = y$$

So we have:

$$\frac{30}{x} = y = 1.5 \\ x = 20$$

I probably did this in a super long way but I hope I got it on the right lines ish.
Re: Grass in pasture grows equally thick and at a uniform rate. It takes 2   [#permalink] 20 Jan 2019, 12:28
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