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# Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the

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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 f the geese that hatched from those eggs survived the first month.Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

Sol: Plugging in answer choices is best bet
540 eggs laid ----> 2/3 hatached so 540*2/3 = 360 and 3/4 of these eggs survived the first month so 3/4*360=270 survived and out of these 2/5 survived the first year. so 270*2/5=96...But is given that 120 geese survived so no of eggs laid must be more than 540 so

Lets take D and check 6000----> 2/3h hatched (400) of these 3/4 survived first month is 300 and out 300 2.5 survied first year which 2/5*300=120----> same as stated in the Question.

So Ans D

600 level is okay
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Let the goose eggs laid at pond = x

Total hatched $$= \frac{2x}{3}$$

Survived in 1st month $$= \frac{2x}{3} * \frac{3}{4} = \frac{x}{2}$$

Not surviving 1st year $$= \frac{x}{2} * \frac{3}{5} = \frac{3x}{10}$$

Surviving 1st year $$= \frac{5x}{10} - \frac{3x}{10} = \frac{2x}{10}$$

Given that $$\frac{2x}{10} = 120$$

x = 120*5 = 600

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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Quote:

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

We can let n = the total number of goose eggs.

We are given that 2/3 of the eggs hatched and 3/4 of the geese that hatched from those eggs survived the first month, and of the geese that survived the first month, 3/5 did not survive the first year (which means that ⅖ did survive the first year). We are also given that a total of 120 geese survived the first year. Thus:

n(2/3)(3/4)(2/5) = 120

12n/60 = 120

n/5 = 120

n = 600

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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
Bunuel wrote:
SOLUTION

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.

Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.

120 geese survived the first year:

1/5*(total) = 120 --> (total) = 600.

Hi Bunuel

can you help me to understand one detail in your solution ? please

ok here all is clear (2/3*3/4 = 1/2 survived the first month.)

but here
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.

why are you subtracting 3/5 from 1 and not just multiplying 3/5 by 1/2 ? as you did in fest step ... can you explan ?

thanks !
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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dave13 wrote:
Bunuel wrote:
SOLUTION

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.

Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.

120 geese survived the first year:

1/5*(total) = 120 --> (total) = 600.

Hi Bunuel

can you help me to understand one detail in your solution ? please

ok here all is clear (2/3*3/4 = 1/2 survived the first month.)

but here
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.

why are you subtracting 3/5 from 1 and not just multiplying 3/5 by 1/2 ? as you did in fest step ... can you explan ?

thanks !

Hi dave13

The reason for doing that is the wording which reads "of the geese that survived the first month, 3/5 did not survive"
which when translated gives us $$\frac{1}{2} - \frac{1}{2}*\frac{3}{5}$$ or $$\frac{1}{2} - \frac{3}{10} = \frac{2}{10} = \frac{1}{5}$$ will survive!

We could also write the equation as 1/2*(1 - 3/5)

Hope this helps you!
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Hi dave13

I have seen may similar Official problems . While i use this approach for a variety of problems, but practicing it would help us problems involving percents/ratio/fractions.
So, lets take a suitable number . That number should be a an integer. Since Eggs cant be laid in fractions.
How to choose a number .
First that number can be LCM of 3,4,5 which is 60
of 60 Eggs 2/3 hatched = 40 Hatched into geese

of40 Geese 3/4 of the geese survived first month= 30 Survived first month

Now If 3/5 did not survive the first year, then 1/5 survived first year

Of 30 geeses survived first month 1/5 did not survive the first year=12

Ok we are given that 120 survived first year out of what ever eggs were laid . we found that 12 survived out of 60 eggs .
laid

So 60*10 eggs laid and of these 12*10 Survived first year.

600 Choice D
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

Problem Solving
Question: 69
Category: Arithmetic Operations with rational numbers
Page: 70
Difficulty: 600

Hi dave13

2/3 hatched and 3/4 survived so it is 2/3 * 3/4 = 2/4 = 1/2 survived.

3/5 did not survived means we have 2/5 that survived.

Of those (1/2) that survived, 3/5 did not survive, meaning 2/5 survived so it is 1/2 * 2/5 = 1/5 survived.

Now if 1/5 x = 120

Then x = 5 * 120 = 600

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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
I have a query wherein if you multiply the fractions successively you get ... 2/3*3/4*3/5 = 3/10 which is the number of eggs that hatched but did not survive the first year, so doesn't 1-(3/10) = 7/10 represent the fraction of the eggs that survived the first year? Though using this fraction we do not get the answer, but cannot find the reason why.
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
Ameya85 wrote:
I used a bit different approach. The total must be LCM of 3, 4, and 5 or else, fraction won't make to 120. This means whatever the total is, it must be multiple of 60. I started with 540 and landed with 112 instead of 120 and I went on to mark 600. Is this approach correct?

Ameya

Yes, It is. You could have worked with 600 first (since it is a nice number) just like I did.
Thank you!
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
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Bunuel wrote:
Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 120 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?

(A) 280
(B) 400
(C) 540
(D) 600
(E) 840

In this case, we can easily test the answer choices.
From here, I'd typically give myself up to 20 seconds to identify a faster approach, but I can already see that I can immediately in lemonade to answer choices, which means I only need to test one answer choice.

We’re told that 2/3 of the goose eggs laid hatch.
Since the answer choices tell us the number of goose eggs laid, we can immediately eliminate choices A and B since 2/3 of 280 and 2/3 of 400 don’t result in integer values (and this real world question doesn’t allow for fractional hatchlings!).

From here, we’ll test choice D (the middle remaining choice). If it works, we’re done. If we end up with more than 120 geese, then the correct answer must be C. If we end up with fewer than 120 geese, then the correct answer must be E.

(D) 600 This tells us the number of goose eggs we start with.
Given: 2/3 of the eggs hatched. So, the total number of hatchlings = 2/3 of 600 = 400
Given: 3/4 of the hatchlings survived the first month. So, the number of 1st month survivors = 3/4 of 400 = 300
Given: Of the geese that survived the first month, 3/5 did not survive the first year, which means 2/5 of those geese survived.. So, the number of survivors = 2/5 of 300 = 120
Perfect!! This matches the information in the question.

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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
Total eggs laid = X
No. of eggs that hatched = (2/3)X
No. of eggs that survived the first week = (3/4)(2/3)X = (1/2)X
No. of eggs that did not survive the first year = (3/5)
No. of eggs that survive the first year = 1 - (3/5) = 2/5 = (1/2)X (2/5) = 1/5X

Solution: (1/5)X = 120
X = 600
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the [#permalink]
No of turtle eggs = x
Of the goose eggs laid at a certain pond, 2/3 hatched
Hatched = 2x/3

Of the goose eggs laid at a certain pond, 2/3 hatched, and 3/4 of the geese that hatched from those eggs survived the first month
Survived 1st Month = 3/4*2x/3 = x/2

Of the geese that survived the first month, 3/5 did not survive the first year
3/5 did not survive 1st year = x/2*3/5 = 3x/10 [Did not survive]

We have to subtract Survived 1st month - did not survive 1st year
Survived 1st year = x/2-3x/10 = x/5

If 120 geese survived the first year and if no more than one goose hatched from each egg,
Survived 1st year = 120

Which means x/5=120, x=600
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