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

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Math Expert
Joined: 02 Sep 2009
Posts: 39660
Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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30 Jan 2014, 01:55
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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

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[Reveal] Spoiler: OA

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

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30 Jan 2014, 01:55
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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.

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

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30 Jan 2014, 03:01
3
KUDOS
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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Location: India
Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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30 Jan 2014, 03:04
1
KUDOS
choice D.
Let the total geese be x
Given:x*(2/3)*(3/4)*(2/5)=120
Therefore,x/5=120
x=600
Math Expert
Joined: 02 Sep 2009
Posts: 39660
Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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01 Feb 2014, 08:56
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.

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

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05 Dec 2014, 01:25
1
KUDOS
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?

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

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05 Dec 2014, 02:11
1
KUDOS
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/ [#permalink]

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11 May 2016, 19:56
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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28 Sep 2016, 03:27
[quote="Bunuel"]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

number of eggs = x

survaivers= $$120=(\frac{2}{3}*\frac{3}{4}*(1-\frac{3}{5})*)x$$

$$\frac{1}{5} *x =120$$
$$x=600$$

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

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28 Sep 2016, 16:43
1
KUDOS
Plug in numbers

I started with D instead of B since it is a multiple of 3

So if 600 eggs then 400 hatched (2/3) then 300 survived (3/4) and 120 (2/5) survived the first year

Manager
Joined: 23 Dec 2013
Posts: 194
Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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29 May 2017, 23:09
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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

This problem tests your ability to work backwards.

120 geese survived each phase.

x*2/3 = eggs that were hatched.

x*2/3*3/4 = eggs that were hatched and survived the first month

x*2/3*3/4*2/5 = eggs that were hatched, survived the first month, and survived the first year

x*2/3*3/4*2/5 = 120

x/3*3/2*2/5 = 120

x/5 = 120

x = 500 + 100 = 600.
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Re: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/ [#permalink]

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01 Jun 2017, 10:24
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/   [#permalink] 01 Jun 2017, 10:24
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