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

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New post 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.

Answer: 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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New post 30 Jan 2014, 03:01
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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
Start with C and lets see..
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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Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the  [#permalink]

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New post 30 Jan 2014, 03:04
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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

When you face a long text question in GMAT, try reading and analyzing one line at a time rather than trying to make sense of the whole question in a go. This is what I would do:

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.
- This means 2/3 *3/4 = 1/2 of the eggs survived the first month.

Of the geese that survived the first month, 3/5 did not survive the first year.
- This means 3/5 of 1/2 (those who survived first month) i.e. 3/10 did not survive the first year and 2/5 of 1/2 = 1/5 survived 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?
- This means 1/5 calculated above is equal to 120 so total eggs laid were 5*120 = 600.

More often than not, by the time you reach the last statement, most of your question would be already solved.
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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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New post 05 Dec 2014, 01:25
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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 3/4 of the  [#permalink]

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New post 05 Dec 2014, 02:11
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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

Answer = 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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New post 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= \(120=(\frac{2}{3}*\frac{3}{4}*(1-\frac{3}{5})*)x\)

\(\frac{1}{5} *x =120\)
\(x=600\)

answer 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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New post 28 Sep 2016, 16:43
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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

So answer is 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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New post 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


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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 3/4 of the  [#permalink]

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New post 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

Answer: 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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New post 10 Mar 2018, 03:48
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.

Answer: D.



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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New post 10 Mar 2018, 04:11
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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.

Answer: D.



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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New post 18 Aug 2018, 20:41
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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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Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the  [#permalink]

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New post 22 Oct 2018, 10:40
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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

Answer 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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New post 15 Apr 2019, 03:26
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]

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New post 06 Sep 2019, 11:49
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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