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In certain pool there are 30 piranhas, which eat each other.

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In certain pool there are 30 piranhas, which eat each other. [#permalink] New post 09 Oct 2009, 09:07
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In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.
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Re: Piranhas in the pool [#permalink] New post 09 Oct 2009, 09:54
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


Max piranhas satisfied :-

for a fish to be satisfied it need to eat 3. So a max of 27 fish can be eaten. So a maximum of 9 fishes can be satisfied.

Min piranhas satisfied :-

A fish needs 3 fish to be satisfied. 1 or 2 is still unstatisfied.

let 15 fish eat the other 15.

So we get 15 fish with 1 fish eaten

Let 7 eat 7.

So we get 1 with 1 and 7 with 2 eaten. Total 8.

Let the one fish with 1 eaten eat one more.

So we get 7 fish with 2 eaten each.

Now let 3 can eat 1 each.

So we get 4 with 3 satisfied.

The last one can eat 1. Which gives us 4 satisfied.



Difficulty :- moderate :). Any prob is simpler with options. (except SC :cry: !!)

Quality :- pretty good
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Re: Piranhas in the pool [#permalink] New post 09 Oct 2009, 10:01
Expert's post
jax91 wrote:
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


Max piranhas satisfied :-

for a fish to be satisfied it need to eat 3. So a max of 27 fish can be eaten. So a maximum of 9 fishes can be satisfied.

Min piranhas satisfied :-

A fish needs 3 fish to be satisfied. 1 or 2 is still unstatisfied.

let 15 fish eat the other 15.

So we get 15 fish with 1 fish eaten

Let 7 eat 7.

So we get 1 with 1 and 7 with 2 eaten. Total 8.

Let the one fish with 1 eaten eat one more.

So we get 7 fish with 2 eaten each.

Now let 3 can eat 1 each.

So we get 4 with 3 satisfied.

The last one can eat 1. Which gives us 4 satisfied.



Difficulty :- moderate :). Any prob is simpler with options. (except SC :cry: !!)

Quality :- pretty good


Thanks for response.

Good thinking but...

Anyone else wants to try...
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Re: Piranhas in the pool [#permalink] New post 10 Oct 2009, 06:55
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The max satisfied nine is agreed to.
The min as per me should be zero because first can be eaten by the second and second by third and third by fourth and so on... And we'll be left with one very fat yet unsatisfied piranah.. Lemme know if it is correct though..
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Re: Piranhas in the pool [#permalink] New post 10 Oct 2009, 07:20
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


In terms of quality it's pretty good, but two comments:
1) You need to define what the minimum number of satisfied piranhas means, because otherwise the answer is 0.
2) If you wish to simulate gmat conditions provide options (although that makes it easier, esp with min, max problems)

For Min:
Assuming the answer is not 0, I took the approach of 1 piranha eats the next 3. So the min would be 30/4 = 7 and 2 uneaten piranha. ANS = 7

For Max:
I took the approach that
P4 ate P1-3
P7 ate P6-P4
P10 ate P9-P7
Following this pattern I arrive at 9.
Although I suspect this might be incorrect :P
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Re: Piranhas in the pool [#permalink] New post 10 Oct 2009, 07:25
rvthryet wrote:
The max satisfied nine is agreed to.
The min as per me should be zero because first can be eaten by the second and second by third and third by fourth and so on... And we'll be left with one very fat yet unsatisfied piranah.. Lemme know if it is correct though..


totally missed that one. Great thinkin! :-D
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Re: Piranhas in the pool [#permalink] New post 10 Oct 2009, 07:49
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yangsta8 wrote:
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


In terms of quality it's pretty good, but two comments:
1) You need to define what the minimum number of satisfied piranhas means, because otherwise the answer is 0.
2) If you wish to simulate gmat conditions provide options (although that makes it easier, esp with min, max problems)

For Min:
Assuming the answer is not 0, I took the approach of 1 piranha eats the next 3. So the min would be 30/4 = 7 and 2 uneaten piranha. ANS = 7

For Max:
I took the approach that
P4 ate P1-3
P7 ate P6-P4
P10 ate P9-P7
Following this pattern I arrive at 9.
Although I suspect this might be incorrect :P


Thank you for your response. I'll try to take into account points you brought up. As for min: I thought it was obvious, when asking about min number of satisfied fishes, that min can take 0 as well.

Answer:
MIN=0 (one fish eats second, second eats third and so on, no satisfied fish at the end)
MAX=9 (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+7=9)
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Piranhas in the pool [#permalink] New post 10 Oct 2009, 11:35
Same here.
In question like this one, min. is always 0.

Max = 9 => 4+3+3+3+3+3+3+3+3


Bunuel wrote:
yangsta8 wrote:
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


In terms of quality it's pretty good, but two comments:
1) You need to define what the minimum number of satisfied piranhas means, because otherwise the answer is 0.
2) If you wish to simulate gmat conditions provide options (although that makes it easier, esp with min, max problems)

For Min:
Assuming the answer is not 0, I took the approach of 1 piranha eats the next 3. So the min would be 30/4 = 7 and 2 uneaten piranha. ANS = 7

For Max:
I took the approach that
P4 ate P1-3
P7 ate P6-P4
P10 ate P9-P7
Following this pattern I arrive at 9.
Although I suspect this might be incorrect :P


Thank you for your response. I'll try to take into account points you brought up. As for min: I thought it was obvious, when asking about min number of satisfied fishes, that min can take 0 as well.

Answer:
MIN=0 (one fish eats second, second eats third and so on, no satisfied fish at the end)
MAX=9 (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+7=9)

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Re: Piranhas in the pool [#permalink] New post 23 Sep 2010, 04:52
Great question Bunuel.. Keep posting
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Re: Piranhas in the pool [#permalink] New post 14 Oct 2010, 09:01
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Hi Bunuel,
MAX=3 (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+1=3)
am I correct?
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Re: Piranhas in the pool [#permalink] New post 14 Oct 2010, 09:16
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sudhanshushankerjha wrote:
Hi Bunuel,
MAX=3 (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+1=3)
am I correct?


MAX=9: (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+7=9).
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Re: Piranhas in the pool [#permalink] New post 15 Oct 2010, 22:50
good question Bunuel. I would give this a 700+ question. Thank you.
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Re: Piranhas in the pool [#permalink] New post 17 Jan 2012, 22:19
Bunnel,

There are 30 fishes, so 10 fishes get 3 each which makes them satified so wont 10 would be the maximum # of satified piranha ? I am confused.
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Re: Piranhas in the pool [#permalink] New post 17 Jan 2012, 22:23
Bunnel, sorry I got it :-(
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Re: Piranhas in the pool [#permalink] New post 18 Jan 2012, 00:52
hurray! i solved it and got the right answer! I hope my logic is ok
I will write it down in a lengthy way to explain what I mean-

among 5 fishes 1 can eat
among 8 fishes 2 can eat
among 11 fishes 3 can eat
among 14 fishes 4 can eat
among 17 fishes 5 can eat
among 20 fishes 6 can eat
among 23 fishes 7 can eat
among 26 fishes 8 can eat
among 29 fishes 9 can eat

so, max 9 piranhas will be happy :)
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Re: In certain pool there are 30 piranhas, which eat each other. [#permalink] New post 22 May 2013, 02:59
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Re: Piranhas in the pool [#permalink] New post 24 Sep 2013, 21:29
Bunuel wrote:
yangsta8 wrote:
Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.


In terms of quality it's pretty good, but two comments:
1) You need to define what the minimum number of satisfied piranhas means, because otherwise the answer is 0.
2) If you wish to simulate gmat conditions provide options (although that makes it easier, esp with min, max problems)

For Min:
Assuming the answer is not 0, I took the approach of 1 piranha eats the next 3. So the min would be 30/4 = 7 and 2 uneaten piranha. ANS = 7

For Max:
I took the approach that
P4 ate P1-3
P7 ate P6-P4
P10 ate P9-P7
Following this pattern I arrive at 9.
Although I suspect this might be incorrect :P


Thank you for your response. I'll try to take into account points you brought up. As for min: I thought it was obvious, when asking about min number of satisfied fishes, that min can take 0 as well.

Answer:
MIN=0 (one fish eats second, second eats third and so on, no satisfied fish at the end)
MAX=9 (7 fishes eat 3 -->7*3+7=28, 2 left eat 6(3+3) from this seven --> 2+7=9)


I fell for the trap and got min as 7, but i agree totally that there could be 0 satisfied fish, while max was 9.

Good question...
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Re: In certain pool there are 30 piranhas, which eat each other. [#permalink] New post 18 Jun 2014, 03:54
Fishes are given numbers as 1 to 30


(1 2 3) (4 5 6) (7 8 9) (10 11 12) (13 14 15) (16 17 18) (19 20 21)
------- ------- ------ ---------- ---------- ---------- ---------
(22 23 24) (25 26 27) 28
-------------------- ----------------------
29 30

Here as we see, satisfied phiranas are 22, 23, 24, 25, 26, 27, 28, 29 and 30 = 9


Bunuel wrote:
In certain pool there are 30 piranhas, which eat each other. Once a piranha eaten 3 others it's satisfied and stops eating, what are the maximum and minimum numbers of satisfied piranhas possible?

NOTE: When piranha A eats a piranha B which ate a number of piranhas previously, it's counted that A piranha still ate only one.
NOTE: Dead satisfied piranha still counts as satisfied.

This is my Q, so please comment about the quality and difficulty level.
Re: In certain pool there are 30 piranhas, which eat each other.   [#permalink] 18 Jun 2014, 03:54
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