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# On a race track a maximum of 5 horses can race together at

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Manager
Joined: 01 Jan 2009
Posts: 66
Location: India
Schools: LBS
On a race track a maximum of 5 horses can race together at  [#permalink]

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10 Oct 2009, 02:56
9
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95% (hard)

Question Stats:

38% (01:41) correct 62% (02:08) wrong based on 398 sessions

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On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number of races we need to conduct to get the top 3 fastest horses?

A. 5
B. 7
C. 8
D. 10
E. 11
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Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: Good Q.  [#permalink]

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10 Oct 2009, 09:13
24
6
I came down to 7. I mean that I can do the task in 7 races.

First 5 races: all horses by five. We'll have the five winners.

Race 6: the winners of previous five races. We'll have the 3 winners.
Now it's obvious that #1 here is the fastest one (gold medal).
For the silver and bronze we'll have 5 pretenders:
1. #2 from the last sixth race,
2. #3 from the last sixth race,
3. the second one from the race with the Gold medal winner from the first five races,
4. the third one from the race with the Gold medal winner from the first five races,
5. the second one from the race with the one which took the silver in the sixth race

Race 7: these five horse: first and second in this one will have the silver and bronze among all 25.

Answer B (7).

Good Q. +1
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Senior Manager
Joined: 31 Aug 2009
Posts: 331
Location: Sydney, Australia
Re: Good Q.  [#permalink]

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10 Oct 2009, 06:45
1
On every race we get the top 3 out of 5.

First 5 Races = Take 3 from each race = 15
Next 3 Races = Take 3 from each race = 9
At this point I figured that we only need 3 horses and we have 2 races. So take the top 2.
Next 2 Races = Take 2 from each race = 4
Last race we get the top 3.

Total races = 5+3+2+1 = 11
Answer = E
Manager
Joined: 01 Jan 2009
Posts: 66
Location: India
Schools: LBS
Re: Good Q.  [#permalink]

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10 Oct 2009, 08:50
1
Its not E. Bit more complicated then that
Manager
Joined: 01 Jan 2009
Posts: 66
Location: India
Schools: LBS
Re: Good Q.  [#permalink]

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10 Oct 2009, 10:35
7 is the correct answer.

Good solution Buneul.
SVP
Joined: 29 Aug 2007
Posts: 1733
Re: Good Q.  [#permalink]

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10 Oct 2009, 20:57
jax91 wrote:
On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number of races we need to conduct to get the top 3 fastest horses?

A)5
B)7
C)8
D)10
E)11

Nice work by both "yangsta8" and "Bunuel". Both solutions are equally logical...

The OA could be controversial as the question is not clear about the method how 1/2/3 are selected...

yangsta8 wrote:
On every race we get the top 3 out of 5.

First 5 Races = Take 3 from each race = 15
Next 3 Races = Take 3 from each race = 9
At this point I figured that we only need 3 horses and we have 2 races. So take the top 2.
Next 2 Races = Take 2 from each race = 4
Last race we get the top 3.

Total races = 5+3+2+1 = 11
Answer = E

Bunuel wrote:
I came down to 7. I mean that I can do the task in 7 races.

First 5 races: all horses by five. We'll have the five winners.

Race 6: the winners of previous five races. We'll have the 3 winners.
Now it's obvious that #1 here is the fastest one (gold medal).
For the silver and bronze we'll have 5 pretenders:
1. #2 from the last sixth race,
2. #3 from the last sixth race,
3. the second one from the race with the Gold medal winner from the first five races,
4. the third one from the race with the Gold medal winner from the first five races,
5. the second one from the race with the one which took the silver in the sixth race

Race 7: these five horse: first and second in this one will have the silver and bronze among all 25.

Answer B (7).

Good Q. +1
Manager
Joined: 18 Jun 2010
Posts: 233
Schools: Chicago Booth Class of 2013
On a race track a maximum of 5 horses can race together at  [#permalink]

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29 Sep 2010, 12:18
1
Why 7 races? I think we can do it in just 6 races, as shown on the picture.
The 6th race will determine the best three winners (Gold, Silver, and Bronze) of the previous 5 races...
Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: Good Q.  [#permalink]

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29 Sep 2010, 12:31
2
1
Financier wrote:
Why 7 races? I think we can do it in just 6 races, as shown on the picture.
The 6th race will determine the best three of winners of the previous 5 races...

We want to get the top 3 fastest horses. The trick here is that though the horse #1 from 6th race will be the fastest one, so gold medal owner but the horse #2 and #3 from this race may not be the second and the third fastest horses out of 25.

For the silver and bronze we would have 5 pretenders:
1. #2 from the 6th race;
2. #3 from the 6th race;
3. the second horse from the first round race with the Gold medal winner;
4. the third horse from the first round race with the Gold medal winner;
5. the second horse from the first round race with horse #2 in the 6th.

So total 7 races are needed.
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Joined: 19 Apr 2010
Posts: 168
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Re: Good Q.  [#permalink]

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01 Oct 2010, 06:09
Nice question.. Thanks for posting
Intern
Joined: 26 Aug 2010
Posts: 49
Location: India
Re: Good Q.  [#permalink]

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03 Oct 2010, 03:03
Bunuel wrote:

For the silver and bronze we would have 5 pretenders:
1. #2 from the 6th race;
2. #3 from the 6th race;
3. the second horse from the first round race with the Gold medal winner;
4. the third horse from the first round race with the Gold medal winner;
5. the second horse from the first round race with horse #2 in the 6th.

So total 7 races are needed.

Bunuel,

It is uncertain to me that how we can be sure to pick horses for 7th race..

Isn't a possibility that second horse from Gold Medal winner group can be slower than the second horse in Bronze Medal winner group?

Lets say: The Gold medal horse took 2 mins, second horse in the Gold medal group took 5 mins to cover the race. While Bronze medal horse took 3 mins and second horse from Bronze medal group took 4 mins.

In that case, we need to change this:
"second horse from the first round race with the Gold medal winner;" with "second horse from the first round race with the Bronze medal winner;"

Please, explain.
Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: Good Q.  [#permalink]

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03 Oct 2010, 04:19
2
samark wrote:
Bunuel wrote:

For the silver and bronze we would have 5 pretenders:
1. #2 from the 6th race;
2. #3 from the 6th race;
3. the second horse from the first round race with the Gold medal winner;
4. the third horse from the first round race with the Gold medal winner;
5. the second horse from the first round race with horse #2 in the 6th.

So total 7 races are needed.

Bunuel,

It is uncertain to me that how we can be sure to pick horses for 7th race..

Isn't a possibility that second horse from Gold Medal winner group can be slower than the second horse in Bronze Medal winner group?

Lets say: The Gold medal horse took 2 mins, second horse in the Gold medal group took 5 mins to cover the race. While Bronze medal horse took 3 mins and second horse from Bronze medal group took 4 mins.

In that case, we need to change this:
"second horse from the first round race with the Gold medal winner;" with "second horse from the first round race with the Bronze medal winner;"

Please, explain.

The trick here is that we should choose the horses for the last race so that each horse to be pretender for either the Silver or the Bronze medal.

Now, second horse from the first round race with horse #3 in the 6th race could be faster than the second horse from the first round race with the Gold medal winner, but if it is so could this horse get any medal? It's obviously slower than horse #3 and also slower that horse #2 (from the last race) so there is no sense to include this horse in the last race. Similar logic works for other horses.

Hope it's clear.
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Joined: 26 Aug 2010
Posts: 49
Location: India
Re: Good Q.  [#permalink]

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03 Oct 2010, 22:40
Bunuel wrote:
samark wrote:
Bunuel wrote:

For the silver and bronze we would have 5 pretenders:
1. #2 from the 6th race;
2. #3 from the 6th race;
3. the second horse from the first round race with the Gold medal winner;
4. the third horse from the first round race with the Gold medal winner;
5. the second horse from the first round race with horse #2 in the 6th.

So total 7 races are needed.

Bunuel,

It is uncertain to me that how we can be sure to pick horses for 7th race..

Isn't a possibility that second horse from Gold Medal winner group can be slower than the second horse in Bronze Medal winner group?

Lets say: The Gold medal horse took 2 mins, second horse in the Gold medal group took 5 mins to cover the race. While Bronze medal horse took 3 mins and second horse from Bronze medal group took 4 mins.

In that case, we need to change this:
"second horse from the first round race with the Gold medal winner;" with "second horse from the first round race with the Bronze medal winner;"

Please, explain.

The trick here is that we should choose the horses for the last race so that each horse to be pretender for either the Silver or the Bronze medal.

Now, second horse from the first round race with horse #3 in the 6th race could be faster than the second horse from the first round race with the Gold medal winner, but if it is so could this horse get any medal? It's obviously slower than horse #3 and also slower that horse #2 (from the last race) so there is no sense to include this horse in the last race. Similar logic works for other horses.

Hope it's clear.

Yes, after much head banging and heated discussion with my fellow study partner. Thanks!
Intern
Joined: 08 Oct 2009
Posts: 7
Re: Good Q.  [#permalink]

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09 Oct 2010, 04:51
if the runner up in the first race is the fastest among all except the winner of the first race.How could you leave that horse?
Senior Manager
Joined: 24 Aug 2009
Posts: 427
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: Good Q.  [#permalink]

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06 Sep 2012, 03:32
Bunuel wrote:
I came down to 7. I mean that I can do the task in 7 races.

First 5 races: all horses by five. We'll have the five winners.

Race 6: the winners of previous five races. We'll have the 3 winners.
Now it's obvious that #1 here is the fastest one (gold medal).
For the silver and bronze we'll have 5 pretenders:
1. #2 from the last sixth race,
2. #3 from the last sixth race,
3. the second one from the race with the Gold medal winner from the first five races,
4. the third one from the race with the Gold medal winner from the first five races,
5. the second one from the race with the one which took the silver in the sixth race

Race 7: these five horse: first and second in this one will have the silver and bronze among all 25.

Answer B (7).

Good Q. +1

Hi Bunuel,

I have a doubt regarding the solution. The question is asking for Fastest 3 horses & not the Top 3 Winners.
Let me put it this way.
Suppose 2 separate races were conducted & timing (in minutes) of these 10 horses are as follows:
Race 1 - 5, 6, 7, 8 , 9, 10 minutes
Race 1 - 8 , 9, 10, 11, 12 minutes

Now you are picking 5 from race-1 & 8 from race 2 because these 2 horses are winners. But these 2 horses are not the fastest horses. The 2 fastest horses from this scenario would be 5 & 6 min.

As per me had the question asked Top 3 horses then your logic would be completely right but instead the question is asking for the fastest 5.

Kindly throw some light this logic.
Your inputs are always valuable.
Manager
Joined: 14 Nov 2011
Posts: 113
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
Re: Good Q.  [#permalink]

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29 May 2013, 20:10
Bunuel wrote:
I came down to 7. I mean that I can do the task in 7 races.

First 5 races: all horses by five. We'll have the five winners.

Race 6: the winners of previous five races. We'll have the 3 winners.
Now it's obvious that #1 here is the fastest one (gold medal).
For the silver and bronze we'll have 5 pretenders:
1. #2 from the last sixth race,
2. #3 from the last sixth race,
3. the second one from the race with the Gold medal winner from the first five races,
4. the third one from the race with the Gold medal winner from the first five races,
5. the second one from the race with the one which took the silver in the sixth race

Race 7: these five horse: first and second in this one will have the silver and bronze among all 25.

Answer B (7).

Good Q. +1

Hi Bunnel,

Is this a GMAT-kind question?
Math Expert
Joined: 02 Sep 2009
Posts: 64216
Re: Good Q.  [#permalink]

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30 May 2013, 00:03
cumulonimbus wrote:
Bunuel wrote:
I came down to 7. I mean that I can do the task in 7 races.

First 5 races: all horses by five. We'll have the five winners.

Race 6: the winners of previous five races. We'll have the 3 winners.
Now it's obvious that #1 here is the fastest one (gold medal).
For the silver and bronze we'll have 5 pretenders:
1. #2 from the last sixth race,
2. #3 from the last sixth race,
3. the second one from the race with the Gold medal winner from the first five races,
4. the third one from the race with the Gold medal winner from the first five races,
5. the second one from the race with the one which took the silver in the sixth race

Race 7: these five horse: first and second in this one will have the silver and bronze among all 25.

Answer B (7).

Good Q. +1

Hi Bunnel,

Is this a GMAT-kind question?

No, I don't think so.
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Joined: 03 Jul 2013
Posts: 21
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Re: On a race track a maximum of 5 horses can race together at  [#permalink]

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16 Jul 2013, 13:55
It is also possible that one group could be made up of all the fastest horses well another group could have the slowest horse. In this case, the selection of #1's from the first five races is distorted.
Senior Manager
Joined: 07 Apr 2012
Posts: 314
Re: On a race track a maximum of 5 horses can race together at  [#permalink]

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21 Sep 2013, 01:50
Isn't it possible to make just one race?
All the horses run the same track, and after 5 races we can get the results for all horses.
Now we can just choose based on the timing the top 3 fastest horses.....
Why is this wrong?
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Posts: 64216
Re: On a race track a maximum of 5 horses can race together at  [#permalink]

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21 Sep 2013, 01:53
ronr34 wrote:
Isn't it possible to make just one race?
All the horses run the same track, and after 5 races we can get the results for all horses.
Now we can just choose based on the timing the top 3 fastest horses.....
Why is this wrong?

On a race track a maximum of 5 horses can race together at a time...
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Posts: 314
Re: On a race track a maximum of 5 horses can race together at  [#permalink]

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21 Sep 2013, 05:40
Bunuel wrote:
ronr34 wrote:
Isn't it possible to make just one race?
All the horses run the same track, and after 5 races we can get the results for all horses.
Now we can just choose based on the timing the top 3 fastest horses.....
Why is this wrong?

On a race track a maximum of 5 horses can race together at a time...

Sorry....

I meant make just one batch of 5 races....
That way every horse has his own time of finishing the track, and we can choose the ones with the best time.
Those will be our fastest horses and we don't have to make any more races....?

The length of the track does not change between races, so 5 (horses every race) * 5 (races) means all the horses
made one run, and each has his time.... now all that is left is to pick the top ones.....
Re: On a race track a maximum of 5 horses can race together at   [#permalink] 21 Sep 2013, 05:40

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