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In a certain pond, 50 fish were caught, tagged, and returned [#permalink]

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18 Aug 2011, 10:50

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In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?

In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond? (A) 400 (B) 625 (C) 1,250 (D) 2,500 (E) 10,000

2/50 re-caught means that 50 fish represents 1/25th of all fish in the pond. 50*25 = 1250, C

In a certain pond, 50 fish were caught, tagged, and returned [#permalink]

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01 Oct 2015, 11:35

VeritasPrepKarishma wrote:

Sachin9 wrote:

so, x * 4% = 50

This is how I solved too.. This works but I dont think this is right... 4% is actually equal to percent of tagged fish in the pond..

Could somebody please confirm if this is right?

This is correct. You are assuming that the total number of fish in the pond is x

4% of x = 50 (Number of tagged fish is 4% of the total fish) You get x = 1250

So total fish in the pond = 1250

Why is the total number of tagged fish 50 as opposed to 98. I got 98 by adding the number of tagged fish in the first catch and the number of tagged fish in the second catch. -> 50+48 = 98

This prompt is about ratios (and in the broader sense, it's an example of 'representative sampling').

To start, we're told that 50 fish are caught, tagged and returned to the pond. There are now an UNKNOWN number of total fish in the pond, but 50 of them are 'tagged.'

Later on, 50 fish are again caught, but 2 of them are ALREADY TAGGED. We're told that the percent of fish IN THIS GROUP that are tagged is approximately = the TOTAL percent of ALL fish that are tagged....With this information, we can set up a ratio...

2/50 = ratio of tagged fish in this sample 50/X = ratio of tagged fish in the pond

This is how I solved too.. This works but I dont think this is right... 4% is actually equal to percent of tagged fish in the pond..

Could somebody please confirm if this is right?

This is correct. You are assuming that the total number of fish in the pond is x

4% of x = 50 (Number of tagged fish is 4% of the total fish) You get x = 1250

So total fish in the pond = 1250

Why is the total number of tagged fish 50 as opposed to 98. I got 98 by adding the number of tagged fish in the first catch and the number of tagged fish in the second catch. -> 50+48 = 98

Very simply - the 50 fish caught in the second catch were not tagged. They were just caught and it was observed that 2 of them are tagged. The leftover 48 were not tagged. The second catch was only to find the approximate percentage of tagged fish in the pond (a technique called sampling).

For example: In a large population, it is difficult to find the number of people with a certain trait, say red hair. So you pick up 100 people at random (unbiased selection) and see the number of people who have red hair. Say, 12 have red hair. So you can generalise that approximately 12% of the whole population has red hair.

Here, since counting the number of total fish in the pond is hard, they tagged 50 and let them disperse evenly in the population. Then they caught 50 and found 2 to be tagged. So approximately 4% of the fish were tagged. So 50 is 4% of the entire fish population of the pond. Note that the method uses huge approximation because of the small sample number. If 1 more tagged fish were caught among the 50, it would change the approximated fish population number by a huge amount. But they have given us that "the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond" so we can make this approximation.
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Re: In a certain pond, 50 fish were caught, tagged, and returned [#permalink]

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21 Feb 2017, 01:30

Hi can you help me with this problem? The last part of the problem It is not clear for me. I don't know if I have to use 50 fish or 48 fish still in the pond

- 2 fish tagged / 50 in the second catch - 48 fish are still in the pond

So the equation is: 48 fish tagged in the pond/Tot in the pond = 2 fish tagged out/50 fish catched Tot in the pond = 48*2/50 = 1200 (aprox. 1250) --> answer is C

Re: In a certain pond, 50 fish were caught, tagged, and returned [#permalink]

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30 Apr 2017, 10:41

Sachin9 wrote:

so, x * 4% = 50

This is how I solved too.. This works but I dont think this is right... 4% is actually equal to percent of tagged fish in the pond..

Could somebody please confirm if this is right?

Hi,

Although solution has already been provided for this. here is my 2 cent.

I think when they say that the percent of tagged fish caught the second time represents the percent of tagged fish in the pond, they are talking about the first 50 that were tagged and left in the pond and not the 50 caught the second time.

Thus, the first 50 tagged fishes are 4% of the entire fish in the pond.

Hope this is clear.
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In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?

(A) 400 (B) 625 (C) 1,250 (D) 2,500 (E) 10,000

We are given that 50 fish were caught, tagged, and returned to the pond, and that a few days later, 50 fish were caught again, of which 2 were tagged. Thus, the percentage of tagged fish is 2/50 = 1/25 = 4%.

Since the the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond, the approximate number of fish in the pond is:

0.04(total fish) = 50

total fish = 50/0.04 = 5000/4 = 1250

Answer: C
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Scott Woodbury-Stewart Founder and CEO

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Re: In a certain pond, 50 fish were caught, tagged, and returned [#permalink]

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07 Oct 2017, 19:04

ScottTargetTestPrep wrote:

Since the the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond, the approximate number of fish in the pond is:

0.04(total fish) = 50

This equation assumes that there are 50 fish tagged in the total population. We do not know that. The only thing we know is that that the percentage of tagged fish in the second catch is 4%. The question says that 4% approximates the number of tagged fish in the pond. So this is the true equation we have:

Quote:

.04 (total) = tagged fish

We are missing two variables. We don't know the total fish and we don't know the tagged fish.

If there are 16 tagged fish, then choice A is correct. If there are 26 tagged fish, then choice B is correct, and etc.

If we assume that the number of fish in the second catch (50) is the number of fish tagged, then yes the total fish would be 1250. However, that's not what the question provides. I think this question is written poorly.

Since the the percentage of tagged fish in the second catch approximates the percentage of tagged fish in the pond, the approximate number of fish in the pond is:

0.04(total fish) = 50

This equation assumes that there are 50 fish tagged in the total population. We do not know that. The only thing we know is that that the percentage of tagged fish in the second catch is 4%. The question says that 4% approximates the number of tagged fish in the pond. So this is the true equation we have:

Quote:

.04 (total) = tagged fish

We are missing two variables. We don't know the total fish and we don't know the tagged fish.

If there are 16 tagged fish, then choice A is correct. If there are 26 tagged fish, then choice B is correct, and etc.

If we assume that the number of fish in the second catch (50) is the number of fish tagged, then yes the total fish would be 1250. However, that's not what the question provides. I think this question is written poorly.

So the question states that "In a certain pond, 50 fish were caught, tagged, and returned to the pond."

From this sentence, we can deduce that there are indeed a total of 50 tagged fish in the pond. The only way to have some other number of tagged fish in the pond is if there were already some number of tagged fish in the pond (in which case, the question would have told us so) or if either more fish were tagged afterward or some of the tagged fish were removed from the pond (again, we would have been told). Since we have no such information, we cannot assume that there might be some other number of tagged fish in the pond.

Perhaps you are missing the fact that 50 fish are caught TWICE: first all of them are tagged, and the second time, the tagged fish are counted.
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Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

In a certain pond, 50 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?

(A) 400 (B) 625 (C) 1,250 (D) 2,500 (E) 10,000

The concept here is that the 50 fish that were caught the second time are REPRESENTATIVE of the entire fish population in the pond. In other words, the RATIO of the # of tagged fish to total fish in second sample = the RATIO of the # of tagged fish in pond to total fish in pond

That is: (# of tagged fish caught the second time)/(total # of fish caught the second time) = (# of tagged fish in pond)/(total # of fish in pond) Let x = total # of fish in pond We get: 2/50 = 50/x Cross multiply to get: 2x = (50)(50) Solve: x = 1250