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Oppenheimer1945
Agree . S1 should be NO­

Bunuel
­
Here is the OE:


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Quote:
­Statement 1: Each body of water contains at least one fish species found in at least one of the other bodies of water.

Elbow Lake has Banded killifish & Black crappie which are not there in any of the other water bodies.
Hence, it should be NO
S1 should be Yes. Elbow Lake does contain at least one fish species found in at least (or in other words, another) one of the other bodies of water.

For example, all the fish below found in Elbow Lake...
  • Largemouth Bass is also found in Warner, Lindsey, and Long Lake.
  • Pumpkinseed is also found in Warner, Linsey, and Barb's Marsh.
  • Yellow Perch is also found in Warner, Linsey, and Long Lake.

The two fish species found only in Elbow Lake has no bearings on if other species found in its lake is found in other bodies of water.

This is true for all of the other bodies of water.

Hope that helps.­
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KarishmaB GMATinsight pls explain this one- did not get the third part
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Statement 1: Each body of water contains at least one fish species found in at least one of the other bodies of water.

Elbow Lake has Banded killifish & Black crappie which are not there in any of the other water bodies.
Hence, it should be NO­
­read it again carefully.
the rest three fish species you didn't mention in Elbow Lake do exist in other bodies of water.

the statement does not ask you to pinpoint a fish species unique to a particular water body, but ask you whether all of fish species living in a particular water body are unique to that water body.­
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An easier/alternative way of doing the third one:

We have to take elbow lake as first species is unique to it.
Moving further in the list of species we can conclude that we must take bobs marsh as 5th (brook stickleback) is unique to it. and further we can conclude we need to consider Lindsey as northern pike is unique to it. Now keep moving down in the list and check if all species belong to either of these three lakes if no then answer is no as there cant be any other set of three (due to the uniqueness stated).
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MartyTargetTestPrep, KarishmaB can you pls explain the solution.
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Yes for statement 1 is correct as it says atleast one,for example if there are 4 species in a lake and 3 of them are not present in any other but the last one is present in some other lake. Hence, yes.
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Just a day earlier I had posted here asking as to why the answer for S1 will be YES, and surprisingly, I understood it a day later. (deleted the prev. post)

The statement says, Each body of water contains at least one species found in at least one of the other bodies of water.

To break this statement down, what it's really trying to ask is whether All of the water bodies have MINIMUM one fish species that is there in some other water body too.

For eg., if Species X is in Lake A, then Species X is also in Lake B.
To mark a yes here, we need just one example of such a case, regardless of whether any other species Y in that Lake A is present in Lake B/C/D... or not.

One would say that answer must be a NO because Banded killfish or Black Crappie are nowhere else to be found except Elbow lake. Fine, but the rest of the species in Elbow lake like the Yellow Perch or the Pumpkinseed or the Largemouth Bass ARE FOUND IN OTHER LAKES TOO, so, eventually, that fulfills our At least criteria.

Thus, it can be said that in every lake, there is one species that is common to some other lake too. And this is what the statement is all about.

So answer to S1 must be a YES
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My solution to this question, since it seems to be marked as 95% difficulty:

Q1: If the question is asking whether each body of water contains at least 1 fish that is present in at least 1 other body of water, then really all we need to do is just find one example of this condition for each body of water:

Warner Lake has the Brown Bullhead, which is also found in Lindsey Lake
Lindsey Lake has the Brown Bullhead, which is also found in Warner Lake
Long Lake has the Bluegill, which is also found in Lindsey Lake
Elbow Lake has the Largemouth Bass, which is also found in Warner, Lindsey AND Long Lakes
Barb's Marsh has the Bluegill, which is also found in Long and Lindsey Lakes

Therefore, this condition is a Yes

Q2: If a species of fish is found in every single body of water, that means that, according to the graph, there should be a species of fish in which the entire row is marked with x marks. However, there is no such species in this table; therefore, this condition is a No

Q3: In order to find a combination of 3 lakes that contain all species of fish put together, first let's find the lakes in which it contains the ONLY instance of certain species:

Elbow Lake is the only lake with Banded killifish and Black crappie, so we must have this lake. Similarly, Barb's Marsh is the only lake with Brook stickleback, Central mudminnow and Northern redbelly dace, so we must have this lake too.

This leaves us with room for just 1 more lake. Now we take Elbow Lake + Barb's Marsh and check which species have not yet been found in this combination; aka which species do not have an x mark in either of the last 2 columns. In this case, it would be the Brown bullhead, Northern pike and Yellow bullhead. We need to find a lake that contains these 3 species. Looking at the table, Lindsey Lake contains the missing species that we are looking for.

Therefore, taking Lindsey Lake + Elbow Lake + Barb's Marsh, we do indeed get all the species of fish.

Thus, this condition is a Yes

Final answer: Yes, No, Yes
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Statement 1:
Each body of water contains at least one fish species found in at least one of the other bodies of water.

What this means:
Every single water body contains at least one fish species that is also found in some other water body.

What we need to look for in the table:
Take one column (water body) at a time. For every column, can we find at least one "x", such that some other column also has an "x" in the same row?

Analysis:

(I have highlighted examples to show that for every water body, we can indeed find at least one fish species that is also found in some other water body (in at least one other). Thus, YES.



Statement 2:
There is at least one species of fish that is found in each of the bodies of water.

What we need to look for in the table:
Take one row (fish species) at a time. Is there any for which there is an "x" in all 5 columns?

Analysis:
We can very quickly eye-ball this. Clearly, there is no row for which there is an "x" in every column. Thus, NO.

Statement 3:
There is at least one set of three of the bodies of water that collectively contain all of the species of fish.

What we need to look for in the table:
Can a set of 3 columns be chosen such that collectively i.e., across these 3 columns, there is at least one x in every row?

Analysis:


One algorithm


Start from the top row to see if we can ensure that every row has at least one x.

-> For rows 1 and 2, we must include Elbow Lake.
-> For rows 3, we could consider Lindsey Lake, Long Lake, or Bob's Marsh. For row 4, we could consider Long Lake or Bob's Marsh. But for row 5 (Brook stickleback), we must include Bob's Marsh.

-> Similarly, for row 6, we could consider Warner Lake or Lindsey Lake. Keep going down row by row. For row 9 (Northern pike), we absolutely must include Lindsey Lake.

We have identified 3 lakes that absolutely MUST be included. Now, we need to check whether, using these 3 lakes, we can ensure that every row has at least one x. Eye-ball this. We can see that every row will have at least one x if we consider the set of 3 lakes as Elbow Lake, Bob's Marsh, and Lindsey Lake. Thus, YES.

So, overall, the answer is -> Yes, No, Yes.

Harsha
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