­A park contains at most five of seven kinds of trees - firs, laurels

­HarshR9 can you have a look at this one?­

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Given: Maples and  Spruces are not in the park.  x M, x S  
5 kinds are leftover

Look at the conditions. Where do M and S appear?

If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

x S means Not (not Both L and O). (Recall If A, then B gives us 'Not B implies Not A) 
In other words, x S implies Both L and O are present.

If Yews are not in the park, then either Laurels or Oaks, but not both are in the park.
Since both L and O are in the park, it implies that Yews are present too. (Not B implies Not A)

So L, O and Y are certainly in the park.

If Firs are in the park, Pines are not.
This means, at most one of F and P are in the park. If F are there, P are not. If P are there, F are not. It is possible that neither are there. 

If maples are in the park, yews are not.
We know that Y are there and M are not. It is consistent with our data. 

Hence, the park has L, O and Y and it could have one of F and  P too. So it could have 3 or 4 kinds of trees. 
Hence option (A) could be true. But (B), (C), (D) and (E) are not possible. 

Answer (A)

Conditionals are discussed here:
https://youtu.be/MmlwcTlHZz8
https://youtu.be/BW8Ijrhjjq8
https://youtu.be/yQYkL1DSslA
 

 
­Sure RenB. This is how I solved this. Hope it helps. In hindsight, starting with the last condition (which talks about spruces) may have been the quicker way to solve. In any case, this is an awesome question. 

The question: If neither maples nor spruces are in the park, then which one of the following could be true?
Note: we are not asked what must be true, only what could be true. Important to keep this in mind. 

Types of trees: F, L, M, O, P, S, Y
Given: neither M nor S are in the park.  
Remaining possibilities for the park: {F, L, O, P, Y}
Examples: FLOPY, FLOY, PLOY, FLOP, FLO, OP, F, L, etc. 

We need to find what could work given the conditions.

-> At most 5.
This condition will definitely be met whatever set/subset is chosen from {F,L,O,P,Y}. No need to worry about this.

-> If maples are in the park, yews are not.
Given that M's are not in the park, Ys can very well still be in the park. FLOPY and any subset of {F,L,O,P,Y} are still possible.

-> If firs are in the park, pines are not.
FLOPY is not possible anymore (F and P cannot be together). But FLOY and PLOY are possible. And so are all other subsets of {F,L,O,P,Y} where F and P are not both in i.e., subsets of {F,L,O,Y} and {P,L,O,Y}. Ex -> FLO, PLO, etc.

-> If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.

Another way to say this: In every other case (except L and O both being in), the park definitely contains firs and spruces. 

i.e., if (L but not O (or) O but not L (or) neither L nor O), then we would see both F and S.

But we already know that the park does not have S. Then, it must be the case that we actually have both L and O in the park. 

So, what is still possible? All subsets of {F,L,O,P,Y} where ->

1) Both L and O are in
2) F and P are never both in. 

LO, LOY, LOF, LOP, FLOY, PLOY

-> If yews are not in the park, then either laurels or oaks, but not both are in the park.

If Y is not in, then L and O cannot both be in.

But we have already established that L and O are both in. This implies that Y must be in.

So, what are the remaining possibilities? FLOY, PLOY, LOY (remove cases not having a Y)

Now that we have processed all the conditions, let's check the choices.

(A) Exactly four kinds of trees are in the park. Could be True. FLOY, PLOY, for example.

(B) Exactly five kinds of trees are in the park. Not possible. We have derived that either 3 or 4 kinds of trees are in the park.

(C) Laurels are not in the park. Not Possible. L, O, and Y are in in all possible cases. 

(D) Oaks are not in the park. Not Possible. L, O, and Y are in in all possible cases. 

(E) Yews are not in the park. Not Possible. L, O, and Y are in in all possible cases. 


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Harsha
Enthu about all things GMAT | Exploring the GMAT space | My website: gmatanchor.com­