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

Question

A park contains at most five of seven kinds of trees - firs, laurels, maples, oaks, pines, spruces, and yews - consistent with the following conditions:

If maples are in the park, yews are not.

If firs are in the park, pines are not.

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

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

If pines are in the park, then which one of the following must be true?

(A) Exactly four kinds of trees are in the park.

(B) Exactly five kinds of trees are in the park.

(C) Neither firs nor maples are in the park.

(D) Neither firs nor oaks are in the park.

(E) Neither laurels nor maples are in the park.

8Harshitsharma · Answer

Short explanation:

Given that pines are in the park, only 2 combinations are possible.

1. y, l, p, o
2. y, l, p, o, s

So A, B, D, E are out and choice C is the answer.

Arya092 · Answer

If Pines are in the park, based on the facts -> 
Figs are not in the park (as per the 2nd statement) ->
Since Figs are not in the park that means both Firs and Spruces are not present Laurels and Oaks are present (as per the 4th statement) -> 
Since both Laurels and Oaks are present, Yews are present (as per the 3rd statement) ->
Since Yews are present Maples are not present.

There is no information about spruces present or not.

Hence, A, B, D and E can be eliminated. Only possible answer is C.

VenkataSai · Answer

How is l,m,p,s not a possbility? can you please explain

guddo · Answer

A park contains at most five of seven kinds of trees - firs, laurels, maples, oaks, pines, spruces, and yews - consistent with the following conditions: 
 
If maples are in the park, yews are not.
 
 If firs are in the park, pines are not.
 
 If yews are not in the park, then either laurels or oaks, but not both, are in the park.
 
 If it is not the case that the park contains both laurels and oaks, then it contains firs and spruces.
 
 If pines are in the park, then which one of the following must be true?

Since pines are in the park, firs cannot be in the park.

Now use the fourth rule. If the park does not contain both laurels and oaks, then it must contain firs and spruces. But firs cannot be in the park. So the park must contain both laurels and oaks.

If laurels and oaks are both in the park, then yews must also be in the park. Otherwise, the rule about yews being absent would require exactly one of laurels and oaks, not both.

Since yews are in the park, maples cannot be in the park.

So  firs and maples must both be out . Spruces are the only tree type still  undetermined .

(A) Exactly four kinds of trees are in the park.

This does not have to be true. Spruces may or may not be in the park.

(B) Exactly five kinds of trees are in the park.

This also does not have to be true. Spruces may or may not be in the park.

(C) Neither firs nor maples are in the park.

This is correct. Pines force firs out, and yews force maples out.

(D) Neither firs nor oaks are in the park.

This is incorrect. Oaks must be in the park.

(E) Neither laurels nor maples are in the park.

This is incorrect. Laurels must be in the park.

Answer: (C)

egmat · Answer

Hi VenkataSai,

Good instinct to stress-test the answer with a specific combo. Let's run  l, m, p, s  through the conditions and watch exactly where it breaks.

Start with the trigger:  pines are in . By condition  2  ( if firs, then not pines ), the contrapositive says  firs are out .

Now look at condition  4 :

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

Your combo has laurels but  no oaks  - so "both laurels and oaks" is false. That fires the rule, and it demands  firs and spruces  both be present. But we just showed  firs can't be in  (pines are in). Contradiction. So l, m, p, s is impossible.

Here's the key move you'd want to lock in:  because firs are forced out the moment pines are in, condition  4 's consequent ("firs and spruces") can never be satisfied. The only way to keep condition  4  happy is to make its  antecedent  false - meaning the park  must contain both laurels and oaks . There's no escape hatch where laurels appears alone.

Once both laurels and oaks are in, condition  3  forces  yews in  (since "exactly one of them" is false), and then condition  1  forces  maples out . That's why maples can't ride along with pines either - so a combo like yours with maples was doomed twice over.

The takeaway: whenever a conditional's  consequent  is already blocked, the  antecedent  is forced false. That single lever is what rules out your combination and drives everything to answer  C .

Answer: C

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

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