We know that a fruit stand carries at least one of the following kinds of fruit: F, K, O, P, T, and W.
The stand does not carry any other type of fruit.
This is a group (in/out) game. Each fruit is either carried by the stand or it isn't. We know that the stand carries at least one type of fruit, so the maximum number of fruits which can be "out" is 5.
IN: _ _ _ _ _ _ | OUT: _ _ _ _ _
Now let's go through our conditions.
Rule 1 - if the stand carries K, then it does not carry P
K --> Not P P --> Not K
Rule 2 - if the stand does not carry T, then it carries K
Not T --> K Not K --> T
Rule 3 - if the stand carries O, then it carries both P and W
O --> P and W Not P or Not W --> Not O
Rule 4 - if the stand carries W, then it carries F or T or both
W --> F and/or T Not F or Not T --> Not W
Notice that we can make a couple deductions using transitive chains.
--> K --> Not P --> Not O Not T --> Not W
--> P --> Not K --> T O --> W --> F and/or T
The question stem asks us which could be the only kind of fruit the stand carries. Which rule will be most important in helping us figure this out? Rule 2 is the only rule whose sufficient condition is the absence of a fruit. Notice that Rule 2 tells us that if the stand does not carry T, then it MUST carry K. The contrapositive tells us that if the stand does not carry K, then it must carry T.
This tells us that the stand must always carry either K or T or both. Kiwi is not an answer choice provided to us, but tangerine is. Therefore, answer choice (D) should be our correct answer. However, let's double check that all the other answer choices are wrong.
If the stand only carries F, then it does not carry T, meaning it must also carry K. Therefore, answer choice (A) is incorrect.
The same reasoning applies for answer choices (B), (C), and (E), making (D) our correct answer.
Hope this helps! Please let us know if you have any further questions.
