We know that a chef is deciding which vegetables to include in a soup. There are seven vegetables: G, J, K, O, P, T, and Y.
Rule 1 tells us that, if J is an ingredient, then it must be added either first or last.
J --> J first OR J last Not J first AND Not J last --> Not J
Rule 2 tells us that, if J is an ingredient, then Y must not be an ingredient.
J --> Not Y Y --> Not J
Rule 3 tells us that either P or Y is an ingredient; however, the soup cannot include both P and Y.
P --> Not Y Y --> Not P
Rule 4 tells us that G, K, O, and T must be ingredients.
Finally, Rule 5 tells us that O must be added at some time before G, and G must be added at some time before both K and T.
> K O > G > T
The question stem tells us that Y is added first. We can conclude from our rules above that this means that neither J nor P can be included in the soup.
Therefore, our ingredients must be Y, G, K, O, and T.
We know that Y is first. Based on the order we outlined under Rule 5, O must be second, G must be third, and K and T must be fourth and fifth, although the order does not matter.
Y O G K/T T/K 1 2 3 4 5
Therefore, answer choice (A) is incorrect because we know that O must be added second.
Answer choice (B) is incorrect because we know that the soup cannot contain J.
Finally, answer choices (C) and (E) are incorrect because T can be fourth and K can be fifth. All we know is that Y, O, and G must be added before K and T. We know nothing about the order of K and T in relation to one another.
Answer choice (D) must be correct because we know that Y is added first and that neither J or P are in the soup. Therefore, the order we outlined under Rule 5 tells us that there must be at least three ingredients added after O. This means that the only possible point at which O can be added is second.
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