# If F is not selected, which one of the following could be true?

tkj97 on July 7, 2020

Confused

I'm a little confused about the options on this question.

shunhe on July 8, 2020

Hi @tkj97,

Thanks for the question! So what we’re doing is assuming we don’t pick F, and then seeing which one of the answer choices could be true. Could, for example, T be the only side dish selected? Or could exactly three main courses be selected? Let’s find out.

Let’s say we don’t pick F. Well, then we need to pick G since we have to have at least one dessert based on rule 1. And if we pick G we have to pick O based on rule 4.

Now we know that we aren’t selecting F, and we also know that we either have to not select N or not select V (or theoretically we could not select either, but we have to at least not select one based on the last rule). And overall, there are three foods that we aren’t selecting (since we’re selecting 5/8). Which means we have to pick at least one of P and W. But if we pick one of P and W, we pick both P and W. So we also have to select both P and W. So far we have

G O P W __ | F N/V __

OK, now note that we have to pick at least one hot food based on rule 2. Well, we already aren’t selecting F. So we have to pick N or T.

G O P W N/T | F V __

So what could be true? Well, we could pick three main courses! If we pick N, then we’ll have N, O, and P, which would be exactly three main courses. And so that’s a possibility and the correct answer for this question.

Hope this helps! Feel free to ask any other questions that you might have.