# Of 200 students surveyed, 120 students liked Soda, 75 students liked juice, and 190 students liked soda or juice. How many students liked soda and juice?

Apr 29, 2018

5 students like soda and juice.

#### Explanation:

This question presents four possibilities.

1. A student likes juice.
2. A student likes soda.
3. A student likes either juice or soda.
4. A student likes juice and soda.

We are given three of the possibilities and asked about the fourth.

It is important to recognise that if a student falls into one of the first two categories, he or she must also fall into one of the last two. For example, say a girl likes soda (2). She must either like only soda (3) or like both soda and juice (4).

In total, $120 + 75 = 195$ students have some sort of preference. In other words, they fall into the four possibilities instead of disliking both drinks.

Now we are told that 190 of them like only one of the two drinks, soda or juice. This leaves $195 - 190 = 5$ students liking soda and juice.