HSCT examples | CCTT MathSummer

Some problems on the HSCT involve groups of people exchanging something such as handshakes or cards with everyone else in the group. The questions involve figuring the total number of exchanges. Some problems may be solved by simply multiplying. For other problems, a diagram may be helpful.

Read carefully the two EXAMPLES below.

There are 4 women in Carmelita's study group. The first time they met, they all copied down each other's phone numbers. How many phone numbers were written in all?

Solution: Each woman already knew her own phone number so she didn't need to write it for herself. Each person needed to write her phone number 3 times. If 4 people write their number 3 times each, 12 (4 x 3) telephone numbers will be written in all.

One night 4 friends went to dinner and clinked glasses together 1 time with each person in a toast to each other. How many clinks were there?

Solution: For this one, it is easiest to draw a diagram. Each line shows a glass clinking with one other person. There were 6 clinks.

Use the examples above to help you solve the following two problems.

1. There were 5 people in Meagan' 5 study group. The first time they met, they all wrote down each other's phone numbers. How many phone numbers were written?

2. Six men at a business lunch each shook each other's hand once. How many handshakes were given?

Did you notice a pattern in the problems above? In the problem on the left, the answer is found by taking (the number of people) x (the number of people - 1).

In the problem on the right, instead of each person giving another person something and getting the same item back, they exchange a handshake. Two people exchange one thing - a handshake, instead of two people exchanging two things (like two phone numbers in the problem on the left). Therefore, the answer will be

The answer is that 15 handshakes were exchanged.