### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Find Out If A Number Is Prime

What is the probability of selecting a prime number out of the following set?

{2, 6, 9, 17, 21, 47, 63, 71, 81}

**Possible Answers:**

6/9

4/9

3/9

5/9

9/4

**Correct answer:**

4/9

Probability is determined by dividing favorable outcomes, by possible outcomes. As there are 9 numbers in the given set, the number of possible outcomes is 9. In the given set, only 2, 17, 47 and 71 are prime numbers (divisible only by 1 and itself). Thus, there are 4 favorable outcomes, yielding a probability of 4/9.

### Example Question #2 : Prime Numbers

How many prime numbers between 20 and 40 are divisible by 9?

**Possible Answers:**

2

1

9

0

**Correct answer:**

0

Prime numbers are by definition only divisible by themselves and 1.

### Example Question #3 : Prime Numbers

How many prime numbers are between 40 and 60?

**Possible Answers:**

6

9

5

8

7

**Correct answer:**

5

A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.

### Example Question #4 : Prime Numbers

How many integers between 2 and 61 are prime numbers, inclusive?

**Possible Answers:**

15

16

18

17

19

**Correct answer:**

18

The key word is “inclusive.” The answer is 18 prime numbers. If you answered 16, you did not include 2 and 61 as prime numbers. If you answered 17, you only included one of the outer limits in the range. If you answered 15, you did not include the outer limits, 2 and 61, as prime numbers and miscounted. There are 18 prime numbers between 2 and 61 when you include the range’s limits.

### Example Question #5 : Prime Numbers

Which of the following sets of numbers contain all prime numbers?

**Possible Answers:**

13, 27, 31

13, 29, 35

13, 25, 31

13, 29, 31

13, 27, 33

**Correct answer:**

13, 29, 31

A prime number can only be divided by the number itself and 1.

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