### All PSAT Math Resources

## Example Questions

### Example Question #1 : Range

Find the range of the following sequence:

1, 3, 4, 6, 11, 23

**Possible Answers:**

6

8

22

5

**Correct answer:**

22

To find the range, subtract the smallest number from the largest number. In this case we get 23 - 1 = 22 so the range is 22.

### Example Question #1 : How To Find Range

What is the range of the data set below?

103, 132, 241, 251, 623, 174, 132, 170, 843, 375, 120, 641, 384, 222, 833

**Possible Answers:**

545

103

740

833

473

**Correct answer:**

740

The range of a set of data is found by subtracting the smallest item from the largest. In this case, 843 - 103 = 740.

### Example Question #2 : Range

Find the range of the data set:

25, 83 , 51, 13, 37, 21, 52, 58

**Possible Answers:**

44

42.5

83

13

70

**Correct answer:**

70

44 is the median of the data. 42.5 is the arithmetic mean. 13 is the minimum value. 83 is the maximum value.

To find the range, subtract the minimum value from the maximum value:

83 - 13 = 70

### Example Question #1 : How To Find Range

F, G, H are the only three numbers in a sequence in which each number is twice the number before it. The three number have an arithmetic mean of 21. What is the value of H?

**Possible Answers:**

24

22

36

30

63

**Correct answer:**

36

We know that H = 2G = 4F, and G = 2F and that (F + G + H)/3=21. If we substitute each term with its F equivalent we get:

(F + 2F + 4F)/3 = 21

7F/3 = 21

7F = 63

F = 9

If we substitute F = 9 into H = 4F, we get H = 36.

The correct answer is 36.

### Example Question #1 : How To Find Range

A set of numbers consists of eleven consecutive even integers. If the median of the set is 62, what is the range of the set?

**Possible Answers:**

**Correct answer:**20

We don't know what the numbers are yet, so let's just call them a_{1}, a_{2}, a_{3}, a_{4}....a_{11}. Let's assume a1 is the smallest, and a11 is the greatest.

If we were going to find the median of our set, we would need to line them all up, from least to greatest.

a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}, a_{7}, a_{8}, a_{9}, a_{10}, a_{11}

The median is the middle number, which in this case about be a_{6}, because there are five numbers before it and five numbers after it.

We know that the median is 62, so that means that there must be five numbers before 62 and five numbers after. Because the numbers are all consecutive even integers, the set must look like this:

52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72

To find the range of this set, we must find the difference between the largest and smallest numbers. The largest is 72, and the smallest is 52, so the range is 72 - 52 = 20.

The answer is 20.

### Example Question #1 : How To Find Range

The median of a set of eleven consecutive odd integers is 39. What is the range of the set?

**Possible Answers:**

29

30

20

10

39

**Correct answer:**

20

Let's represent the eleven integers as A, B, C, D, E, F, G, H, I, J, and K. Let's assume that if we lined them up from least to greatest, the set would be as follows:

A, B, C, D, E, F, G, H, I, J, K

The median in this set is the middle number. In this case, the middle number will always be F, because there are five numbers before it and five numbers after it.

We are told that the median is 39. Thus F = 39, and our set looks like this:

A, B, C, D, E, 39, G, H, I, J, K

Since we know that all the numbers are consecutive odd integers, the set must consist of the five odd numbers before 39 and the five odd numbers after 39. In other words, the set is this:

29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49

The question asks for the range of the set, which is the difference between the largest and smallest numbers. In this case, the range is 49 – 29 = 20.

The answer is 20.

### Example Question #1 : Range

Find the range.

**Possible Answers:**

**Correct answer:**

First, arrange the numbers from highest to lowest, then subtract the highest number from the lowest number.

### Example Question #1 : How To Find Range

Marker Colors |
Students |

Blue |
13 |

Pink |
10 |

Orange |
5 |

Brown |
5 |

Green |
7 |

The above chart shows the number of students in a class who chose each of the five marker colors available.

What is the range of the students’ choices?

**Possible Answers:**

**Correct answer:**

The range of a data set is the distance between the smallest number and the largest number. To find the range, you subtract the smallest number (5) from the largest number (13). Therefore, the range is 8.

### Example Question #1 : How To Find Range

Find the range of the following set of numbers:

**Possible Answers:**

**Correct answer:**

To find the range of a data set, subtract the smallest number in the set from the largest: