ACT Math : How to find the missing number in a set

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Sets

Ryan’s class lined up in order of birthdays. If Ryan is the 11th oldest and 9th youngest, how many students are in his class?

 

Possible Answers:

19

18

20

21

11

Correct answer:

19

Explanation:

  Ryan is the 11th oldest and 9th youngest, so there are 10 students older than him and 8 younger than him. The 10 older plus the 8 younger plus Ryan himself gives a total of 10+8+1 = 19. (The trick is not to double-count Ryan.)

 

 

Example Question #2 : Sets

What is the next integer in this series of numbers?

1, 4, 7, 10, 13, ?

Possible Answers:

16

15

18

17

14

Correct answer:

16

Explanation:

Each number is the previous number + 3.

Example: 1 + 3 = 4

13+3 = 16

Example Question #3 : Sets

If the average and median of the group of integers shown below is equal to x, what is the value of x?

40, 11, 62, x, 20, 51, 2

 

Possible Answers:

31

14

26

28

Correct answer:

31

Explanation:

First, we must find the average of these 6 numbers. This is done by adding all of them and dividing by the number of values we have (in this case, 6). 

Next, we have to make sure that this number is also the median.  Since the median is the middle number of our values put in ascending order, we have to put our values in increasing order:

2, 11, 20, 31, 40, 51, 62

When we do this, we see that 31 is indeed the “middle number” so we are happy with choosing 31 as our correct answer

 

Example Question #4 : Sets

The following series of numbers follows a rule to progress from number to number.  What is the value of Y?

4, 15, 59, Y, 939

Possible Answers:

789

95

329

 97

235

Correct answer:

235

Explanation:

Each number from set is:

(Previous Number x 4) – 1

Example: (4 x 4) – 1 = 15

Answer: (59 x 4) – 1 = 235

Example Question #5 : Sets

There is a set of numbers. The mean of this set of numbers is equal to the median.  If four of the numbers are 10, 15, 15, and 17, what is the fifth number?

Possible Answers:

13

18

15

12

16

Correct answer:

18

Explanation:

Since the set contains two 15s, along with 10 and 17, the median can only be 15, no matter what the fifth number is. So now we know that the mean is equal to 15, since it is equal to the median. Now an equation can be set up to solve this problem. 15 = (10 + 15 + 15 + 17 + x)/5. Solving for x we get an answer of 18.

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