Identify these questions

Building on our learning of number series that go ‘up’ and ‘down’, let’s now look at an interesting type of number series where the values go up and down (and vice versa).

They’re questions that look like this:

What is the next number in this series?

4, 2, 6, 3, ?

A 4 B 6 C 9 D 12

OR,

The numbers in each pair of brackets follow the same rule.

Find the missing number.

[8, 18, 9] [2, 12, 6] [?, 14, 7] [12, 22, 11]

A 3 B 4 C 5 D 6

A distinguishing characteristic of these types of questions is that subsequent values can be higher or lower than the previous value and there is generally some form of alternation e.g. higher, lower, higher, lower etc....

This adds another level of difficulty because you are likely dealing with multiple groups of patterns within the same series.

The strategy to answer these questions

To answer these questions, you will be required to:

1. Identify the relationship (this relationship or pattern will hold true for all the numbers) between the numbers, and,
2. Use that relationship to find the missing number or the grouped number set.

Here are rules to uncovering the pattern when the number series is alternating (for example, if a number is less than the previous number and then the number that follows is greater than the previous):

• Treat each movement separately. I.e. The ‘up’ movements in numbers should be treated as one area to focus on and the ‘down’ movement in numbers should be treated as another separate area.
• With each separate area, following the standard rules for ‘up’ and ‘down’. It is likely that the relationship that holds together numbers going up are derived from addition and/or multiplication and numbers going down are derived from subtraction and/or division.
  

If we examine the example below.

2 5 4 7 6 9 8

You can see that from 2 to 5, the pattern is adding up by three units (2 + 3 = 5) and then from 5 to 4, you are subtracting by one unit (5 – 1 = 4).

You should test this on a few other numbers in the series and if they hold true, the relationship identified would be 'add three units and then minus one unit'.

This pattern would then be repeated for the other numbers.

Example Question/s

Watch video for explanation of the following question/s:

The numbers in each of the three brackets follow the same rule. Find the missing number.

[14, 25, 32] [22, 31, 42] [?, 48, 56]

A 8 B 10 C 12 D 16

The numbers in each of the three brackets follow the same rule. Find the missing number.

[28, 4, 7] [36, 6, 6] [72, 8, ?]

A 5 B 6 C 7 D 9

Key Rules to remember

• A number series that alternates requires you to address and group like movements together and figure out the pattern for the grouped movement.
• Deal with ‘up’ movements by considering addition, multiplication and/or combinations.
• Deal with ‘down’ movements by considering subtraction, division and/or combinations.

Practice time!

Now, it's your turn to practice.

Click on the button below and start your practice questions. We recommend doing untimed mode first, and then, when you're ready, do timed mode.

Every question has two solutions videos after you complete the question. The first is a quick 60 second video that shows you how our expert answers the question quickly. The second video is a more in-depth 5-steps or less explainer video that shows you the steps to take to answer the question. It's really important that you review the second video because that's where you'll learn additional tips and tricks.

Once you're done with the practice questions, move on to the next checkpoint.

Now, let’s get started on your practice questions.

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