CCAT number series questions

Math & Logic

A number series hides one rule that turns each term into the next. Find the rule from the gaps between numbers, then apply it one more time.

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How to solve these

Mini-lesson

A number series hides one rule that turns each term into the next. Find the rule from the gaps between numbers, then apply it one more time.

1
Write the gaps between terms
Look at how you get from each number to the next: +3, +6, +12. Seeing the gaps as their own little series is usually where the pattern appears.
2
Decide the operation
Steady gaps mean adding or subtracting. Gaps that grow fast mean multiplying. A mix (times 2, then plus 1) is common at higher difficulty, so test 'x then +' if a single step does not fit.
3
Apply the rule once more
Once the rule fits every step, use it on the last number to get the answer, then sanity-check it against the options.

Hacks

If numbers shrink, the rule is subtraction or division. 81, 27, 9, 3 is divide by 3 each time.
If numbers grow much faster than adding would, suspect multiplication.
When nothing simple fits, check the gaps-of-the-gaps, or whether two interleaved series are at play.

Avoid these

Assuming a constant difference when the gaps are actually changing.
Stopping at the rule and forgetting to do the final step to reach the next term.

Worked example

Answer shown

An original, CCAT-style item with the full reasoning. This is the kind of question you will drill.

Difficulty 1

Find the next number: 1, -2, -5, -8, -11, ?

Answer: A. Here is why:

The rule is: add -3.
Applying it to -11 gives -14.

Frequently asked questions

What are CCAT number series questions?

Find the pattern in a sequence of numbers and supply the next term. They fall under the Math & Logic part of the CCAT, mixed in among the other types across the 50-question test.

How many number series questions are on the CCAT?

The CCAT does not label or fix the count per type. Items are mixed, so you cannot predict how many number series questions you will see. Training every type is the only reliable preparation.

How do I get faster at number series questions?

Reps under the real clock. However you like to learn, speed only comes from repeated timed practice — and honest per-type numbers show you whether it is working. That feedback loop is the skill the CCAT actually rewards.