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Practice Number Series questions for the Cognitive Abilities Test — Grade 3 (Level 9). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
24 questions available · medium difficulty · CogAT Grade 3 · Free, no registration required
A sequence of numbers is given and the child works out what comes next. It measures inductive reasoning with quantity - noticing a pattern from a few instances and extending it - and, like the other quantitative subtests, keeps the arithmetic light so the reasoning is what shows.
Five or six numbers followed by a blank, with four or five choices. The sequences move by a constant step or by doubling, the direction stays the same throughout, and the line is short enough to hold in view all at once.
At level 9 — grade 3
Level 9 sequences move by a constant step or double, and stay short enough for a third grader to hold the whole line in view. Most lost marks are arithmetic slips on the final step rather than failures to see the pattern, which is worth knowing before assuming the reasoning is the problem.
The first two gaps are often equal even when the sequence is not arithmetic, so a child who checks two gaps and commits gets caught by items designed around exactly that. Checking every gap costs little at this length.
Descending sequences get read as ascending surprisingly often, particularly under time pressure. The result of getting this backwards is usually one of the offered choices.
The reasoning can be entirely right and the answer still wrong because the final calculation went astray. Since the numbers are small, re-checking that last step is cheap and catches most of these.
Teach the gaps: have your child work out the difference between each pair of neighbouring numbers and look at those differences as a row of their own. It is a mechanical move that turns most sequences at this level into an obvious pattern, and it generalises to the harder items later. Counting aloud in steps - threes, fours, sixes - also builds the fluency that makes the gaps visible without effort.
At this level, adding or subtracting a fixed amount, and doubling. The useful habit is checking the gap between every pair rather than assuming the first gap holds.
Usually an arithmetic slip on the final step. The reasoning is the hard part and it is already done, so re-checking the last calculation is worth the couple of seconds.
Not directly, though fluency helps because it frees attention for the pattern. The numbers stay small so that finding the rule is what determines the score.
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Correct answer: D
Find the gap between each pair of numbers. From 4 to 8 is 4, from 8 to 12 is 4, and the gap stays 4 all the way along. Adding 4 to 20 gives 24, so D is correct. Choice C comes from adding 2 instead of 4, and choices B and A do not follow any steady gap in the list.
Correct answer: A
The gaps here are not the same each time, so look at the gaps themselves. They are 1, then 2, then 3, then 4, growing by one each step. The next gap must be 5, and 11 + 5 = 16, making A correct. Choice C comes from repeating the gap of 4 instead of growing it, choice D from adding 3, and choice A from jumping the gap to 7.
Correct answer: D
Look at the gap between each pair of numbers. It is 3 every time, all the way along the list. Adding 3 to 15 gives 18, making D correct. Choice C comes from adding 1, choice B from adding 2, and choice A from jumping to the next multiple of 10 instead of following the gap.
Correct answer: A
The numbers are getting smaller, so find how much is taken away each time. From 100 to 90 is 10, and the gap stays 10 all the way down. Taking 10 from 60 gives 50, making A correct. Choice C comes from subtracting 5, choice D from subtracting 20, and choice A from going back up instead of down.
Correct answer: B
The gaps here keep changing, so try multiplying instead of adding. Each number is double the one before it: 1 to 2, 2 to 4, 4 to 8, 8 to 16. Doubling 16 gives 32, making B correct. Choice D comes from adding 4, choice A from adding 8, which is the previous gap, and choice B from adding 2.
Correct answer: C
The gaps are not equal, so look at the gaps themselves: 2, then 3, then 4, then 5. They grow by one each time, so the next gap must be 6. Adding 6 to 16 gives 22, making C correct. Choice D comes from repeating the gap of 5 instead of growing it, choice A from adding 4, and choice B from jumping the gap to 8.
Correct answer: D
The numbers get smaller by the same amount each time. From 90 to 80 is 10, and that gap of 10 holds all the way down. Taking 10 from 50 gives 40, making D correct. Choice A comes from subtracting 5, choice B from subtracting 20, and choice C from subtracting 15.
Correct answer: A
The gaps are not equal, so look at the gaps themselves: 3, then 5, then 7, then 9. They grow by 2 each time, so the next gap is 11, and 25 + 11 = 36. That makes A correct. Choice B comes from adding 5, choice C from adding 10, and choice D from skipping ahead an extra step in the pattern.
Correct answer: B
The gaps keep growing, so try multiplying instead of adding. Each number is double the one before: 5 to 10, 10 to 20, 20 to 40, 40 to 80. Doubling 80 gives 160, making B correct. Choice A comes from adding 40, which is the previous gap, choice D from adding 20, and choice B from adding 60.
Correct answer: C
Look at the gaps rather than the numbers: they are 2, then 3, then 4, then 5, growing by one each step. The next gap must be 6, and 17 + 6 = 23, making C correct. Choice A comes from repeating the gap of 5 instead of growing it, choice D from adding 4, and choice B from adding 7.