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Practice Number Series questions for the Cognitive Abilities Test — Grade 4 (Level 10). Every question includes a full explanation of why the correct answer is right and why the tempting distractors are wrong.
23 questions available · medium difficulty · CogAT Grade 4 · 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.
Longer sequences whose step itself changes as the line goes on - differences that grow or shrink, or operations that alternate. Some items run two patterns on alternating positions, so no single rule fits the line read straight through.
At level 10 — grade 4
Level 10 introduces sequences whose step changes as they go, and this is a real conceptual jump - the child has to look at the differences rather than the numbers. Fourth graders shown that move explicitly pick it up quickly; those who are not can stall on items well within their ability.
Sequences at this level frequently have differences that grow or shrink rather than hold constant. Working out the gaps between terms and then looking at how those gaps behave finds the pattern that inspecting the terms alone will not.
The pattern usually lives in the differences rather than the numbers, and a child staring at the terms can miss something obvious one level down. Writing the gaps out mentally is a mechanical move that solves most items at this level.
Some items run two patterns on alternating positions, so no single rule fits the line as a whole. When a sequence seems to jump about with no logic, reading every other term is the thing to try.
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: C
This list uses two rules that take turns: multiply by 3, then subtract 2. Check it — 2 × 3 = 6, 6 − 2 = 4, 4 × 3 = 12, 12 − 2 = 10. The next step is a multiply, so 10 × 3 = 30, making C correct. Choice A comes from subtracting 2 again instead of switching back to multiplying. Choice B comes from doubling 10, and choice D from adding 4.
Correct answer: D
Two rules take turns here: add 1, then multiply by 3. Check it — 1 + 1 = 2, 2 × 3 = 6, 6 + 1 = 7, 7 × 3 = 21. The next step is an add, so 21 + 1 = 22, making D correct. Choice A comes from adding 3 instead of 1. Choice B comes from doubling 21, and choice C from adding 7, the number two steps back.
Correct answer: A
The gaps are not equal, so look at the gaps themselves: 4, then 5, then 6, then 7. They grow by one each step, so the next gap is 8, and 27 + 8 = 35. That makes A correct. Choice B comes from repeating the gap of 7 instead of growing it. Choice C comes from adding 9, and choice D from adding 6.
Correct answer: B
Each number is three times the one before: 3 to 9, 9 to 27, 27 to 81. Three times 81 is 243, making B correct. Choice A comes from doubling 81 instead of tripling it. Choice C comes from adding 27, the number before 81, and choice D from multiplying 81 by 4.
Correct answer: A
The gap between each pair of numbers is 6 every time. Adding 6 to 30 gives 36, making A correct. Choice B comes from adding the gap twice, 30 + 6 + 6, which skips a whole step in the list. Choice C is the number that comes before 30, so it moves backwards along the list instead of forwards. Choice D comes from doubling 30 rather than adding the gap.
Correct answer: B
The numbers fall by 25 each time: 200 to 175, 175 to 150, and so on. Taking 25 from 100 gives 75, making B correct. Choice A comes from subtracting the gap twice, 100 − 25 − 25, which skips a step. Choice C is the number that comes before 100, so it moves back up the list instead of down. Choice D repeats the 100 already shown instead of taking another step.
Correct answer: B
Each number is double the one before: 4 to 8, 8 to 16, 16 to 32. Doubling 32 gives 64, making B correct. Choice A comes from adding 16, the number just before 32, rather than doubling. Choice C is the term that comes before 32, so it moves backwards along the list, and choice D comes from multiplying 32 by 4.
Correct answer: C
The gaps are not equal, so look at the gaps themselves: 3, then 5, then 7, then 9. They grow by 2 each step, so the next gap is 11, and 26 + 11 = 37. That makes C correct. Choice A comes from repeating the gap of 9 instead of growing it. Choice B comes from adding 2, the first number in the list, and choice D from doubling 26.
Correct answer: D
The gap between each pair of numbers is 13 every time. Adding 13 to 65 gives 78, making D correct. Choice A comes from doubling 65 rather than adding the gap. Choice B comes from adding the gap twice, 65 + 13 + 13, which skips a step, and choice C is the number before 65, so it moves backwards.
Correct answer: B
Each term is 9 more than the one before: 6 + 9 = 15, 15 + 9 = 24, 24 + 9 = 33, 33 + 9 = 42. The gap is the same every time, so this is a constant-difference series and no ratio or growing-gap rule fits (15 is not a whole-number multiple of 6, and the gaps never change size). The next term is 42 + 9 = 51, choice B. Choice A, 50, comes from counting the gap as 8 instead of 9. Choice C, 52, comes from rounding the gap of 9 up to a friendly 10 and never adjusting. Choice D, 60, comes from adding the gap twice: 42 + 9 + 9 = 60.