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Practice Number Analogies 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
Two complete pairs of numbers are given, each following the same rule, then a third pair with its second number missing. The child works out the rule and applies it. Despite the name the arithmetic stays deliberately simple - what is measured is whether a child can find a relationship, not whether they can calculate.
Three bracketed pairs in a row, the last carrying a question mark, then four or five numeric choices. The rules are single operations on small whole numbers: add a constant, subtract a constant, double, or halve.
At level 9 — grade 3
Level 9 uses one-step rules on small whole numbers, and the ambiguity between doubling and adding is the characteristic difficulty - both fit the first pair often enough that a third grader who does not check the second will get a run of items wrong for one fixable reason.
Three to six is doubling, and it is also adding three. Both are true, and only one survives the second pair. Testing a candidate rule against the second pair before using it is the whole technique at this level.
If the pairs run from larger to smaller, the missing number is smaller than its partner. Children who have found the right relationship still lose the item by applying it in the wrong direction, and the reversed result is usually among the choices.
The numbers are small on purpose. A child doing heavy arithmetic has probably found a more complicated rule than the item intends, and complicated rules that happen to fit two pairs are almost always the wrong ones.
Make the check explicit: find the rule from the first pair, say it aloud, then test it on the second before touching the third. Almost every mark lost at this level goes to skipping that middle step. If the rule fails the second pair that is useful information rather than a setback - it means going back and finding another relationship in the first.
No - the numbers stay small deliberately. What is tested is spotting the relationship. A child who is fast at calculation but does not think to check the rule against the second pair will still lose marks.
Then one of them fails on the second pair, which is exactly what the second pair is for. If both genuinely survive, they will give the same answer.
Analogies give separate pairs that each follow the same rule; series give one running sequence. The reasoning overlaps, but analogies always supply a second example to check against.
10 example questions with full explanations. Use the interactive practice above to work through the complete set.
Correct answer: C
Look at both complete pairs to find the one rule that works for each. 2 becomes 6 and 3 becomes 9, and multiplying by 3 is the only rule that fits both. So 4 becomes 4 × 3 = 12, making C correct. Choice B comes from adding 3 instead of multiplying, which fits the first pair but not the second. Choice A comes from multiplying by 4, and choice C from doubling.
Correct answer: D
Check both complete pairs to find one rule that works for each. 10 becomes 5 and 8 becomes 4, and halving is the only rule that fits both. Half of 6 is 3, making D correct. Choice A comes from subtracting 5, which works for the first pair but not the second. Choice B comes from doubling instead of halving, and choice C from subtracting 4.
Correct answer: A
The first pair alone is not enough, because 1 becomes 4 whether you add 3 or multiply by 4. The second pair settles it: 2 becomes 5 by adding 3, but multiplying by 4 would give 8. So the rule is add 3, and 3 + 3 = 6, making A correct. Choice D comes from multiplying by 3, choice C from adding 4, and choice A from multiplying by 4.
Correct answer: B
Look for one rule that fits both complete pairs. 12 becomes 4 and 9 becomes 3, and dividing by 3 works for both. Dividing 15 by 3 gives 5, making B correct. Choice C comes from subtracting 8, which fits the first pair only. Choice D comes from multiplying by 3 instead of dividing, and choice A from subtracting 3.
Correct answer: C
Adding 6 turns 5 into 11, but it turns 7 into 13 rather than 15, so that rule fails on the second pair. Doubling and then adding 1 turns 5 into 11 and 7 into 15, so it fits both. Applying it to 6 gives 6 × 2 + 1 = 13, making C correct. Choice A comes from doubling only, choice B from adding 8, and choice C from tripling.
Correct answer: C
Check both complete pairs for one rule that fits each. 10 becomes 7 and 8 becomes 5, and taking away 3 works for both. Taking 3 from 6 gives 3, making C correct. Choice B comes from subtracting 4 instead of 3, choice D from subtracting 2, and choice A from adding 3 rather than subtracting it.
Correct answer: D
The first pair could be doubling or adding 3, so use the second pair to decide. 7 becomes 14 by doubling, but adding 3 would give 10, so the rule is doubling. Doubling 9 gives 18, making D correct. Choice A comes from adding 2, choice B from adding 7, and choice C from adding 11.
Correct answer: A
8 becomes 4 and 12 becomes 6, so each number becomes half of itself. Half of 10 is 5, making A correct. Choice C comes from subtracting 2, which fits neither complete pair. Choice D comes from doubling instead of halving, and choice A from subtracting 3.
Correct answer: B
Look for one rule that fits both complete pairs. 6 becomes 11 and 9 becomes 14, and adding 5 works for both. Adding 5 to 4 gives 9, making B correct. Choice A comes from multiplying by 5, choice C from adding 4, and choice D from adding 6.
Correct answer: C
The first pair fits either multiplying by 5 or adding 16, so check the second pair. 3 becomes 15 by multiplying by 5, while adding 16 would give 19, so the rule is multiply by 5. Multiplying 5 by 5 gives 25, making C correct. Choice A comes from multiplying by 6, choice B from doubling, and choice D from adding 19.