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Practice Number Analogies 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
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.
The same structure over a wider number range, with rules that combine two steps - double then add one, multiply then subtract - among the harder items. A few relationships are not arithmetic at all but depend on a property of the number itself.
At level 10 — grade 4
Level 10 widens the number range and begins including rules that combine two operations among the harder items. Fourth graders also meet their first relationships that are not straightforward arithmetic, which need introducing explicitly or they will not be looked for.
Many items at this level need two operations, and a single-step rule fitting one pair will fail the other. When no simple rule works for both, the answer is not that the item is broken but that the rule has two parts.
Some items relate numbers by something other than an operation - a number and its square, a number and how many factors it has. Children looking only for arithmetic will not find these, and the items are placed to reward those who look wider.
This remains the commonest error at every level. A rule confirmed on one pair is a guess; the second pair is what turns it into an answer, and checking takes a few seconds.
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
Check both complete pairs for one rule. 12 becomes 48 and 9 becomes 36, and multiplying by 4 works for both. Multiplying 7 by 4 gives 28, making C correct. Choice A comes from adding 4 to 7 instead of multiplying. Choice B comes from multiplying by 3, and choice D from multiplying by 5.
Correct answer: D
24 becomes 6 and 16 becomes 4, so each number is divided by 4. Dividing 20 by 4 gives 5, making D correct. Choice A comes from multiplying 20 by 4 instead of dividing. Choice B comes from subtracting 4, and choice C from dividing by 2 rather than by 4.
Correct answer: A
The first pair fits either adding 8 or doubling and adding 1, so use the second pair to decide. 9 becomes 19 by doubling and adding 1, while adding 8 would give 17, so the rule is double then add 1. That gives 6 × 2 + 1 = 13, making A correct. Choice B comes from doubling 6 and forgetting the extra 1. Choice C comes from adding 8, the rule that fits only the first pair, and choice D from adding 2.
Correct answer: B
100 becomes 25 and 80 becomes 20, so each number is divided by 4. Dividing 60 by 4 gives 15, making B correct. Choice A comes from dividing by 2 instead of 4. Choice C comes from subtracting 4, and choice D from multiplying 60 by 4.
Correct answer: C
3 becomes 12 and 5 becomes 20, so each number is multiplied by 4. Multiplying 8 by 4 gives 32, making C correct. Choice A comes from multiplying by 3 instead of 4. Choice B comes from multiplying by 5, and choice D from adding 4 to 8.
Correct answer: D
45 becomes 9 and 35 becomes 7, so each number is divided by 5. Dividing 25 by 5 gives 5, making D correct. Choice A comes from subtracting 5 from 25 instead of dividing. Choice B comes from adding 5, and choice C from multiplying 25 by 5.
Correct answer: C
Check both complete pairs for one rule. 14 becomes 23 and 21 becomes 30, and adding 9 works for both. Adding 9 to 35 gives 44, making C correct. Choice A comes from subtracting 9 instead of adding it. Choice B comes from multiplying 35 by 9, and choice D from adding 9 twice.
Correct answer: D
50 becomes 38 and 43 becomes 31, so each number has 12 taken away. Taking 12 from 27 gives 15, making D correct. Choice A comes from adding 12 instead of subtracting it. Choice B comes from multiplying 27 by 12, and choice C from subtracting 12 twice.
Correct answer: A
18 becomes 36 and 25 becomes 50, so each number is doubled. Doubling 40 gives 80, making A correct. Choice B comes from halving 40 instead of doubling it. Choice C comes from tripling, and choice D from adding 2 rather than multiplying by it.
Correct answer: B
The rule takes two steps, so test it on both complete pairs: 4 × 3 − 1 = 11 and 6 × 3 − 1 = 17, so the rule is multiply by 3 then subtract 1. Applying it to 5 gives 5 × 3 − 1 = 14, making B correct. Choice C comes from multiplying by 3 and forgetting the second step. Choice A comes from adding 1 instead of subtracting it, and choice D from adding 7, the gap in the first pair, which fails on the second pair.