Logical reasoning · lesson 4 of 30 · free

Number analogies — Logical reasoning for kids

In “3 : 10 :: 5 : 26 :: 7 : ?” the sign “:” means “goes with”. Each pair follows the same hidden rule. Guess a rule from the first pair, test it on the second, then use it.

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How to think it through

Same rule, both pairs — “the rule that turns the first number into the second must work for every pair”

Look at the first pair and guess a rule: × something, + something, square it, square it and add or take away 1, cube it …
Test the rule on the second pair. If it fails, try another rule.
Use the rule that fits both pairs on the last number.

Use it for: Analogy questions in reasoning tests, and getting quick with squares and cubes.

Worked example: Find the rule, then the missing number. 3 : 10 :: 5 : 26 :: 7 : ? → 50

3 → 10: × 3 + 1 works, and so does 3 × 3 + 1 (square and add 1).
Test on 5: 5 × 3 + 1 = 16 ✗, but 5 × 5 + 1 = 26 ✓. The rule is “square it and add 1”.
7 × 7 + 1 = 50.

Check: 3² + 1 = 10, 5² + 1 = 26, 7² + 1 = 50 ✓

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✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

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🏁 Lesson 4 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Number Analogy Worksheet

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