Quantitative aptitude · lesson 27 of 30 · free

Number problems — Quantitative aptitude for kids

Number problems hide simple patterns. Consecutive numbers are spaced evenly, so the middle one is the average. Two numbers from their sum and difference come straight out. Swapping the digits of a two-digit number changes it by 9 × the difference of the digits.

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The method

Use the structure — “consecutive numbers share a middle; sum and difference give both numbers; swapping digits changes by 9 × the gap”

  1. n consecutive numbers with sum S: the middle (average) is S ÷ n.
  2. From sum and difference: larger = (sum + difference) ÷ 2, smaller = (sum − difference) ÷ 2.
  3. Swapping the digits changes the number by 9 × (difference of the digits).
  4. “k times another, difference D”: smaller = D ÷ (k − 1).

Use it for: Number puzzles in aptitude, Olympiad and scholarship tests, and early algebra.

Worked example: The digits of a two-digit number add up to 11. When the digits swap places, the number goes up by 27. What is the number? → 47

  1. 27 ÷ 9 = 3, so the digits differ by 3 (and the ones digit is bigger).
  2. Tens digit = (11 − 3) ÷ 2 = 4, ones digit = 7: the number is 47.

Check: 74 − 47 = 27 and 4 + 7 = 11 ✓

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🏁 Lesson 27 test

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

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🖨️ Number Problems Worksheet

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