Lesson eLearning

Find the sum of all whole numbers less than 100 that are multiples of 4 but not multiples of 6.

hard 4 marks Class 6 · Mathematics · Whole Numbers
Answer
768

The correct answer is 768 — Subtract the sum of multiples of 12 from the sum of multiples of 4: (1200-432=768).

Step-by-step solution

  1. List all multiples of 4 below 100: (4,8,12,dots,96).
  2. Sum all these multiples: (4\times(1+2+dots+24)=4\times300=1200).
  3. Multiples of 4 that are also multiples of 6 are exactly the multiples of (\text{lcm}(4,6)=12).
  4. List multiples of 12 below 100: (12,24,dots,96).
  5. Sum these multiples: (12\times(1+2+dots+8)=12\times36=432).
  6. Subtract the sum of multiples of 12 from the sum of multiples of 4: (1200-432=768).
Common mistake: forgetting to exclude multiples of 12 or mis‑calculating sums

Concept tested: arithmetic series, LCM, exclusion principle

Published · How this solution was prepared and checked

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