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Maths olympiad question · P2–P4★★ Medium

Clever sums: olympiad question 4

A medium question on clever sums for P2–P4, with a step-by-step solution, diagrams and the answer. The first few questions of a competition paper are often clever sums, and the Hua Xia Cup has them in every year from P1 to P6.

The question

Work this out the clever way.

14 × 31 + 31 × 86 = ?

What is the answer?

Show the hints (2)
  1. Hint 1: Do the two parts share a number?
  2. Hint 2: Take the shared 31 outside and work out the sum in brackets first.

Worked solution

Have a go first, then read the solution step by step.

  1. 1.Both parts have the factor 31: 31 × (14 + 86).
  2. 2.The brackets make exactly 100: 31 × 100 = 3100.

Answer: 3100

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