IMC 2011 Q11
11. What is the value of \(19\frac{1}{2} \times 20\frac{1}{2}\)?
- A 250
- B \(380\frac{1}{4}\)
- C \(390\frac{1}{4}\)
- D 395
- E \(399\frac{3}{4}\)
Intermediate Mathematical Challenge 2011, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(399\frac{3}{4}\)
\(19\tfrac{1}{2} \times 20\tfrac{1}{2} = (20 - \tfrac{1}{2}) \times (20 + \tfrac{1}{2}) = 20^2 - (\tfrac{1}{2})^2 = 400 - \tfrac{1}{4} = 399\tfrac{3}{4}\).
Solution © UK Mathematics Trust, from the IMC 2011 solutions. Longer versions with investigations: Solutions and investigations (PDF).