IMC 2004 Q17
17. \(A\), \(B\), \(C\), \(D\), \(E\), \(P\) and \(Q\) are points on the number line as shown. One of the points represents the product of the numbers represented by \(P\) and \(Q\). Which is it?
- A
- B
- C
- D
- E
Intermediate Mathematical Challenge 2004, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B
As \(P\) and \(Q\) both lie between 0 and 1, their product will be greater than 0 but smaller than \(P\) and smaller than \(Q\). Of the options available, only \(B\) satisfies these conditions. (Furthermore, its position is correct since \(P\) is approximately equal to \(\tfrac{1}{2}\), which means that the product of \(P\) and \(Q\) lies approximately half way between 0 and \(Q\).)
Solution © UK Mathematics Trust, from the IMC 2004 solutions.