PK 2016 Q9
9. Four numbers \(a\), \(b\), \(c\), \(d\) are such that \(a + 5 = b^2 - 1 = c^2 + 3 = d - 4\). Which of them is the largest?
- A \(a\)
- B \(b\)
- C \(c\)
- D \(d\)
- E more information required
Pink Kangaroo 2016, Question 9. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D \(d\)
Note that \(d = c^2 + 7\), so \(d > c\); \(d = b^2 + 3\), so \(d > b\); and \(d = a + 9\), so \(d > a\). Hence \(d\) is the largest.
Solution © UK Mathematics Trust, from the PK 2016 solutions.