Merchant Taylors’ School 11+ Averages Question

In this video, Singapore Maths Academy solves a high-level 11+ maths question from Merchant Taylors’ School Specimen Paper 1, Question 31c. This problem involves understanding how means and medians interact across overlapping groups — a concept that tests both numerical fluency and logical deduction.

You’re told that the mean weight of 5 children is 45kg, the mean of the lightest three is 42kg, and the mean of the heaviest three is 49kg. The task is to find the median weight — the middle value when the weights are arranged in order.

We break down the problem step by step, using algebra and careful reasoning to find the total weight of each group, deduce individual values, and isolate the median. This is exactly the sort of question that sets apart strong problem-solvers in Merchant Taylors’ School 11+ entrance exams and other top independent school assessments.