A medium question on remainders for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P3 to P6 papers; harder ones need several remainder conditions to hold at once.
The question
Ms Chan has 55 pencils.
She shares them equally among her class, and 1 is left over — not enough for one more each.
The class has between 19 and 32 pupils.
How many pupils are in the class?
Show the hints (2)
💡Hint 1: Without the 1 left over, the pencils would share out exactly. How many pencils is that?
💡Hint 2: The class size is a factor of 55 − 1, between 19 and 32.
Worked solution
Have a go first, then read the solution step by step.
1.Pencils given out: 55 − 1 = 54, so the class size is a factor of 54.
2.Between 19 and 32, the only factor of 54 is 27 (54 = 27 × 2).
3.Check: 55 ÷ 27 = 2 remainder 1, and 1 is less than 27, as it should be.
⚠️Common mistake: looking for factors of 55 without first taking away the 1 left over.
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