An easy question on working backwards for P2–P3, with a step-by-step solution, diagrams and the answer. Working-backwards questions appear in the Hua Xia Cup's P1 to P5 first rounds, qualifying rounds and finals.
The question
May thinks of a number.
She multiplies it by 2, then adds 1, and gets 11.
What number did May think of?
Show the hints (2)
💡Hint 1: Work back from 11: what was it before adding 1?
💡Hint 2: Going backwards, use the opposite: adding becomes subtracting, multiplying becomes dividing.
Worked solution
Have a go first, then read the solution step by step.
1.Before adding 1: 11 − 1 = 10.
2.Before multiplying by 2: 10 ÷ 2 = 5.
⚠️Common mistake: dividing first. The last step (adding 1) is the first to undo.
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