A 32-litre can is full of pure juice. Each time, 8 litres are drawn out and replaced with water. What is the fewest number of such operations after which juice makes up less than half of the can?

2Correct answerYour answer3Correct answerYour answer4Correct answerYour answer5Correct answerYour answer

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CorrectNot quiteAnswer B

Correct answer: B

Each operation keeps $\frac{3}{4}$ of the juice.
After 1 operation: 24 litres; after 2: 18 litres — still more than half of 32 (16 litres).
After 3 operations: $18 \times \frac{3}{4} = 13.5$ litres, which is less than 16.

Worth noting

Two operations would be the answer only if 8 litres of JUICE left each time $(32 - 16 = 16)$ . After the first operation the 8 litres drawn out are partly water.

Concept: Repeated replacement against a threshold
Typical timeTypical: 100 s
Your timeYours: —

The rule this testsMixtures and replacement

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A 32-litre can is full of pure juice. Each time, 8 litres are drawn out and replaced with water. What is the fewest number of such operations after which juice makes up less than half of the can?

Explanation