Multiple choice

There are three measuring jars 𝑋, π‘Œ and 𝑍. First, π‘Œ is filled with milk and then emptied into an empty breaker 𝑃. Next, π‘Œ and 𝑍 are both filled with water and then the contents of both the jars are emptied into another empty vessel 𝑄. Finally, 𝑋 is filled with water drawn from 𝑄. If the capacity (in litres) of 𝑋 is at least 4 and at most 8, that of π‘Œ is at least 5 and at most 12, and that of 𝑍 is at least 7 and at most 13, then the volume of milk in 𝑃 as a percentage of the volume of water in 𝑄 is at most

  1. 80%

  2. 125%

  3. 140%

  4. 150%
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B Correct answer
AI explanation

To maximize the volume of milk in P as a percentage of the volume of water in Q, maximize Y and minimize the sum of Y and Z. The maximum capacity of Y is 12 litres, the minimum capacity of Y is 5 litres, and the minimum capacity of Z is 7 litres. The minimum volume of water in Q is the minimum sum of Y and Z, which is 5 plus 7, equaling 12 litres. Therefore, the maximum percentage is 12 divided by 12, which is 1.25, or 125%. The result is 125%.

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