There are three boxes. One contains apples, another contains oranges and the…
2017
There are three boxes. One contains apples, another contains oranges and the last one contains both apples and oranges. All three are known to be incorrectly labeled. If you are permitted to open just one box and then pull out and inspect only one fruit, which box would you open to determine the contents of all three boxes?
- A.
The box labeled ‘Apples’
- B.
The box labeled ‘Apples and Oranges’
- C.
The box labeled ‘Oranges’
- D.
Cannot be determined
Attempted by 44 students.
Show answer & explanation
Correct answer: B
Key idea: because all labels are wrong, the box labeled ‘Apples and Oranges’ cannot contain both; it must contain only apples or only oranges.
Open the box labeled ‘Apples and Oranges’ and pull one fruit.
If the fruit is an apple: that box contains only apples. The box labeled ‘Oranges’ cannot contain oranges (its label is wrong) and cannot contain apples (those are already in the identified box), so it must contain both. Therefore the box labeled ‘Apples’ must contain only oranges.
If the fruit is an orange: that box contains only oranges. The box labeled ‘Apples’ cannot contain apples and cannot contain oranges (those are already in the identified box), so it must contain both. Therefore the box labeled ‘Oranges’ must contain only apples.
Conclusion: Opening the box labeled ‘Apples and Oranges’ and inspecting one fruit lets you identify that box and then deduce the contents of the other two boxes.
Note: opening a box labeled with a single fruit (either ‘Apples’ or ‘Oranges’) is ambiguous because one sample might be the same fruit whether the box is pure or mixed, so that choice does not always allow full deduction.