GATE CS 2017 Set 2 — Question 62
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
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 labelled. 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?
Correct answer
(B) The box labelled 'Apples and Oranges'
Solution
Let the boxes be labeled 'Apples', 'Oranges', and 'Apples and Oranges'. We are told all labels are incorrect. If we open the box labeled 'Apples and Oranges', it must contain either only apples or only oranges.
1.If it contains apples:
- Box labeled 'Apples and Oranges' Apples
- Box labeled 'Oranges' cannot contain oranges (wrong label) and cannot contain apples (already found), so it must contain Apples and Oranges.
- Box labeled 'Apples' must contain Oranges.
- Box labeled 'Apples and Oranges' Oranges
- Box labeled 'Apples' cannot contain apples (wrong label) and cannot contain oranges (already found), so it must contain Apples and Oranges.
- Box labeled 'Oranges' must contain Apples.
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