GATE EE 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 labels be A (Apples), O (Oranges), and A&O (Apples and Oranges).
We know all boxes are incorrectly labelled.Consider opening the box labelled 'Apples and Oranges' (A&O).
Since it's incorrectly labelled, it cannot contain both apples and oranges. It must contain either only apples or only oranges.
Now, consider the box labelled 'Apples'. It cannot contain only apples (because the A&O box does). It also cannot contain both apples and oranges (because it's incorrectly labelled). Therefore, the box labelled 'Apples' must contain only oranges.
By elimination, the box labelled 'Oranges' must contain both apples and oranges.
Now, consider the box labelled 'Oranges'. It cannot contain only oranges (because the A&O box does). It also cannot contain both apples and oranges (because it's incorrectly labelled). Therefore, the box labelled 'Oranges' must contain only apples.
By elimination, the box labelled 'Apples' must contain both apples and oranges.In both scenarios, by opening the 'Apples and Oranges' box and inspecting one fruit, you can determine the contents of all three boxes.
We know all boxes are incorrectly labelled.Consider opening the box labelled 'Apples and Oranges' (A&O).
Since it's incorrectly labelled, it cannot contain both apples and oranges. It must contain either only apples or only oranges.
1.If you pull out an apple from the A&O box:
Since it's incorrectly labelled, and you found an apple, this box must contain only apples.Now, consider the box labelled 'Apples'. It cannot contain only apples (because the A&O box does). It also cannot contain both apples and oranges (because it's incorrectly labelled). Therefore, the box labelled 'Apples' must contain only oranges.
By elimination, the box labelled 'Oranges' must contain both apples and oranges.
2.If you pull out an orange from the A&O box:
Since it's incorrectly labelled, and you found an orange, this box must contain only oranges.Now, consider the box labelled 'Oranges'. It cannot contain only oranges (because the A&O box does). It also cannot contain both apples and oranges (because it's incorrectly labelled). Therefore, the box labelled 'Oranges' must contain only apples.
By elimination, the box labelled 'Apples' must contain both apples and oranges.In both scenarios, by opening the 'Apples and Oranges' box and inspecting one fruit, you can determine the contents of all three boxes.
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