GATE CS Mastery
Cheat sheets

GATE CS 2017 Set 2 · General Aptitude

Question 62

MCQPrinted as GA Q.72 marksWrong answer: −2/3Medium (estimate)

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?

Choose one option
Official answer and solution
Official answer
B
From
Official GATE 2017 answer key

Solution

Apply deductive elimination using the fact that every single box is incorrectly labelled.

We have three boxes with labels:

  • Box 1: labelled 'Apples'
  • Box 2: labelled 'Oranges'
  • Box 3: labelled 'Apples and Oranges'

We are given that all three boxes are incorrectly labelled.
Therefore:

  • The box labelled 'Apples and Oranges' cannot contain both apples and oranges; it must contain either only apples OR only oranges.

Strategy: Open the box labelled 'Apples and Oranges' and draw one fruit:

  1. Case 1: The drawn fruit is an Apple:
    • Since this box cannot be mixed, it must be the 'Apples' box.
    • Now consider the box labelled 'Oranges': it cannot be 'Oranges' (because all labels are wrong) and it cannot be 'Apples' (which was just identified). Therefore, it must be the 'Apples and Oranges' box.
    • The remaining box labelled 'Apples' must then be the 'Oranges' box.
  2. Case 2: The drawn fruit is an Orange:
    • By symmetry, this box is the 'Oranges' box.
    • The box labelled 'Apples' must be the 'Apples and Oranges' box.
    • The box labelled 'Oranges' must be the 'Apples' box.

In both cases, inspecting a single fruit from the box labelled 'Apples and Oranges' uniquely identifies the contents of all three boxes.
This corresponds to option B.

Final answer

B

Common trap

Opening a single-fruit labelled box (e.g. 'Apples'); drawing an apple from it leaves ambiguity whether it is truly apples or the mixed box.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2017 Computer Science and Information Technology (CS) Session 2
Question
62 of 65, printed as GA Q.7
Section
General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.