• S
    SwaseekhGATE Preparation
General
  • Dashboard
  • Syllabus
  • Questions
  • Aptitude
  • Mock Tests
  • TCS NQT 2026
Account
  • Pricing
  • Contact
  1. GATE CS
  2. PYQs
  3. General Aptitude

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

GATE 2017 · General Aptitude · Logical Reasoning · medium

Answer: Open the box labeled 'Apples and Oranges'. Answer: B.

  1. Key insight: the 'A and O' box holds only apples or only oranges: Since all labels are incorrect, the box labeled 'Apples and Oranges' cannot contain both. It must contain only apples or only oranges. One draw is sufficient to distinguish these two cases.
  2. Case 1: draw an apple from the 'A and O' box: 'A and O' box = Apples only. The box labeled 'Apples' cannot contain apples (wrong label), so it contains oranges or both. Since Apples only is taken by the 'A and O' box, the 'Apples' labeled box is either oranges or both. The box labeled 'Oranges' cannot contain oranges (wrong label), so it contains apples or both. Apples only is already assigned to 'A and O' box. Therefore 'Oranges' labeled box = Both. Then 'Apples' labeled box = Oranges only. All three resolved.
  3. Case 2: draw an orange from the 'A and O' box: 'A and O' box = Oranges only. By similar reasoning: 'Oranges' labeled box cannot have oranges, so it has apples or both; since oranges only is assigned, it has Apples only or Both. 'Apples' labeled box cannot have apples, so it has oranges or both; since oranges only is assigned, it has Both. Then 'Oranges' labeled box = Apples only. All three resolved.
  4. Why other boxes fail: Opening the 'Apples' box: if you draw an apple, the box could still be 'both' (apples and oranges) — one apple does not rule out the presence of oranges. You cannot be certain. Similarly for the 'Oranges' box. Only the 'A and O' box is guaranteed to be pure (one type only), so one draw is conclusive.