Reasoning : Logical Reasoning & Analytical Ability

Q 200 / 325

UPSC CSE Prelims 2016

When three friends A, B and C met, it was found that each of them wore an outer garment of a different colour. In random order, the garments are: jacket, sweater and tie; and the colours are: blue, white and black. Their surnames in random order: Ribeiro, Kumar and Singh. Further, we know that:

  1. Neither B nor Ribeiro wore a white sweater
  2. C wore a tie
  3. Singh’s garment was not white
  4. Kumar does not wear a jacket
  5. Ribeiro does not like to wear the black colour
  6. Each of the friends wore only one outer garment of only one colour

What is the colour of the tie?

EXPLANATION

Correct Option (2)

The problem requires deducing the specific attributes (surname, garment, and colour) for each friend based on the given clues. A systematic approach helps in eliminating possibilities and arriving at the unique solution.

  • Initial Garment-Surname Deduction:

    • Clue 2 states that C wore a tie.
    • Clue 4 states that Kumar does not wear a jacket.
    • Given that C wears the tie, the remaining garments are a jacket and a sweater. Since Kumar does not wear the jacket, Kumar must wear the sweater.
    • Therefore, the person wearing the jacket must be either Ribeiro or Singh.
    • Summary of Garment-Surname links: Kumar wears the Sweater, C wears the Tie, and the Jacket is worn by either Ribeiro or Singh.

  • Friend-Surname-Garment Assignment:

    • Clue 1 states, "Neither B nor Ribeiro wore a white sweater."
    • Since Kumar wears the sweater, Ribeiro cannot be Kumar. This means Ribeiro wears either the Jacket or the Tie.
    • If Ribeiro wears the sweater, it cannot be white. If B wears the sweater, it cannot be white.
    • Let's consider the possibility that Kumar's sweater is white. If Kumar's sweater is white, then Kumar cannot be B (due to Clue 1). This implies that A must be Kumar.
    • If A is Kumar (wearing a White Sweater), then B must be Singh (wearing the Jacket), and C must be Ribeiro (wearing the Tie).

  • Colour Deduction and Verification:

    • Based on the assignment: A = Kumar (Sweater), B = Singh (Jacket), C = Ribeiro (Tie).
    • Clue 3 states, "Singh’s garment was not white." Since B is Singh and wears a Jacket, B's Jacket is not white.
    • Clue 5 states, "Ribeiro does not like to wear the black colour." Since C is Ribeiro and wears a Tie, C's Tie is not black.
    • We have three garments (Sweater, Jacket, Tie) and three colours (Blue, White, Black).
    • From our assumption, Kumar (A) wears a White Sweater.
    • The remaining garments are B's Jacket and C's Tie, and the remaining colours are Blue and Black.
    • B (Singh)'s Jacket is not white (Clue 3), so it must be Blue or Black.
    • C (Ribeiro)'s Tie is not black (Clue 5), so it must be Blue or White.
    • Since the Sweater is White, the Tie cannot be White. Therefore, C's Tie must be Blue.
    • If C's Tie is Blue, then B's Jacket must be Black (as Blue is taken and the Jacket cannot be White).
    • This leads to a consistent and unique solution:
      • A is Kumar, wearing a White Sweater.
      • B is Singh, wearing a Black Jacket.
      • C is Ribeiro, wearing a Blue Tie.
    • All clues are satisfied by this configuration. The colour of the tie (worn by C) is Blue.

Incorrect Options:

Options 1 (Black), 3 (White), and 4 (Cannot be determined) are incorrect because the logical deductions, based on all provided clues, lead to a unique and consistent assignment where the tie is Blue. Any other colour for the tie would contradict one or more of the given conditions.