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GATE 2026 XH5 (Psychology) – Question 20

Reasoning and Comprehension · Quantitative reasoning · 2 marks · Multiple select

Three players named Arun, Babita and Chandu play a game by tossing an unbiased coin in turn whose rules are as follows:

Initially each player has 100 candies. If the tossing of this coin results in a ‘head’ then the player who tosses receives 10 candies from each of the other two players, whereas, if the toss results in a ‘tail’ then the player who tosses has to give away 20 candies to each of the other two players. A player with the highest number of candies at the end will be the winner. The game is started by Arun, followed by Babita and finally stopped after Chandu’s turn. Given that Arun is the only winner, which of the following hold(s) true?

  1. Arun has 90 candies more than Chandu
  2. Both Babita and Chandu have the same number of candies
  3. Arun has 90 candies more than Babita
  4. Babita and Chandu together have 120 candies

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Correct answer: (A) Arun has 90 candies more than Chandu; (B) Both Babita and Chandu have the same number of candies; (C) Arun has 90 candies more than Babita

Explanation

A head gives the tosser +20 and each of the others $-10$. A tail gives the tosser $-40$ and each of the others $+20$. Going through the 8 outcomes of the three tosses (Arun, Babita, Chandu), the totals are: HHH $(100, 100, 100)$, HHT $(130, 130, 40)$, HTH $(130, 40, 130)$, HTT $(160, 70, 70)$, THH $(40, 130, 130)$, THT $(70, 160, 70)$, TTH $(70, 70, 160)$ and TTT $(100, 100, 100)$. Only HTT has Arun as the sole winner, with 160, 70 and 70. So Arun has 90 more than each of the others (A and C), and Babita and Chandu are equal (B). Together they have 140, not 120.