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CAT 2022 Slot 2 · DILR · Games and Tournaments · medium

CAT 2022 Slot 2 DILR: Coin-Toss Betting Game

Four friends — W, X, Y and Z — play a coin-toss betting game over 5 rounds. Each starts with ₹100. In each round, a coin is tossed and the actual outcome (Heads/Tails) is recorded; before the toss, every player independently predicts Heads (H) or Tails (T). A fixed stake for that round is at risk for each player: if a player's prediction matches the actual outcome, that player wins an amount equal to the round's stake (added to their balance); if it does not match, the player loses an amount equal to the stake (deducted from their balance). The stake is the same for all four players in a given round but differs across rounds.

| Round | Actual outcome | Stake (₹) | W's bet | X's bet | Y's bet | Z's bet |
|-------|-----------------|-----------|---------|---------|---------|---------|
| 1 | H | 10 | H | T | H | T |
| 2 | T | 20 | H | T | T | H |
| 3 | H | 15 | T | H | H | H |
| 4 | H | 25 | H | H | T | H |
| 5 | T | 30 | T | H | T | T |

Question 1

Single correct option

Which player has the highest balance at the end of the 5 rounds?
  1. A. W
  2. B. X
  3. C. Y
  4. D. Z
Show answer and solution

Answer: (C) Y

Compute round-by-round for each player (win = +stake, loss = −stake): W: +10−20−15+25+30 = 30 net → balance 130. X: −10+20+15+25−30 = 20 net → balance 120. Y: +10+20+15−25+30 = 50 net → balance 150. Z: −10−20+15+25+30 = 40 net → balance 140. Y's final balance of ₹150 is the highest.

Question 2

Numerical answer

What is X's final balance (in ₹) at the end of the 5 rounds?
Show answer and solution

Answer: 120

X's bets: T,T,H,H,H against outcomes H,T,H,H,T. Matches: round 2 (T=T, +20), round 3 (H=H, +15), round 4 (H=H, +25). Mismatches: round 1 (T≠H, −10), round 5 (H≠T, −30). Net = −10+20+15+25−30 = +20. Final balance = 100+20 = ₹120.

Question 3

Single correct option

In how many of the 5 rounds did Z's prediction match the actual outcome?
  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 1
Show answer and solution

Answer: (B) 3

Z's bets: T,H,H,H,T against outcomes H,T,H,H,T. Round 1: T≠H (no). Round 2: H≠T (no). Round 3: H=H (yes). Round 4: H=H (yes). Round 5: T=T (yes). Z matched the outcome in 3 rounds.

Question 4

Numerical answer

What is the combined final balance (in ₹) of all four players put together?
Show answer and solution

Answer: 540

Final balances: W=130, X=120, Y=150, Z=140 (each computed as 100 plus/minus the round-wise stakes based on matches). Sum = 130+120+150+140 = ₹540.

Question 5

Single correct option

Which two players lost their bet in Round 1?
  1. A. W and Y
  2. B. X and Z
  3. C. W and Z
  4. D. X and Y
Show answer and solution

Answer: (B) X and Z

Round 1 outcome is H. Bets: W=H (match, win), X=T (mismatch, lose), Y=H (match, win), Z=T (mismatch, lose). So X and Z lost in Round 1.
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Original question written in the CAT 2022 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake