Horse Race Betting Puzzle

CAT 2008 Slot 1 · DILR · Medium · Logical Reasoning

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Passage / data set

Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

Question 1 of 2

Which of the following cannot be true?

  1. A.

    At least two horses finished before Spotted

  2. B.

    Red finished last

  3. C.

    There were three horses between Black and Spotted

  4. D.

    There were three horses between White and Red

  5. E.

    Grey came in second

Answer

D

Explanation

Total investment = Rs. (3000+2000+1000)=(3000 + 2000 + 1000) = Rs. 6000. To break even (return Rs. 6000):

  • Case 1: Black 2nd (3000×1000=30003000 \times 1000 = 3000), Red 3rd (30003000). Total = 6000.
  • Case 2: Black 1st (4000×1000=40004000 \times 1000 = 4000), White 3rd (20002000). Total = 6000.
  • Case 3: White 2nd (3×2000=60003 \times 2000 = 6000). Total = 6000.

Evaluating option (4): If there were three horses between White and Red, one must be 1st and the other 5th. But in none of the valid cases are White and Red at positions 1st and 5th. Thus, Option (4) cannot be true.

Question 2 of 2

Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?

  1. A.

    Spotted came in first

  2. B.

    Red finished last

  3. C.

    White came in second

  4. D.

    Black came in second

  5. E.

    There was one horse between Black and White

Answer

C

Explanation

If Grey is 4th, looking at the valid configurations:

  • If Black is 2nd, Red is 3rd, Grey is 4th   ⟹  \implies Spotted is 1st, White is 5th.
  • If Black is 1st, White is 3rd, Grey is 4th   ⟹  \implies Spotted is 2nd, Red is 5th.

Option (3) states 'White came in second', which contradicts all valid arrangements when Grey is 4th. Therefore, Option (3) cannot be true.

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