Answer the following questions on the basis of the following information: Long…
2025
Answer the following questions on the basis of the following information:
Long ago, King Ashoka, organised a horse riding competition. The entry fee for a participation was one gold coin and the total number of coins collected would be distributed among the first four winners. All the four winners were awarded with a different number of coin, however the winner in the first position got the maximum coins and so on. So that the winner in the fourth position got the least number of coins.
W, X, Y, Z were the first four winners in the competition so that:
I. W did not come first, X did not come second, Y did not come third and Z did not come fourth.
II. X won more coins than Y.
III. Z won more coins than X.
Y, one of four winners ended the competition in position number
- A.
4
- B.
2
- C.
1
- D.
3
Show answer & explanation
Correct answer: A
Concept: In a ranking-and-arrangement puzzle, a comparative clue on the underlying quantity (here, coins won) fixes a comparative clue on rank position, because rank position and the quantity move in opposite directions -- the person with more of the quantity always occupies the lower (better) position number. Two such comparisons chain together into a single relative order among three people; a position-exclusion clue for each person is then used to eliminate every arrangement except the one consistent with all of them.
Application:
Translate the coin comparisons into rank order. Condition II says X won more coins than Y, so X ranks ahead of Y: Rank(X) is less than Rank(Y). Condition III says Z won more coins than X, so Z ranks ahead of X: Rank(Z) is less than Rank(X).
Combining the two gives a single chain: Rank(Z) < Rank(X) < Rank(Y). So among Z, X and Y, the relative finishing order (best to worst) is fixed as Z, then X, then Y -- only W's place in this chain is still open.
W can be inserted into four possible slots relative to the Z-X-Y chain: before Z, between Z and X, between X and Y, or after Y. This gives exactly four candidate full arrangements of positions 1 to 4.
W first, Z second, X third, Y fourth -- but Condition I says W did not come first, so this arrangement is eliminated.
Z first, W second, X third, Y fourth -- checking every exclusion in Condition I: W is not first (W is second), X is not second (X is third), Y is not third (Y is fourth), Z is not fourth (Z is first). Every exclusion is satisfied, so this arrangement survives.
Z first, X second, W third, Y fourth -- but Condition I says X did not come second, so this arrangement is eliminated.
Z first, X second, Y third, W fourth -- this violates both the rule that X did not come second and the rule that Y did not come third, so it is eliminated.
Cross-check: The one surviving arrangement -- Z first, W second, X third, Y fourth -- is checked independently against the original coin-based order: Z (1st) has more coins than X (3rd), and X (3rd) has more coins than Y (4th), which exactly matches Rank(Z) < Rank(X) < Rank(Y) derived above, confirming the arrangement is consistent with every condition.
Since this is the only arrangement consistent with all the conditions, Y ended the competition in position 4.