Read the following data and answer the questions that follow: Australia,…

2024

Read the following data and answer the questions that follow: Australia, England, Sri Lanka, Pakistan and India were placed first through fifth in a World Cup cricket tournament, not necessarily in that order.

In an interview, the captains of the above teams made the following statements — Australia: We were not fifth. England: Sri Lanka finished third. Sri Lanka: Australia ended up behind India. Pakistan: India is the losing finalist. India: Pakistan didn't win the cup.

Among the above statements, all were true except those made by the captains of the cup winner and the losing finalist.

Which of the following statements are not true?

I. Sri Lanka finished the tournament behind Australia which finished behind India.

II. India was the losing finalist.

III. Australia finished the tournament with third placing.

IV. Pakistan finished behind England.

  1. A.

    I and II only

  2. B.

    II and III only

  3. C.

    Both III and IV only

  4. D.

    None

Show answer & explanation

Correct answer: B

Concept: In a puzzle where a fixed number of participants' statements are allowed to be false — here, only the captains of the cup-winning and losing-finalist teams — every other statement is a firm true constraint. A statement that would automatically stay true (or automatically stay false) regardless of who holds the two 'may-lie' ranks reveals a contradiction if that speaker is assigned to lie (or forced to tell the truth) — that self-check narrows the two liar-ranks step by step until the ranking is pinned down uniquely.

Application: Label the teams A (Australia), E (England), S (Sri Lanka), P (Pakistan), I (India), with ranks 1 (winner) through 5 (last). The five statements are: A — 'we were not fifth'; E — 'Sri Lanka finished third'; S — 'Australia ended up behind India'; P — 'India is the losing finalist'; I — 'Pakistan didn't win the cup'. Exactly the rank-1 and rank-2 captains' statements are false; all three others are true.

  1. Australia's statement ('not fifth') is automatically true whenever Australia is 1st or 2nd, so Australia can never be the required liar at rank 1 or 2 — assigning it there would force a false statement that is actually true.

  2. If Australia were 5th, the same statement would be false, but rank 5 isn't one of the two permitted-to-lie ranks, so its statement would need to be true — another contradiction. Australia is therefore 3rd or 4th.

  3. Suppose India's statement ('Pakistan didn't win') is false. That forces Pakistan to be the winner, so Pakistan's own statement ('India is the losing finalist') must also be false, i.e. India isn't 2nd. But India, as the assumed second liar, would then have to be the losing finalist (2nd) — a direct contradiction. So India's statement is true: Pakistan did not win the cup, and India itself is not the winner or the losing finalist.

  4. The winner is therefore England or Sri Lanka — Australia, India and Pakistan are all ruled out by the previous two steps. If Sri Lanka were the winner, its own statement would need to be false, so Australia would have to finish ahead of India; and for England's statement ('Sri Lanka finished third') to also fail, England itself would have to be the losing finalist (2nd). But then Pakistan — not being either liar in this case — would need its own statement true, i.e. India ranks 2nd, which clashes with England already holding that rank. So Sri Lanka cannot be the winner.

  5. By elimination, England is the winner, and its own statement must be false: Sri Lanka does not finish third.

  6. For the losing-finalist rank (2nd), Sri Lanka is the only remaining candidate besides Pakistan. If Sri Lanka held that rank, its own statement would need to be false (Australia ahead of India), while Pakistan — now not a liar — would need its own statement true, i.e. India ranks 2nd; but Sri Lanka already holds 2nd in that case, a contradiction. So Pakistan is the losing finalist, and its own statement is false as required: India isn't 2nd.

  7. The remaining ranks 3rd, 4th and 5th go to Australia, Sri Lanka and India. Sri Lanka's statement must now be true (Australia finishes behind India), which fails if Australia is 3rd (Australia would then be ahead of whichever of the two remaining ranks India takes), so Australia is 4th; Sri Lanka isn't 3rd (England's statement being false rules that out), so Sri Lanka is 5th and India is 3rd.

Result: England (1st) — Pakistan (2nd) — India (3rd) — Australia (4th) — Sri Lanka (5th).

Cross-check: verify all five original statements against this order.

Captain's statement

Holds under this order?

Australia: 'we were not fifth'

Yes — Australia is 4th, and Australia is not one of the two permitted liars.

England: 'Sri Lanka finished third'

No — Sri Lanka is 5th; England is the winner, whose statement must be false.

Sri Lanka: 'Australia ended up behind India'

Yes — Australia (4th) is indeed behind India (3rd), and Sri Lanka is not one of the two permitted liars.

Pakistan: 'India is the losing finalist'

No — India is 3rd, not 2nd; Pakistan is the losing finalist, whose statement must be false.

India: 'Pakistan didn't win the cup'

Yes — Pakistan is 2nd, not 1st, and India is not one of the two permitted liars.

All five check out, confirming this order is the unique valid one.

Now evaluate the four statements:

  • I. Sri Lanka finished behind Australia which finished behind India — Sri Lanka (5th) is behind Australia (4th), and Australia (4th) is behind India (3rd): both parts hold, so statement I is TRUE.

  • II. India was the losing finalist — India is 3rd, not 2nd, so statement II is NOT true.

  • III. Australia finished the tournament with third placing — Australia is 4th, not 3rd, so statement III is NOT true.

  • IV. Pakistan finished behind England — Pakistan (2nd) is indeed behind England (1st), so statement IV is TRUE.

The statements that are not true are II and III, so the correct choice is 'II and III only'.

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