Directions: Each question below consists of a question and three statements…

2024

Directions: Each question below consists of a question and three statements numbered I, II and III. You have to decide whether the data in the statements are sufficient to answer the question. Read the three statements and choose your answer.

Six persons — P, Q, R, S, T and U — attend a function on different days of a week from Monday to Saturday, not necessarily in that order. Who among them attends the function on Thursday?

Statement I: P attends the function three days after U, who is not the first person to attend. One person attends the function between T and R. T attends the function three days after Q.

Statement II: Two persons attend the function between S and R, who attends immediately after P. Three persons attend the function between P and Q. S attends the function before T.

Statement III: U attends the function two days before T, who attends immediately after P. One person attends the function between Q and S.

  1. A.

    Both statements I and II together are necessary to answer the question whereas statement III alone is not sufficient to answer the question

  2. B.

    Only statement III alone is sufficient to answer the question whereas both statements I and II are not sufficient to answer the question

  3. C.

    All the three statements together are not sufficient to answer the question

  4. D.

    Any two of the given statements are necessary to answer the question

  5. E.

    Only statement II alone is sufficient to answer the question whereas both statements I and III are not sufficient to answer the question

Show answer & explanation

Correct answer: E

Concept

In a Data Sufficiency problem you judge each statement (and combinations) only by whether it pins down a single answer to the exact question asked — here, the person on Thursday. A statement is sufficient if, after applying its clues, exactly one person can occupy Thursday; if two or more remain possible, that statement is insufficient. Each clue is read as a position relation on the six days: "X days after" is a fixed gap, "immediately after" is a gap of 1, and "n persons between" is a gap of n+1.

Setup

Six slots run Monday(1) to Saturday(6); Thursday is day 4. We test each statement alone.

Statement I alone

Clues: P = U + 3, U is not on Monday, |T - R| = 2 (one person between), T = Q + 3.

  1. T = Q + 3 allows (Q,T) = (1,4), (2,5) or (3,6); P = U + 3 with U not on Monday allows (U,P) = (2,5) or (3,6).

  2. Fitting these gap-pairs with |T - R| = 2 leaves three different valid orders: Q,R,U,T,S,P / Q,U,S,T,P,R / S,U,Q,R,P,T.

  3. Across these three orders the Thursday person is sometimes R and sometimes T.

Two different Thursday answers survive, so Statement I alone is NOT sufficient.

Statement II alone

Clues: |S - R| = 3 (two persons between S and R), R = P + 1 (R immediately after P), |P - Q| = 4 (three persons between P and Q), S before T.

  1. |P - Q| = 4 on a 6-day line forces {P,Q} to be {1,5} or {2,6}; combined with R = P + 1 (so P cannot be day 6), the live cases are P=5,Q=1 / P=1,Q=5 / P=2,Q=6.

  2. Add |S - R| = 3 with R = P + 1: only P=5 (so R=6) leaves room for S three slots from R, giving S=3.

  3. Now P=5, R=6, Q=1, S=3 fill days 5,6,1,3; days 2 and 4 remain for T and U, and "S before T" forces T=4 (Thursday) and U=2.

  4. This yields the single order Q(Mon), U(Tue), S(Wed), T(Thu), P(Fri), R(Sat).

Exactly one arrangement survives and the Thursday person is fixed as T, so Statement II alone IS sufficient to answer the question.

Statement III alone

Clues: T = U + 2, T = P + 1 (T immediately after P, so P sits one day after U), |Q - S| = 2 (one person between Q and S).

  1. Because P = U + 1 and T = P + 1, the three form a consecutive block U, P, T, which can sit at days 1-3, 2-4, 3-5 or 4-6.

  2. |Q - S| = 2 then has several placements for the remaining people, leaving four valid orders.

  3. Across them the Thursday person is sometimes Q, sometimes S, sometimes U.

Several Thursday answers survive, so Statement III alone is NOT sufficient.

Cross-check and conclusion

Only Statement II, on its own, narrows the schedule to a single arrangement and fixes Thursday as T; Statement I alone and Statement III alone each leave more than one possibility. So the question is answered by one statement acting alone, while the other two alone are not enough.

This is why requiring "any two statements" is wrong: the sufficient statement needs no partner. (As a consistency check, Statement I and Statement II happen to agree on the same single order, while Statements I and III together, and II and III together, are mutually contradictory and yield no valid week — so a blanket "any two are necessary" rule does not hold here.)

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