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GATE 2022 IN GA Q.4: solution and answer

GATE 2022 · INGA Q.4 · 1 mark · MCQ

Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:

  • P sits next to S and T.
  • Q sits diametrically opposite to P.
  • The shortest distance between S and R is equal to the shortest distance between T and U.

Based on the above statements, Q is a neighbor of

  1. (A)

    U and S

  2. (B)

    R and T

  3. (C)

    R and U

  4. (D)

    P and S

See the question in the paper
GATE 2022 IN GA question 4Tap to open full size

Answer and solution

ANSWER

Q is a neighbour of R and U. Option (C).

Official answer: CSource: Official answer key, GATE 2022 IN (IIT Kharagpur)

  1. Take the six seats as equally spaced round the table, which is the usual reading when a question uses "diametrically opposite". Number them to going round and put P in seat . With 6 seats, the seat diametrically opposite seat is seat , so Q is in seat .

  2. P sits next to S and T. P's two neighbours are seats and , so S and T fill seats and between them, in some order.

  3. That leaves R and U for seats and , which are exactly Q's two neighbours. So Q sits next to R and U, whichever way round they are.

  4. Check that the third statement can hold. Take S in seat and T in seat (the mirror case is the same). If R is in and U is in , then S–R and T–U are each seat apart. If R is in and U is in , they are each seats apart (diametrically opposite). Both arrangements satisfy the statement, and in both of them Q's neighbours are R and U. So the statements are consistent, and the third one is not needed to find the answer.

  5. Rule out the other options. S and T are both two seats away from Q, so (A) and (B) are wrong. P is opposite Q, not next to Q, so (D) is wrong.

  6. So Q is a neighbour of R and U, which is option (C).

KEY IDEA

Fix P in one seat. With six equally spaced seats, Q opposite P is three seats away. S and T take both of P's neighbouring seats, so the only seats left for R and U are the two next to Q. The distance statement only confirms the arrangement is possible. It is not needed to get the answer.

WATCH OUT FOR

Trying to use the S–R / T–U distance condition to pin down one exact arrangement, and then worrying that it allows two. Both arrangements give Q the same neighbours. Another slip is counting seats unevenly, so that Q is not placed exactly three seats from P.

From the GATE 2022 IN paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

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