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CAT DILR

CAT logical reasoning: arrangements practice

Arrangement puzzles test whether you can turn a paragraph of conditions into a grid and then enumerate cases without losing track. The best habit is to draw the skeleton first (seats, slots or positions), place the fixed facts, and then branch only where the conditions leave a real choice. Try the short set below and write all the valid arrangements before you answer.

Key ideas

  • Draw the skeleton (positions 1 to n) before reading the conditions twice.
  • Place definite facts first, then conditions that fix an absolute position.
  • Treat 'immediately next to' pairs as a single block.
  • When a condition leaves two possibilities, branch and keep both alive.
  • Check every final arrangement against all the conditions.

Common traps

  • Losing a valid case because you branched too early on a weak condition.
  • Reading 'left of' as 'immediately left of'.
  • Stopping at the first arrangement that works.

Practice set: Four friends in a row

Four friends, P, Q, R and S, sit in a row in seats numbered 1 to 4 from left to right. P sits somewhere to the left of Q. P does not sit in seat 1. S does not sit in seat 1.

Practice questions with solutions

Try each question first, then open the solution.

  1. Who sits in seat 1?

    • A R
    • B P
    • C Q
    • D S
    Show answer and solution

    Answer: A. R

    P and S cannot be in seat 1, and Q is to the right of P, so Q cannot be in seat 1 either. Only R can.

  2. In how many different ways can the friends be seated?

    Type in the answer (no options).

    Show answer and solution

    Answer: 3

    The valid arrangements, left to right, are R P Q S, R P S Q and R S P Q.

  3. Who can sit in seat 4?

    • A P
    • B Either Q or S
    • C R
    • D Only Q
    Show answer and solution

    Answer: B. Either Q or S

    Seat 4 holds S in RPQS and Q in RPSQ and RSPQ.

  4. If S sits next to R, who sits in seat 4?

    • A P
    • B Q
    • C S
    • D R
    Show answer and solution

    Answer: B. Q

    S next to R gives R S P Q only. So Q is in seat 4.

Keep practising