GATE CE 2017 Set 2 — Question 63
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?
Correct answer
(C) T is immediately to the left of P or P is immediately to the right of Q
Solution
Let the seats be numbered 1 to 6 in counter-clockwise order. Facing the center, 'right' is counter-clockwise and 'left' is clockwise.
Now, and switch seats. There are two cases:
Case 1: was at seat 2. After the switch, is at seat 2 and is at seat 6. The arrangement is . Here, is immediately to the right of .
Case 2: was at seat 5. After the switch, is at seat 5 and is at seat 6. The arrangement is . Here, (at 4) is immediately to the left of (at 5).In both cases, either 'T is immediately to the left of P' or 'P is immediately to the right of Q' is true. Thus, (C) must necessarily be true.
1.Let be at seat 1.
2. is two places to the right of : . is at seat 3.
3. is three places to the left of : . is at seat 6.
4. is opposite . In a 6-seat circle, opposite pairs are (1,4), (2,5), and (3,6). Since is at 1 and is at 3, and must occupy seats 2 and 5. The remaining seat 4 is occupied by .
Initial arrangement: .Now, and switch seats. There are two cases:
Case 1: was at seat 2. After the switch, is at seat 2 and is at seat 6. The arrangement is . Here, is immediately to the right of .
Case 2: was at seat 5. After the switch, is at seat 5 and is at seat 6. The arrangement is . Here, (at 4) is immediately to the left of (at 5).In both cases, either 'T is immediately to the left of P' or 'P is immediately to the right of Q' is true. Thus, (C) must necessarily be true.
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