ISRO EC 2023 Q.86: solution and answer

ISRO 2023 · ECQ.86 · 2 marks · MCQ

Eight friends P, Q, R, S, T, V, W and Y are sitting around a square table. 1. Out of eight, four persons are sitting at the corners of the table and the other four are sitting at the mid-points of each side of the table. 2. Persons at the corners are facing the centre while the persons at the mid-points of side are facing outside. 3. S is third to the right of P. P is facing the centre. 4. Y is not sitting beside P or S. 5. T is third to the right of R. 6. R is not sitting at the mid-point of any side of the table. 7. R is also not beside Y. 8. There is only one person between P and V. 9. Q is not sitting beside V. How many people are there between T and Q? (2 Marks)

(A)
1
(B)
2
(C)
3
(D)
None

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

There is exactly 1 person (Y) between T and Q, which is option (A).

Official answer: ASource: ISRO's revised and final answer key of 16 February 2024

Number the 8 seats $0$ to $7$ going clockwise as seen from above, with corners at even numbers ( $0, 2, 4, 6$ ) and side mid-points at odd numbers ( $1, 3, 5, 7$ ). Place P at corner $0$ , facing the centre.
A person facing the centre has the right hand towards the anticlockwise side, and a person facing outwards has it towards the clockwise side. S is third to the right of P, so S is $3$ seats anticlockwise from P: seat $5$ (a mid-point).
Y is not beside P (seats $1, 7$ ) or beside S (seats $4, 6$ ), so Y is in seat $2$ or seat $3$ .
Exactly one person sits between P and V, so V is in seat $2$ or seat $6$ . R is not at a mid-point, so R is a corner: seat $2$ , $4$ or $6$ . Corners face the centre, so T, third to the right of R, is $3$ seats anticlockwise from R.
Try $R = 2$ . Then $T = 7$ . Y cannot be in seat $2$ , so $Y = 3$ , which is beside R. This breaks condition 7, so it is rejected.
Try $R = 6$ . Then $T = 3$ , so Y must be seat $2$ . V then has no seat, since seats $2$ and $6$ are both taken. Rejected.
Try $R = 4$ . Then $T = 1$ . Seat $3$ is beside R, so $Y = 2$ , and then $V = 6$ . The seats left, $3$ and $7$ , go to Q and W. Seat $7$ is beside V (seat $6$ ), so Q is not in $7$ . Hence $Q = 3$ and $W = 7$ .
The full arrangement is P $= 0$ , T $= 1$ , Y $= 2$ , Q $= 3$ , R $= 4$ , S $= 5$ , V $= 6$ , W $= 7$ . Between T (seat $1$ ) and Q (seat $3$ ) there is only Y in seat $2$ , so there is $1$ person.

KEY IDEA

In a circular seating puzzle, fix one person, number the seats, and decide which way a person's right hand points from the direction they face (towards the anticlockwise side when facing the centre). Then place people with the direct conditions and test each possible position for the others against the negative conditions.

WATCH OUT FOR

Taking right to mean clockwise for everyone, forgetting that corner persons face the centre while mid-point persons face outwards. This reverses the direction of right and gives a different arrangement.

From the ISRO EC 2023 paper. Also Q.86 of the ISRO Scientist/Engineer Computer Science 2023 paper. Every question of this paper · The full paper (PDF, ISRO) · All 11 ISRO Reasoning questions, with notes

ISRO EC 2023 Q.86: solution and answer

Answer and solution

More ISRO Reasoning questions