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CAT 2017 Slot 1 · DILR · Grid Puzzles and Matching · medium

CAT 2017 Slot 1 DILR: Hotel Room Allocation

A small hotel has three floors numbered 1 (lowest) to 3 (top). Each floor has three rooms in a row, labelled from left to right as x01, x02 and x03, where x is the floor number (so the rooms on floor 2 are 201, 202 and 203). Nine guests – A, B, C, D, E, F, G, H and I – are each allotted a different room. The following information is known:

1. A and C stay on the same floor, with exactly one room between them.
2. B stays in the room directly above I, and D stays in the room directly below I.
3. H stays in the leftmost room of a floor that is lower than A's floor.
4. E and G stay on the same floor, but G's room is not the rightmost room on that floor.
5. F stays on a floor lower than E's floor.
6. C stays in the room directly above F.

Question 1

Single correct option

Who stays in room 202?
  1. A. B
  2. B. D
  3. C. I
  4. D. C
Show answer and solution

Answer: (C) I

Deduction: Clue 2 forces B, I, D into one column on floors 3, 2 and 1 respectively. A and C (clue 1) occupy the two end rooms of one floor. They cannot be on floor 1, because H must be on a lower floor than A (clue 3). If A and C were on floor 3, F (directly below C) would be on floor 2, and clue 5 would require E on floor 3 – but floor 3 would already be full (A, B, C) ✗. So A and C take the ends of floor 2, I takes 202, B is in 302 and D in 102. H must be at the left end of floor 1 (room 101), so F, directly below C, must be in 103 – which means C is in 203 and A in 201. E and G take the remaining rooms 301 and 303 on floor 3, and since G is not at the right end, G = 301 and E = 303. F (floor 1) is below E ✓.

Final allotment:

| Floor | Left (x01) | Middle (x02) | Right (x03) |
|---|---|---|---|
| 3 | G (301) | B (302) | E (303) |
| 2 | A (201) | I (202) | C (203) |
| 1 | H (101) | D (102) | F (103) |

Room 202 (floor 2, middle) is occupied by I.

Question 2

Single correct option

Who stays in the room directly below E's room?
  1. A. A
  2. B. C
  3. C. I
  4. D. F
Show answer and solution

Answer: (B) C

From the final allotment:

| Floor | Left (x01) | Middle (x02) | Right (x03) |
|---|---|---|---|
| 3 | G (301) | B (302) | E (303) |
| 2 | A (201) | I (202) | C (203) |
| 1 | H (101) | D (102) | F (103) |

E is in 303 (floor 3, right). The room directly below is 203, occupied by C. (F is two floors below E, in 103.)

Question 3

Numerical answer

What is the sum of the room numbers of A and F?
Show answer and solution

Answer: 304

From the final allotment:

| Floor | Left (x01) | Middle (x02) | Right (x03) |
|---|---|---|---|
| 3 | G (301) | B (302) | E (303) |
| 2 | A (201) | I (202) | C (203) |
| 1 | H (101) | D (102) | F (103) |

A is in room 201 and F is in room 103. Sum = 201 + 103 = 304.

Key step: A and C must be on floor 2 — if they were on floor 3, F (below C) would be on floor 2 and E would have to be on the already-full floor 3.

Question 4

Single correct option

Which of the following pairs of guests stay on the same floor?
  1. A. A and E
  2. B. B and C
  3. C. H and F
  4. D. G and I
Show answer and solution

Answer: (C) H and F

From the final allotment:

| Floor | Left (x01) | Middle (x02) | Right (x03) |
|---|---|---|---|
| 3 | G (301) | B (302) | E (303) |
| 2 | A (201) | I (202) | C (203) |
| 1 | H (101) | D (102) | F (103) |

Floor 1: H, D, F. So H and F share a floor. A (floor 2) and E (floor 3) do not; B (3) and C (2) do not; G (3) and I (2) do not.
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Original question written in the CAT 2017 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake