Eight people — P, Q, R, S, T, U, V and W — entered an empty lift together at the ground floor (floor 0) of a building with floors numbered 0 to 12. The lift then moved only upwards. It stopped only at floors where at least one person got out, and nobody else entered it. All eight had got out by the time it made its last stop. The following is known:
1. The lift made exactly four stops, and the last stop was on floor 11.
2. Between any two consecutive positions of the lift (counting the ground floor as the starting position), it never travelled more than 3 floors.
3. Exactly one of the four stops was on an even-numbered floor, and exactly three people got out there.
4. P and Q got out together at the first stop, and nobody else got out there.
5. R got out alone.
6. S, T and U got out together, and nobody got out in a group larger than theirs.
7. V got out exactly 3 floors above the floor where S got out.
8. R got out before V did, and W did not get out with P.
1. The lift made exactly four stops, and the last stop was on floor 11.
2. Between any two consecutive positions of the lift (counting the ground floor as the starting position), it never travelled more than 3 floors.
3. Exactly one of the four stops was on an even-numbered floor, and exactly three people got out there.
4. P and Q got out together at the first stop, and nobody else got out there.
5. R got out alone.
6. S, T and U got out together, and nobody got out in a group larger than theirs.
7. V got out exactly 3 floors above the floor where S got out.
8. R got out before V did, and W did not get out with P.
Question 1
Single correct option
On which floor did R get out?
- A. 3
- B. 5
- C. 6
- D. 9
Show answer and solution
Answer: (B) 5
Stops: the four gaps from floor 0 must add up to 11 with each gap at most 3, so the gaps are three 3's and one 2. The possible stop sets are {2,5,8,11}, {3,5,8,11}, {3,6,8,11} and {3,6,9,11}. Exactly one even floor leaves {3,5,8,11} and {3,6,9,11}.
The even stop has 3 people, so S, T, U got out there (the only group of 3). P and Q are at the first stop (3). V is 3 floors above S.
- Stops {3,6,9,11}: S at 6, V at 9, so R must be alone at 11. But then R gets out after V, which contradicts clue 8.
- Stops {3,5,8,11}: S at 8, V at 11, R alone at 5, W at 11.
| Floor | Got out |
|---|---|
| 3 | P, Q |
| 5 | R |
| 8 | S, T, U |
| 11 | V, W |
R got out on floor 5.
The even stop has 3 people, so S, T, U got out there (the only group of 3). P and Q are at the first stop (3). V is 3 floors above S.
- Stops {3,6,9,11}: S at 6, V at 9, so R must be alone at 11. But then R gets out after V, which contradicts clue 8.
- Stops {3,5,8,11}: S at 8, V at 11, R alone at 5, W at 11.
| Floor | Got out |
|---|---|
| 3 | P, Q |
| 5 | R |
| 8 | S, T, U |
| 11 | V, W |
R got out on floor 5.
Question 2
Numerical answer
How many people were in the lift when it left floor 5?
Show answer and solution
Answer: 5
From the solution (3: P, Q; 5: R; 8: S, T, U; 11: V, W), 8 people started, 2 got out at floor 3 and 1 at floor 5.
People in the lift after floor 5 = 8 − 3 = 5 (S, T, U, V, W).
People in the lift after floor 5 = 8 − 3 = 5 (S, T, U, V, W).
Question 3
Single correct option
Which of the following pairs of people got out on the same floor?
- A. V and W
- B. R and V
- C. T and W
- D. Q and R
Show answer and solution
Answer: (A) V and W
Final arrangement: 3 → P, Q; 5 → R; 8 → S, T, U; 11 → V, W.
- V and W: both at 11 ✓
- R and V: 5 and 11 ✗
- T and W: 8 and 11 ✗
- Q and R: 3 and 5 ✗
Answer: V and W.
- V and W: both at 11 ✓
- R and V: 5 and 11 ✗
- T and W: 8 and 11 ✗
- Q and R: 3 and 5 ✗
Answer: V and W.
Question 4
Numerical answer
The lift takes 2 seconds to pass from one floor to the next and halts for 10 seconds at every stop. How many seconds after leaving the ground floor does the lift arrive at its last stop?
Show answer and solution
Answer: 52
The last stop is floor 11, so the lift travels 11 floors: 11 × 2 = 22 seconds.
It halts at the three earlier stops (3, 5, 8) on the way: 3 × 10 = 30 seconds. The halt at floor 11 comes after arrival, so it is not counted.
Total = 22 + 30 = 52 seconds.
It halts at the three earlier stops (3, 5, 8) on the way: 3 × 10 = 30 seconds. The halt at floor 11 comes after arrival, so it is not counted.
Total = 22 + 30 = 52 seconds.
Saved on this device. Sign in or create a free account to keep it on every device.