The persons whose names are vowels live in flats C only.
From I and II together:
M lives in flat A of floor no. 1. Two floors are below the floor in which R lives. R lives in flat B.
O lives immediately above I. J and O live on the same floor.
| Floor | Case 1 | Case 2 | Case 3 |
| | A | B | C | A | B | C | A | B | C |
| 4 | J/ | /J | O | | | | | | |
| 3 | | R | I | J | R | O | | R | |
| 2 | | | | | | I | J/ | /J | O |
| 1 | M | | | M | | | M | | I |
D lives immediately below Q. D does not live in flat B. E and Q live on the same floor. So, cases 1 and 2 are invalid.
| Floor | Case 3a | Case 3b |
| | A | B | C | A | B | C |
| 4 | /Q | Q/ | E | | | |
| 3 | D | R | | Q | R | E |
| 2 | J/ | /J | O | D | J | O |
| 1 | M | | I | M | | I |
So, it can't be determined who lives in flat A of floor no. 3. So, statements I and II together are not sufficient.
From II and III together:
There are two floors in between I and Z but they live in different flats. U lives above I. M lives in flat A of floor no. 1.
| Floor | Case 1 |
| | A | B | C |
| 4 | Z/ | /Z | U/ |
| 3 | | | U/ |
| 2 | | | U/ |
| 1 | M | | I |
O lives immediately above I. J and O live on the same floor.
| Floor | Case 1 |
| | A | B | C |
| 4 | Z/ | /Z | U/ |
| 3 | | | U/ |
| 2 | J/ | /J | O |
| 1 | M | | I |
D does not live in flat B. G lives to the immediate west of J on the same floor.
| Floor | Case 1 |
| | A | B | C |
| 4 | Z/ | /Z | U/ |
| 3 | | | /U |
| 2 | G | J | O |
| 1 | M | | I |
So, it can't be determined who lives in flat A of floor no. 3. So, statements II and III together are not sufficient.
From I and III together:
Two floors are below the floor in which R lives. R lives in flat B.
There are two floors in between I and Z but they live in different flats. U lives above I.
| Floor | Case 1 |
| | A | B | C |
| 4 | Z/ | /Z | |
| 3 | | R | |
| 2 | | | |
| 1 | | | I |
D lives immediately below Q. E and Q live on the same floor. G lives to the immediate west of J on the same floor.
| Floor | Case 1 | Case 2 | Case 3 |
| | A | B | C | A | B | C | A | B | C |
| 4 | Z/ | /Z | U | Z/Q | Q/Z | E/ | Z/Q | Q/Z | /E |
| 3 | Q/ | R | E/ | | R | U | Q | R | E/ |
| 2 | /Q | /Q | E/ | /Q | /Q | E/ | | | U |
| 1 | | | I | | | I | | | I |
So, it can't be determined who lives in flat A of floor no. 3. So, statements I and III together are not sufficient.
From I, II and III together:
From II and III, we got the following case:
| Floor | Case 1 |
| | A | B | C |
| 4 | Z/ | /Z | U/ |
| 3 | | | /U |
| 2 | G | J | O |
| 1 | M | | I |
Two floors are below the floor in which R lives. R lives in flat B.
| Floor | Case 1 | Case 2 |
| | A | B | C | A | B | C |
| 4 | Z/ | /Z | U | Z/ | /Z | |
| 3 | | R | | | R | U |
| 2 | G | J | O | G | J | O |
| 1 | M | | I | M | | I |
D lives immediately below Q. E and Q live on the same floor. D does not live in flat B.
| Floor | Case 1 |
| | A | B | C |
| 4 | Q | Z | E |
| 3 | D | R | U |
| 2 | G | J | O |
| 1 | M | | I |
So, D lives in flat A of floor no. 3.
So, all the three statements together are necessary.
Study Notes
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