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Question :

In the question given below, two statements numbered as I and II are given. You have to decide whether the data provided in the statements are sufficient to answer the question.

Seven persons A, B, C, D, E, F and G live in a building consisting of seven floors, but not necessarily in the same order. The floors are numbered as 1 to 7 from bottommost to topmost floor. If D lives immediately below F, then who among the following lives exactly on the middle floor of a building?

Statement I: Four persons live between B and E, who lives on an even numbered floor below B and G. Three persons live between A and G.

Statement II: Two persons live between A and D. G lives immediately below C but not below A. B lives on an odd numbered floor.

1. If the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question.

2. If the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.

3. If the data in either statement I alone or statement II alone are sufficient to answer the question.

4. If the data in both statement I and statement II together are sufficient to answer the question.

5. If the data in both statement I and statement II together are not sufficient to answer the question.

Correct Answer : 1
Solution :

It is given that,

Seven persons A, B, C, D, E, F and G live in a building consisting of seven floors, but not necessarily in the same order.

The floors are numbered as 1 to 7 from bottommost to topmost floor.

D lives immediately below F.

From statement I alone:

Four persons live between B and E, who lives on an even numbered floor below B and G.

Three persons live between A and G.

Floors Persons
7B
6
5G
4
3
2E
1A

D lives immediately below F.

Floors Persons
7B
6
5G
4F
3D
2E
1A

So, finally we get:

Floors Persons
7B
6C
5G
4F
3D
2E
1A

Therefore, F lives exactly on the middle floor of a building.

So, statement I alone is sufficient to answer the question.

From statement II alone:

D lives immediately below F.

Case 1Case 2Case 3Case 4Case 5Case 6
Floors Persons Persons Persons Persons Persons Persons
7F
6DF
5DF
4DF
3DF
2DF
1D

G lives immediately below C but not below A.

Two persons live between A and D.

Case 1Case 2Case 3Case 3aCase 5Case 6Case 6a
Floors Persons Persons Persons Persons Persons Persons Persons
7FCCC
6DFGGGC
5CDFFAG
4GCDDAA
3AGCF
2AGDFF
1AADD

B lives on an odd numbered floor.

Case 1Case 2Case 3Case 3aCase 5Case 6Case 6a
Floors Persons Persons Persons Persons Persons Persons Persons
7FB/ECBCCB/E
6DFGEGGC
5CDFFAB/EG
4GCDDEAA
3AGBCFB/EB/E
2EAEGDFF
1BB/EAABDD

Thus, no definite answer can be concluded.

So, statement II alone is not sufficient.

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