Concept:This is a data sufficiency puzzle. We need to check which statements together give a unique arrangement of boxes on shelves
1 to
9.
Explanation:Let the shelves be numbered from
1 (bottom) to
9 (top). We need to find the number of boxes between
A and
H.
Analyzing statement I alone:
From statement I, we get these two possible cases:
Here
A and
H are not fixed. So statement I alone is not sufficient.
Analyzing statement II alone:
From statement II, we get many possible cases:
Here also
A and
H are not fixed. So statement II alone is not sufficient.
Analyzing statement III alone:
Statement III gives several possibilities for
A,
C,
G, and
H. So statement III alone is not sufficient.
Combining statements I and II:
Statement I gives two cases. In the first case,
I is at
7, so
G immediately below
I would be at
6, but
E is already at
6. Thus that case is rejected. The second case gives this unique arrangement:
In this arrangement, boxes between
A (shelf
7) and
H (shelf
1) are on shelves
6,
5,
4,
3, and
2. That is
5 boxes. So statements I and II together are sufficient.
Combining statements I and III:
The possible arrangements still have multiple cases:
So the positions of
A and
H are not unique. Hence I and III together are not sufficient.
Combining statements II and III:
The possible arrangements still have multiple cases:
So II and III together are not sufficient.
Therefore, the question can be answered only by combining statements I and II.
Answer:Data given in both statements I and II are sufficient to answer the given question. Option B.