GATE 2026 DA Q.43: solution and answer

GATE 2026 · DAQ.43 · 2 marks · MCQ

Consider the concept hierarchies as shown in the figure.

Which of the following options denotes the total number of possible data cuboids from these concept hierarchies?

GATE 2026 DA question 43: Three vertical concept hierarchies drawn side by side, each a chain of three nodes joined by a line, top to bottom. — Figure from the GATE 2026 DA paper. It is part of the question.

(A)
$4^{3}$
(B)
$2^{3}$
(C)
$2!$
(D)
$4!$

Answer and solution

ANSWER

Option (A): the total number of possible cuboids is $4^{3} = 64$ .

Official answer: ASource: Official answer key, GATE 2026 DA (IIT Guwahati)

The figure shows three dimensions, each with a concept hierarchy of $3$ levels: time (Year, Month, Day), location (Country, State, City) and item (Item Category, Item Type, Item).
A cuboid is obtained by choosing, for every dimension, one abstraction level to group by. Besides the three named levels, each dimension also has the virtual top level 'all', where that dimension is aggregated away completely.
So each dimension offers $L_{i} + 1 = 3 + 1 = 4$ choices of level, and the choices for different dimensions are independent.
By the multiplication rule, the total number of cuboids is $\prod_{i = 1}^{n} (L_{i} + 1)$ .
Here $n = 3$ and every $L_{i} = 3$ , so the total is $4 \times 4 \times 4 = 4^{3} = 64$ .
The value $2^{3} = 8$ would be the count if no dimension had a hierarchy, so each dimension offered only 'present' or 'aggregated away'. That does not apply, because every dimension has several levels.
$2!$ and $4!$ equal $2$ and $24$ , and neither equals $64$ . Hence the answer is option (A), $4^{3}$ .

KEY IDEA

With concept hierarchies, a cuboid picks one level per dimension, including the top level 'all'. The count is $\prod (L_{i} + 1)$ , where $L_{i}$ is the number of levels of dimension $i$ excluding 'all'.

WATCH OUT FOR

Using $2^{n}$ , the count for dimensions without hierarchies, and choosing option (B). Another slip is counting only the $3$ named levels per dimension and forgetting the virtual level 'all', which gives $3^{3}$ and is not an option.

From the GATE 2026 DA paper. Every question of this paper · Download the full paper · All 3 Data warehousing questions, with notes