Test Level 2: Cubes & Dices - CAT MCQ

There are 5 × 5 = 25 cubes on one face.
Now, there will be an edge comprising 5 cubes which shall be common to both the faces coloured green.
Thus, the number of cubes with at least one face green = (25 × 2) - 5 = 50 - 5 = 45.
Thus, answer option 4 is correct.

The diagrammatic representation of the same is as shown.

On the face, as shown in the figure, there are 9 cubes marked W1 with only one face coloured white. Similarly, there will be 9 cubes with only one face, each coloured white.
Now, on the edge common to both the faces coloured white, there shall be 3 cubes with two faces each coloured white as represented by W2.
Thus, total number of cubes = 9 × 2 + 3 = 18 + 3 = 21.
Hence, answer option 3 is correct.

The diagrammatic representation of an orange face is as shown, with the adjacent faces marked as shown.

The face with a face coloured orange with small cubes marked as O1 will be the small cubes with only one face coloured orange.
There are 9 such cubes. There shall be 9 such cubes on the adjacent face as well.
Thus, there shall be 18 cubes like this in all.
Hence, answer option 3 is correct.

Clearly, upon colouring the cube as stated and then cutting it into 125 smaller cubes of equal sizes, we get a stack of cubes as shown in the figure.

The figure can be analysed by assuming the stack to be composed of 5 horizontal layers.
There are 4 corner cubes in layer 1, and 4 corner cubes in layer 5, having three green faces each.
Thus, there are 8 such cubes.

There are 9 central cubes in each of the layers 2, 3 and 4, which are without any colour.

Thus, there are 9 × 3 = 27 such cubes.

The dot will lie opposite to one of the shaded surfaces.
Therefore, figure (2) cannot be formed.

Number 3 appears in the same position both times.
The pattern of numbers is as given below.
From first orientation, write the numbers in clockwise direction.
3 - 5 - 2
From second orientation, write the numbers in clockwise direction.
3 - 1 - 6
Hence, 2 is opposite to number 6 and 5 is opposite to number 1.

Opposite faces cannot come adjacent to each other.
Hence, answer figure (b) can be created by folding the given figure.

Four characters will be adjacent to each character.
As shown, *, ?, # and $ are adjacent to character +.
So, the only character that will be opposite to '+' is '@'.

As per figure (A), we get that @ is opposite to *, % is opposite to # and $ is opposite to =. The characters which are in the adjacent faces cannot be opposite to each other.
From this, it is clear that only figure (c) is possible.
So, option (3) is the correct answer.