MH CET MBA Abstract Reasoning (Non-Verbal) Syllabus

What is the method to solve a Paper Cutting and Unfolding problem?

Mentally reverse the folds one at a time; for each unfold, reflect the cut pattern across the fold line, so the final shape is symmetric about every crease used.

How many lines of symmetry will the unfolded pattern have if a square is folded twice (once horizontally, once vertically) before cutting?

The pattern will be symmetric about both the horizontal and vertical center lines (two lines of symmetry), reflecting the cut into all four quadrants.

A standard six-faced die: what is the sum of the numbers on any pair of opposite faces?

On a standard (Western) die the opposite faces always sum to 7: 1 opposite 6, 2 opposite 5, and 3 opposite 4.

In dice problems, what does it mean if two faces are 'adjacent'?

Adjacent faces share a common edge; on a standard die, two faces are adjacent if they are NOT opposite (i.e. their numbers do not sum to 7).

State the rule used to find opposite faces from two views of the same die.

If a number appears in the same position in both views while others rotate, that number's opposite stays hidden. More generally, any face common to both views cannot be opposite to the differing faces; deduce opposites by elimination.

If two different dice views share two common faces, how do you find what is opposite the third (changing) face?

The two common faces are adjacent to both the changing faces; therefore the two differing faces are opposite each other.

How many faces, edges, and vertices does a cube have?

A cube has 6 faces, 12 edges, and 8 vertices.

A painted cube is cut into n x n x n smaller cubes. How many small cubes have exactly 3 faces painted?

Always 8 — the corner cubes, regardless of n (for n >= 2).

A painted cube cut into n x n x n smaller cubes: how many small cubes have exactly 2 faces painted?

12 x (n - 2) — these are the edge cubes excluding corners.

A painted cube cut into n x n x n smaller cubes: how many small cubes have exactly 1 face painted?

6 x (n - 2)^2 — these are the central cubes on each of the six faces.

A painted cube cut into n x n x n smaller cubes: how many small cubes have NO face painted?

(n - 2)^3 — the inner core cubes that were never on the surface.

For a cube painted and cut into 3 x 3 x 3 (27 cubes), give the count of cubes with 3, 2, 1, and 0 painted faces.

3 faces: 8; 2 faces: 12; 1 face: 6; 0 faces: 1 (total 27).

What is the task in an Embedded (Hidden) Figures problem?

Locate and identify a given simple figure that is completely contained within a larger, more complex figure without any rotation or distortion of the simple figure.

What is the key rule for the hidden figure in Embedded Figures problems?

The target figure must appear in the larger figure exactly as given — same shape, same proportions, and same orientation (it is not rotated, resized, or flipped).

What strategy helps when searching for an embedded figure?

Trace the outline of the given simple figure within the complex one, focusing on its distinctive angles and lines, and ignore extra lines of the complex figure that are not part of the target.

What is required in a Figure Formation (Fragment Assembly) problem?

Determine which set of given fragments/pieces can be joined together (without overlap or gaps) to form a specified complete figure, or select the figure that can be made from the given parts.

What is a good check when assembling fragments into a complete figure?

Verify that the edges of the pieces match (complementary curves and straight edges) and that the total area and key features of the pieces account for the whole target figure with no missing or extra parts.

In a figure series, an arrow rotates 45 degrees clockwise each step. After 8 steps from pointing North, where does it point?

8 x 45 = 360 degrees, a full turn, so it points North again (same as the start).

How do you handle a figure series where TWO independent rules operate simultaneously?

Track each element separately — for example one element rotates while another changes shading or moves — and apply both rules together to the next frame.

What does 'order of letters is preserved' tell you about whether a transformation is a water image rather than a mirror image of text?

Water image keeps the left-to-right letter order the same (each letter flipped top-to-bottom), while mirror image reverses the letter order; preserved order indicates a water image.

In dice problems, what is the 'common face rotation' rule?

When one face is common (same number, same orientation) between two views, rotate the rest mentally about that fixed face to match the other numbers and thereby determine adjacency and opposites.

Why can a single number never appear twice on a standard die?

A standard die shows each of the numbers 1 through 6 exactly once, one per face, so no number repeats.

In paper punching, if a square is folded in half once and one hole is punched near the fold, where will the holes be after unfolding?

Two holes appear, symmetric about the fold line; both sit near the center crease, mirror images of each other.

What feature counts are most useful for solving Figure Classification problems quickly?

Number of straight lines, number of curved lines, number of enclosed regions, number of dots/elements, and presence/type of symmetry.

In a 2x2 figure analogy where the first figure gains an internal dot and rotates 90 degrees, how do you build the answer figure?

Apply the same two changes to the third figure: add the corresponding internal dot and rotate it 90 degrees in the same direction.

What is the difference between an 'open' and 'closed' figure, often tested in classification?

A closed figure has a fully enclosed boundary (like a triangle or circle); an open figure has at least one gap so its boundary does not fully enclose an area (like a 'C' or a zigzag line).

When unfolding a paper that was folded along a diagonal before cutting, what symmetry results?

The cut pattern becomes symmetric about that diagonal fold line — the design on one side is mirrored across the diagonal onto the other side.

In embedded figure questions, why might a candidate figure be rejected even if its shape appears inside?

Because it appears rotated, flipped, or scaled differently — the embedded answer must match the given figure's exact orientation and size, so any such mismatch disqualifies it.

For a cube painted on all faces and cut into 4 x 4 x 4 (64 cubes), how many small cubes have exactly one painted face?

6 x (4 - 2)^2 = 6 x 4 = 24 cubes with exactly one painted face.

What is the general approach to ALL non-verbal reasoning figure problems (the unifying skill)?

Identify the consistent rule or relationship by comparing figures feature by feature (rotation, reflection, count, shading, position), then apply that rule to derive or select the required figure.