Q4·CSAT · Prelims 2026

Geometry — Solid Cube Cuts

ReasoningSpatial Reasoning — Cube CutsSeries & Pattern● Hard

Question

A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted x₍n₎. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x4?

Options

Answer

Explanation

Let us analyze the problem under the condition that the pieces remain unmoved after each cut. This matches the standard planar cuts model across a single coordinate space.

Three orthogonal cuts through the center of a cube generate exactly 2 × 2 × 2 = 8 identical pieces. This satisfies the condition that the pieces are identical after the third cut (x_3 = 8).

Now, let us apply the fourth cut (n=4) without moving any of the existing 8 pieces.

If the fourth cut passes through all 8 pieces (parallel to one of the faces, creating a new slicing layer), it divides each of the 8 pieces into 2 parts, creating 8 × 2 = 16 pieces (x_4 = 16).

If the fourth cut is applied diagonally or selectively through the configuration, it can cut through a subset of the pieces. For example, if it cuts through exactly 4 pieces, the total becomes 8 + 4 = 12 pieces (x_4 = 12).

If the fourth cut misses the object completely or replicates an existing cut, the count stays at 8 (x_4 = 8).

However, starting with 8 pieces and adding a single straight cut cannot result in 5 total pieces, as a straight cut can only add parts, never decrease the total number of pieces (x_4 \ge 8). Therefore, 5 is mathematically impossible.

Applying a single planar cut across an established set of pieces can only increase the total count, making any final value lower than the baseline count impossible.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Section

Analytical Reasoning

Sub-topic

Spatial Reasoning — Cube Cuts

Type

Series & Pattern

Difficulty

Hard

Source hint

Standard spatial logic — maximum pieces via planar cuts

See all questions on Spatial Reasoning — Cube Cuts

Browse every tagged question across all years

Explore →

Back to CSAT 2026