SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 12 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What is the minimum number of cuts required to divide a cuboid into 8 equal cuboids?

(a)2
(b)3
(c)5
(d)4

Answer

Why

Correct — B.
One plane cut splits each piece into at most two, so each cut at most doubles the count.

After 1 cut: at most 2 pieces
After 2 cuts: at most 4 pieces
After 3 cuts: at most 8 pieces

Three cuts through the middle, one parallel to each pair of faces, give 2 × 2 × 2 = 8 equal cuboids → option (b)

Why the others are wrong

(a)
2 — 2 cuts make at most 4 pieces, since each cut at most doubles the count. Two cuts at right angles give 2 × 2 × 1 = 4 cuboids, half of what is asked.
(c)
5 — 5 cuts is more than needed. Three cuts already give 8 equal cuboids, and the question asks for the minimum.
(d)
4 — 4 cuts can give 8 equal cuboids (3 parallel cuts make 4 slabs, one cut across halves each: 4 × 2 = 8), but 3 cuts do it with one fewer.

Concept

With cuts that run straight through the whole block, a, b and c cuts parallel to the three pairs of faces give (a + 1)(b + 1)(c + 1) pieces. Spread the cuts over all three directions to use the fewest.

For 8 pieces: one cut each way gives 2 × 2 × 2 = 8 with 3 cuts. All cuts in one direction need 7, and 3 + 1 needs 4.

The doubling bound is why nothing beats 3: even if pieces are stacked before a cut, each piece still splits into at most two. For 8 pieces the 1 + 1 + 1 grid meets that bound exactly.

Key facts

One plane cut splits each piece into at most two, so n cuts give at most 2ⁿ pieces.
a, b and c cuts in the three directions give (a + 1)(b + 1)(c + 1) pieces.
8 equal cuboids need 3 cuts, one parallel to each pair of faces through the middle.

Study next

A cube cut into n³ equal cubes without moving the pieces: 3(n − 1) cutsPainted-cube counting: small cubes with 0, 1, 2 or 3 painted facesThe most pieces a cake or cube gives for a set number of cuts

Common traps

Choosing 4 because 3 parallel cuts plus 1 across make 8: spreading the cuts over three directions saves one.
Carrying the doubling idea to the 64-cube cake: stacking could reach 64 in 6 cuts, but its key is 9 (3 in each direction). That key assumes the pieces stay in place, which the stem never states.

17 Sep 2025, 16:00, Quant Q.12 asks the same for a cubical cake cut into 64 identical cubes, keyed 9 (option b): with the pieces left in place, 3 cuts in each direction give 4 × 4 × 4 = 64.

Related PYQs

No directly related past PYQ was found.

Topic: Right Prism, Right Circular Cone, Right Circular Cylinder, Sphere, Hemispheres, Rectangular Parallelepiped, Regular Right Pyramid with triangular or square base — all 99 SSC CGL questions on it, every solved shift.