SSC CGL 2025 Tier-I · 17 September 2025, Shift 3 · 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 11 September 2026.

Where this paper and its answers come from

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.

A large cubical cake needs to be cut into 64 smaller, identical cubical pieces. What is the minimum number of straight cuts required?

(a)8
(b)9
(c)16
(d)63

Answer

Why

Correct — B.
Edge count: 64 = 4³, so the cake splits into 4 pieces along each edge
Cuts per edge: 4 pieces need 4 − 1 = 3 parallel cuts
Three directions: 3 + 3 + 3 = 9 cuts → option (b)

Check: (3 + 1) × (3 + 1) × (3 + 1) = 64 identical cubes

Why the others are wrong

(a)
8 — 8 cuts leave one of the nine needed planes uncut. Split them 3 + 3 + 2 and you get 4 × 4 × 3 = 48 pieces, and those are not cubes.
(c)
16 — 16 is 4 × 4, the number of pieces in one layer of the cut cake, not a count of cuts. Nine cuts already give all 64.
(d)
63 — 63 = 64 − 1 counts one new piece per cut, as if each cut split a single piece. A straight cut through the whole cake splits every piece it crosses.

Concept

A straight cut through the whole cake is a plane. Parallel planes along one edge split it into (cuts + 1) slabs, so n pieces along an edge need n − 1 cuts.

Cuts in the three directions multiply: a, b and c cuts give (a + 1)(b + 1)(c + 1) pieces. For 64 identical cubes every edge needs 4 pieces, hence 3 cuts in each direction.

The key of 9 assumes the pieces stay where they are between cuts.

If you could stack pieces and cut them together, 6 cuts would do (each cut at most doubles the piece count, and 2⁶ = 64). 6 is not offered.

Key facts

n equal pieces along one edge need n − 1 parallel cuts.
a, b and c cuts in the three directions give (a + 1)(b + 1)(c + 1) pieces.
Cutting a cube into n³ identical cubes without moving pieces takes 3(n − 1) cuts.

Study next

Painted cube cut into n³ small cubes: cubes with 3, 2, 1 or 0 faces paintedLargest identical cubes from a cuboid, using the HCF of its edges

Common traps

Counting pieces instead of cuts along an edge: 4 pieces need 3 cuts, not 4.
Assuming each cut adds only one piece, which gives 63.

11 Sep 2024, 16:00, Quant Q.15 counts pieces edge by edge in the same way: a 50 × 150 × 175 cm cuboid cut into the largest identical cubes (edge 25 cm, the HCF) gives 2 × 6 × 7 = 84, the keyed answer.

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 51 SSC CGL questions on it, every solved shift.