2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 5: Basic Numeracy
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
a8
b9
c12
d16
AnswerUPSC’s answer is (b).
Making 64 identical pieces from a cube means a 4 × 4 × 4 arrangement of small cubes. Each direction needs 3 straight cuts to make 4 equal slabs, so the minimum is 3 + 3 + 3 = 9 cuts, taking the pieces as left in place after each cut, which is the usual convention for such puzzles. For n equal slices along one edge you need n − 1 cuts.
Why each option is right or wrong
- (a) Wrong. 8 cuts cannot make 4 slices in all three directions; each direction needs 3.
- (b) Right. 3 cuts in each of three directions gives 9 and a 4 × 4 × 4 block of 64 pieces.
- (c) Wrong. 12 would be 4 cuts per direction, which makes 5 slices, not 4.
- (d) Wrong. 16 is far more than needed for a 4 × 4 × 4 split.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.