UPSC Prelims 2026 · CSAT
Question 24: Logical Reasoning and Mental Ability
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 by 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 x_4?
AnswerUPSC’s answer is (a).
n plane cuts of a solid give at most (n³ + 5n + 6)/6 pieces, which is 15 for n = 4, so 16 is impossible. The rest can follow identical pieces after three cuts. Three equal-spaced parallel cuts give 4 slabs; a fourth parallel cut gives 5, while a fourth cut across all slabs gives 8. Two parallel cuts plus one crossing cut give 6 equal pieces; a fourth cut across both directions gives 12.
Why each option is right or wrong
- (a) Right: four plane cuts give at most 15 pieces, so 16 cannot occur.
- (b) Possible: two parallel cuts, one crossing cut, then a cut in the third direction give 12.
- (c) Possible: four equal slabs cut across give 8.
- (d) Possible: four equal slabs and one more parallel cut give 5.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.