UPSC Prelims 2023 · CSAT
Question 5: Basic Numeracy
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots ?
AnswerUPSC’s answer is (b).
Let f be the number of fours and s the number of sixes; singles fill the rest, so count the pairs (f, s) with 4f + 6s <= 25. s = 0: f = 0 to 6, 7 ways. s = 1: 4f <= 19, f = 0 to 4, 5 ways. s = 2: 4f <= 13, f = 0 to 3, 4 ways. s = 3: 4f <= 7, f = 0 or 1, 2 ways. s = 4: 4f <= 1, f = 0, 1 way. Total = 7 + 5 + 4 + 2 + 1 = 19.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: undercounts; the cases s = 0 to 4 give 19, not 18.
- (b) Right: 7 + 5 + 4 + 2 + 1 = 19.
- (c) Wrong: overcounts; s = 5 would need 30 runs, more than 25.
- (d) Wrong: overcounts by two.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.