UPSC Prelims 2021 · CSAT
Question 19: Basic Numeracy
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
AnswerUPSC’s answer is (d).
Count integers from 700 to 1000 whose digits add to 10. For 7ab, a + b = 3: 703, 712, 721, 730, which is 4 numbers. For 8ab, a + b = 2: 802, 811, 820, which is 3. For 9ab, a + b = 1: 901, 910, which is 2. The number 1000 has digit sum 1. Total 4 + 3 + 2 = 9. Remember: fix the hundreds digit, then list the pairs of remaining digits that make up the rest of the sum.
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) 6 falls three short of 4 + 3 + 2 = 9.
- (b) 7 falls two short of 9.
- (c) 8 falls one short of 9.
- (d) Right: 4 numbers from the 700s, 3 from the 800s and 2 from the 900s.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2021, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.