UPSC Prelims 2018 · CSAT
Question 36: Basic Numeracy
While writing all the numbers from 700 to 1000, how many numbers occur in which the digit at hundred's place is greater than the digit at ten's place, and the digit at ten's place is greater than the digit at unit's place?
AnswerUPSC’s answer is (c).
Count numbers from 700 to 999 whose hundred's digit is greater than the ten's digit, which is greater than the unit's digit. For hundred's digit h, pick any two different smaller digits from 0 to h - 1 and write them in decreasing order: C(h,2) numbers. For h = 7 that is 21, for h = 8 it is 28, for h = 9 it is 36. Total = 21 + 28 + 36 = 85. The number 1000 does not qualify.
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) 61 does not equal 21 + 28 + 36.
- (b) 64 does not equal 21 + 28 + 36.
- (c) Correct: 21 + 28 + 36 = 85.
- (d) 91 does not equal 21 + 28 + 36.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.