2022 CSAT, all questions
UPSC Prelims 2022 · CSAT
Question 79: Basic Numeracy
What is the number of numbers of the form 0·XY, where X and Y are distinct non-zero digits?
a72
b81
c90
d100
AnswerUPSC’s answer is (a).
In 0.XY, X and Y are distinct non-zero digits. X can be any of 1 to 9, which is 9 ways, and Y any of the other 8 non-zero digits, which is 8 ways. So 9 × 8 = 72. Zero is excluded from both places, and repeated digits such as 0.11 are excluded by the word distinct, which is why the answer is not 81.
Why each option is right or wrong
- (a) Correct: 9 × 8 = 72.
- (b) 81 allows X and Y to be equal.
- (c) 90 allows zero in one of the places.
- (d) 100 counts every two-digit decimal.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.