Prelims 2022 · CSAT / Quantitative Aptitude · Question 79
What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits?
Answer
72
Key fact: Numbers of the form 0.XY have two decimal places, with X and Y as distinct non-zero digits.
- X can be chosen in 9 ways (1 to 9).
- For each choice of X, Y can be chosen in 8 ways (any non-zero digit except X).
- Total numbers = 9 × 8 = 72.
Option check:
- (a) 72 — Correct.
- (b) 81 — Incorrect; this would allow repetition.
- (c) 90 — Incorrect; this wrongly counts zero or repetition.
- (d) 100 — Incorrect; this counts all two-digit pairs including zero and repetition.