Civil Services Prep

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?

  1. 72
  2. 81
  3. 90
  4. 100

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.
  1. X receives three coins of different denominations : 1, 2, 5, 10 and 20. If the total amount received by X is…
  2. For two distinct real numbers x and y, which of them is bigger? Statement I : x^2 Statement II : y
  3. If x and y are integers, then is x even? Statement I : x^2 y^2 is even. Statement II : 1 + x^2 + y^2 is odd.
  4. X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the…
  5. If x, y and z are integers, each greater than 1, then is x a prime number? Statement I : xy^2 = 116 Statement…
  6. Which of the following conclusions are valid? 1. Seven Sanskriti Angans, representing different regions of…