CAT 2024 - Slot 3 Quant Question 21
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CAT 2024 Slot 3 - Quant
We need to consider single-digit, two-digit and three-digit numbers
Single digit: There are only nine numbers for a single-digit number (not including zero since we are looking for positive integers only)
Double digits: The ten's digit can be chosen in 9 ways (not including 0), and the unit digit can be chosen in 9 ways (including 0 but excluding the digit used in the ten's place). Hence, a total of 81 numbers.
Three-digit: The hundred's digit can be 1, 2, 3 or 4; hence, there are four options for the hundred's digit; for the ten's digit, there will be 9 options (numbers from 0 to 9 except the one chosen in the hundred's place); for unit's digit there would be 8 options. Hence, a total of 288 numbers
Giving the total numbers as 288 + 81 + 9 = 378