CAT 2024 Question Paper | Quant Slot 3

CAT Questions

CAT 2024 Quant was dominated by Algebra followed by Arithmetic. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 14 The number of all positive integers up to 500 with non-repeating digits is

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Video Explanation

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Explanatory Answer

Single digit numbers where none of the digits is repeated = 1 to 9
⇒ n(single digit numbers)= 9
Double digit numbers = AB (where A is any number from 1 to 9 and B is any number except A)
⇒ n(double digit numbers) = 9 × 9 = 81
Triple digit numbers = ABC (where A is any number from 1 to 4, B is anything except A and C is anything except A, B)
⇒ n(triple digit numbers) = 4 × 9 × 8 = 288
Total number of numbers = 288 + 81 + 9 = 378

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The question is "The number of all positive integers up to 500 with non-repeating digits is"

Hence, the answer is '378'

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