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IPMAT Indore 2023 - QA (MCQ) Q16 Explanation
December 30, 2024
Explanation:
(c)
Number of 3-digits numbers divisible by 3, i.e. multiples of 3
m(3) = [999/3] - [99/3] = [333] - [33] = 333- 33 = 300
Number of 3-digits numbers divisible by 4, i.e. multiples of 4
m(4) = [999/4] - [99/4] = [249.75] - [24.75] = 249- 24 = 225
Number of 3-digits numbers divisible by 12 (LCM of 3 & 4) i.e. multiples of 12
m(12) = [999/12] - [99/12] = [83.25] - [8.25] = 83 - 8 = 75
Total number of 3-digits divisible by 3 or 4 = m(3) + m(4) – m(12)
= 300+ 225 – 75 = 450
So, the number which are neither divisible by 3 nor 4 = 900 - 450 = 450
Required probability = 450 = 1/2 Ans.