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Question 290016
JEE Mathematics · Hard

Permutations and Combinations: Mixed MCQ

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MixedHardQuestion 290016

Question

The number of integers between 1 and 1000 that are divisible by neither 3 nor 5 is:
  1. A
    533
    Correct
  2. B
    466
  3. C
    400
  4. D
    600

Correct answer

533

Explanation

By inclusion-exclusion: divisible by 3 = 333, by 5 = 200, by 15 = 66. Divisible by 3 or 5 = 333+200−66 = 467. Neither = 1000−467 = 533.

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