How many positive integers from 1 to 100 are not divisible by 2, 3, or 5?
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By inclusion-exclusion: ∣div by 2∣=50, ∣div by 3∣=33, ∣div by 5∣=20, ∣div by 6∣=16, ∣div by 10∣=10, ∣div by 15∣=6, ∣div by 30∣=3. So ∣div by 2, 3, or 5∣=50+33+20−16−10−6+3=74. Answer: 100−74=26.