Question : How many natural numbers up to 2001 are divisible by 3 or 4 but NOT by 5?
Option 1: 768
Option 2: 801
Option 3: 934
Option 4: 1067
Correct Answer: 801
Solution :
Numbers which is divisible by 3 or 4 up to 2001 are = $\frac{2001}{3} + \frac{2001}{4} - \frac{2001}{12}$
= 667 + 500 – 166 = 1001
Numbers which are divisible by 3 or 4 but not by 5 up to 2001 are = $1001 - \frac{2001}{15} - \frac{2001}{20} + \frac{2001}{60}$
= 1001 – 133 – 100 + 33
= 801
Hence, the correct answer is 801.
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