Question : How many numbers are there between 1 and 200 which are divisible by 3 but not by 7?
Option 1: 38
Option 2: 45
Option 3: 57
Option 4: 66
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Correct Answer: 57
Solution :
The numbers from 1 to 200 which are multiple of 3 are 3,6,9,...,198.
The total number of multiples of 3 = $\frac{198 - 3 }{3}$ + 1 = 66
LCM of 3 and 7 is 21.
The numbers from 1 to 200 which are multiples of 21 are 21, 42,...,189.
The total number of multiples of 21 = $\frac{189 - 21}{21}$ + 1 = 9
The total numbers between 1 and 200 which are divisible by 3 but not by 7 = 66 – 9 = 57
Hence, the correct answer is 57.
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