How many numbers are there between 1 to 200 which are divisible by 3 but not by 7?
57
Step 1 — Count multiples of 3 up to 200:
\(\left\lfloor \dfrac{200}{3} \right\rfloor = 66\)
Step 2 — Count multiples of both 3 and 7, i.e. multiples of 21:
\(\left\lfloor \dfrac{200}{21} \right\rfloor = 9\)
Step 3 — Subtract:
\(66 - 9 = 57\)
Therefore, 57 numbers between 1 and 200 are divisible by 3 but not by 7.
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Important Questions from Integers
How many three digit whole numbers are there between 75 and 405?
Find the number of integers between $1$ and $150$ (inclusive) having $7$ as one of the digits but which are not divisible by $7$.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Consider the following statements :
1. The sum of 5 consecutive integers can be 100.
2 The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
