Question

The number of numbers lying between $100$ and $500$ that are divisible by $7$ but not by $21$ is

• A. 57
• B. 19
• C. 38
• D. None of these

Answer 1

Answer: (C)

The numbers between $100$ and $500$ that are divisible by
$7$ are $105,112,119,126,133,140,147,\dots ,483,490,497.$
Let such numbers be $n$.
Then, $497=105+(n-1)\times 7$;
or $n=57$.
The numbers between $100$ and $500$ that are divisible by
$21$ are $105,126,147,\dots ,483$.
Let such numbers be $m$.
Then $483=105+(m-1)\times 21$;
or $m=19$.
Hence, the required number $=n-m$
$=57-19=38$.