Question

How many natural numbers are there between $23$ and $100$ which are exactly divisible by $24$?

• A. $8$
• B. $11$
• C. $12$
• D. $13$
• E. None of these

Answer 1

Answer: (D)

$13$

Required numbers are $24,30,36,40,.....96$
This is an A.P. in which $a=24,d=6,l=96$
Let the number of terms in it be $n$.
Then $t_n=96$ $\Rightarrow$ $a+(n-1)d=96$
$\Rightarrow$ $24+(n-1)\times 6=96$
$\Rightarrow$ $(n-1)=12$
$\Rightarrow$ $n=13$
Required number of numbers $=13$