Question

How many $2$ - digit positive integers are divisible by $4$ or $9$?

• A. $32$
• B. $22$
• C. $30$
• D. $34$
• E. $10$
• F. $15$

Answer 1

The correct option is C $30$

Series for the required condition:

$12,16,20,....96$

Two digit positive integers divisible by $4$ are

$96=12+(n-1)4$

$\Rightarrow n=22$

Series for two digits divisible by $9$ is

$18,27,....,99$

Two digit positive integers divisible by $9$

$99=18+(m-1)9$

$\Rightarrow m=10$

Number divisible by both $4$ and $9$

$=2$ i.e. $36,72$

Total numbers $=22+10-2=30$