Question

How many even integers n, where $100\le n\le 200$, are divisible neither by seven nor by nine?

• A. $40$
• B. $37$
• C. $39$
• D. $38$

Answer 1

The correct option is C $39$

Even no$:$ divisible by $7$ will be $112,\mathrm{126...},196$

$196=112+(n-1)\times 14$

$\frac{84}{14}=n-1\Rightarrow n=7.$

Even no$:$ divisible by $9$ will be $108,126,...,198$

$198=108+(n-1)\times 18$

$\frac{90}{18}=n-1\Rightarrow n=6$

Even no$:$ divisible by $9$ or $7=7+6-1=12.$

Hence total no$:$ which is not divisible by $9$ 0r $7=51-12=39.$