Correct Answer: 71

Solution : The numbers that are divisible by both 2 and 7 = 2 × 7 = 14
The smallest number divisible by 14 = 14
The largest number divisible by 14 = 994 (nearest to 1000)
Let the required number be $n$.
Now, $a_n=a+(n-1)d$, where $a_n$ = last term, $a$ = first term $d$ is the common difference.
⇒ $994=14+(n-1)14$
⇒ $984=14+14n-14$
⇒ $984=14n$
$\therefore n=71$
Hence, the correct answer is 71.