Question : Ramu had to select a list of numbers between 1 and 1000 (including both), which are divisible by both 2 and 7. How many such numbers are there?
Option 1: 142
Option 2: 71
Option 3: 97
Option 4: 642
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.
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