Question
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
✓
Answer
For the number to be divisible by both 2 and 5, they have to be divisible by the LCM of 2 and 5 = 10.
The numbers divisible by 10 between 101 and 999
Are 110, 120, 130, ...., 990
Here
$a = 110$
$d = 10$
$a_n = a + (n - 1)d$
$\Rightarrow 990 = 110 + (n - 1)(10)$
$\Rightarrow 990 = 110 + 10n - 10$
$\Rightarrow 890 = 10n$
$\Rightarrow n = 89$
Thus, 89 numbers between 101 and 999 are divisible by both 2 and 5.
The numbers divisible by 10 between 101 and 999
Are 110, 120, 130, ...., 990
Here
$a = 110$
$d = 10$
$a_n = a + (n - 1)d$
$\Rightarrow 990 = 110 + (n - 1)(10)$
$\Rightarrow 990 = 110 + 10n - 10$
$\Rightarrow 890 = 10n$
$\Rightarrow n = 89$
Thus, 89 numbers between 101 and 999 are divisible by both 2 and 5.
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