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Question
How many numbers are there between 101 and 999, which are divisible by both 2 and 5?
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Solution
The numbers which are divisible by both 2 and 5 are divisible by 10 also. Now, the numbers between 101 and 999 which are divisible 10 are 110, 120, 130, .., 990. Clearly, these number are in AP
Here, a = 110 and d = 120 - 110 = 10
Let this AP contains n terms. Then,
an = 990
⇒ 110+(n-1) × 10 = 990 [an = a+ (n-1) d]
⇒ 10n + 100 =990
⇒ 10n = 990 -100 = 890
⇒ n =89
Hence, there are 89 numbers between 101 and 999 which are divisible by both 2 and 5.
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