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How many numbers are there between 101 and 999, which are divisible by both 2 and 5?

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100

answer is B.

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Detailed Solution

Given numbers are 101 and 999.
Since the numbers which are divisible by both 2 and 5 are divisible by 10 also, so the numbers between 101 and 999 which are divisible by 10 are

110, 120, 130, …, 990.

Let first term

a 1

= 110, second term

a 2

= 120 and third term

a 3

=130

∴ d = a 2 − a 1 d = 120 − 110 ⇒ d = 10 Again, d = a 3 − a 2 d = 130 − 120 d = 10

As the value of d is same, these number are in A.P.
Let the A.P. contain n terms:

∴ a n = 990

Formula for the

n t h

term:

a n = a + n − 1 × d

Applying the formula for nth term of A.P.:

∴ 110 + (n − 1) × 10 = 990 ⇒ 110 + 10 n − 10 = 990

⇒ 10 n = 990 − 100 ⇒ n = 89010 ⇒ n = 89

Therefore, there are 89 numbers between 101 and 999 which are divisible by both 2 and 5.
Hence, option (2) is correct.

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