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Q.

Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.

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a

20

b

50

c

39

d

89

answer is D.

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Detailed Solution

Given that, we need to find numbers that are divisible by both 2 and 5 between 102 and 998.
We know, numbers divisible by both 2 and 5 will be the numbers that are divisible by (2 × 5) = 10.
Therefore, the numbers between 102 and 998 which divisible by 10 or 2 and 5, are 110,120, 130, 140…………….990.
The above sequence forms an AP.
We know that, general term or nth term of A.P is

a_{n}

= a + (n – 1) d, where a is the first term, d is a common difference and n is the number of terms.
Here, first term, a = 110 and common difference, d = 120 - 110 = 10 and last term

a_{n}

= 990.
Substitute the value of a, d, and an in

a_{n}

= a + (n – 1) d.

990 = 110 + (n − 1) × 10 990 = 110 + 10 n − 10 990 = 100 + 10 n 10 n = 990 − 100 10 n = 890 n = 89010 n = 89

Hence, there are 89 natural numbers between 102 and 998 which are divisible by both 2 and 5.
The correct option is (4).

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