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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 an  = 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 an = 990.
Substitute the value of a, d, and an in an = a + (n – 1) d.
990=110+(n−1)×10 990=110+10n−10 990=100+10n 10n=990−100 10n=890 n= 890 10 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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Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.