Question

How many numbers from 1 to 100 are there each of which is not only exactly divisible by 4 but also has 4 as a digit
a)7
b)10
c)20
d)12

Answer 1

Hint: Take the number in range of 1 - 100 and get the multiples of 4. Now By all these numbers find the numbers which have digit 4 in them. Make a separate list of these numbers. Now find the number of elements in the list This number is the required result in the given question.

Complete step by step answer:
Given in question, the statement we need to solve: The number of numbers in range 1 to 100 divisible by 4 and has one of their digits being equal to the value 4. The multiples of 4 in range 1-10 are given by:
4 ,8
The multiples of 4 in range 11-20 are given by:
12,16,20
The multiples of 4 in range 21-30 are given by:
24,28
The multiples of 4 in range 31-40 are given by:
32,36,40
The multiples of 4 in range 41-50 are given by:
44,48
The multiples of 4 in range 51-60 are given by:
52,56,60
The multiples of 4 in range 61-70 are given by:
64,68
The multiples of 4 in range 71-80 are given by:
72,76,80
The multiples of 4 in range 81-90 are given by:
84,88
The multiples of 4 in range 91-100 are given by:
92,96,100
The total list of multiple of 4 be named as L.
By representing L mathematically, we set the equation in the form of:
L= {4,8, 12, 16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100}
By taking numbers with digit 4 we make a list M.
By representing the list M mathematically, we get it in the form of:
M= {4,24,40,44,48,64 and 84}
The number of numbers in the above set are 7.
So, number of numbers not only divisible by 4 but also have a digit as 4 in range 1-100 are 7

So, the correct answer is “Option A”.

Note: Be careful do not miss any of multiples As 4×25=100. There must be 25 teams in the list L. Use this for verification. If you miss any your answer might go wrong. Students generally forget to count 4 as it is the first one. So, Don’t forget any term.