Question

how many three digit numbers which are neither divisible by 4 nor
5 is​

Answer 1

540  three digit numbers are neither divisible by 4 nor  5

Step-by-step explanation:

Number divisible by 4

from 100 to 999

are 100 , 104 ,............................ 996

= 225 numbers

Number divisible by 5

from 100 to 999

are 100 , 105 ,............................ 995

= 180 numbers

but these both contains number divisible by 20

Number divisible by 20

from 100 to 999

are 100 , 105 ,............................ 980

= 45 numbers

Number Divisible by either 4 or 5

= 225 + 180 - 45

= 360

Number neither divisible by  4 or 5

= 900 - 360

= 540

540  three digit numbers are neither divisible by 4 nor  5

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Answer 2

The three digits numbers which are neither divisible by 4 nor 5=540

Step-by-step explanation:

Three digit numbers are

100,101,102,.....,999

Three digits number divisible by 4

100,104, ....996

$a=100$

$d=104-100=4$

When the difference between two consecutive terms is constant then the sequence is  in A.P

Given terms in A.P

$a_n=a+(n-1)d$

Substitute the values

$996=100+(n-1)4$

$996-100=4(n-1)$

$\frac{896}{4}=n-1$

$224=n-1$

$n=224+1=225$

The three digit number divisible by 4=225

Three digits number is divisible by 5

100,105,....995

d=105-100=5

The difference between two consecutive term is constant

Therefore, it forms an A.P

$995=100+(n-1)5$

$995-100=5(n-1)$

$\frac{895}{5}=n-1$

$179=n-1$

$n=179+1=180$

The three digits number is divisible by 4 and 5 are

100,120,140,....980

d=120-100=20

The difference between two consecutive terms is constant

Therefore, it forms an A.P

$980=100+(n-1)(20)$

$980-100=20(n-1)$

$880=20(n-1)$

$\frac{880}{20}=n-1$

$44=n-1$

$n=44+1=45$

Total three digits number=900

The three digits numbers which are neither divisible by 4 nor 5=900-(225+180-45)=540

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