Find the number of integers between 100 and 1000 that are

(i) divisible by 7

(ii) not divisible by 7

Solutions

Expert Solution

(i) We have to find out the number of integers between 100 and 1000 that are divisible by 7 and the number of terms that are not divisible by 7.

We can see that every consecutive number that is divisible by 7 has a common difference of 7. So, all the numbers that we will get between 100 and 1000 that are divisible by 7 will form an AP.

The next number after 100 which is divisible by 7 is 105.

The largest three-digit number divisible by 7 :

1000÷7 has 6 as remainder.

1000-6 = 994

So nth term of AP = 994

First term = 105

Common difference, d = 7

a+(n-1)d = an

=> 105+(n-1)7 = 994

=> n-1 = (994-105)/7

= 127

=> n = 128

Hence there are 128 integers which are divisible by 7.

(ii) There are 899 numbers between 100 and 1000.

128 integers are divisible by 7.

Number of integers which are not divisible by 7 = 899-128 = 771.

• 128 integers are divisible by 7.

• 771 integers are not divisible by 7.

Nikhil Thakur answered 1 year ago

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