# The total number of positive integers not exceeding 1000 that are divisible by 7 or 11 is

Solution:   Let A and B denotes the sets of positive integers not

Exceeding 1000 that are divisible by 7 and 11 respectively .

Now ,    $n(A)=[\frac{1000}{7}]=142;n(B)=[\frac{1000}{11}]=90$

$\Rightarrow$            $n(A\cap B)=[\frac{1000}{7\times 11}]=12.$

$\therefore$             $n(A\cup B)=n(A)+n(B)-n(A\cap B)=142+90-12=220.$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
##### Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-