How many numbers between 500 and 700 are divisible by 11?

Correct option is B

Given:

We need to find how many numbers between 500 and 700 are divisible by 11.

Concept Used:

A number is divisible by 11 if it is a multiple of 11.
The numbers in the given range form an arithmetic sequence with:

First term a= smallest multiple of 11 in the range

Last term l= largest multiple of 11 in the range

Common difference d=11

The formula for the number of terms in an arithmetic sequence is:

​$$n = \frac{l - a}{d} + 1$$​​

Solution:

The smallest multiple of 11 ≥ 500 is:

​$$\frac{500}{11} \approx 45.45$$​​

The next whole number is 46, so:

​$$46 \times 11 = 506$$​​

The largest multiple of 11 ≤ 700 is:

​$$\frac{700}{11} \approx 63.63$$​​

The whole number part is 63, so:

63×11=693

n =$$\frac{693 - 506}{11} + 1$$​​

=$$\frac{187}{11} + 1$$​​

= 17 + 1 = 18

Option (B) is right.