How many numbers between 100 and 300 are divi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To find the number of integers between $100$ and $300$ divisible by $11$,we identify the first and last multiples of $11$ in this range.The first

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(A) To find the number of integers between $100$ and $300$ divisible by $11$,we identify the first and last multiples of $11$ in this range.The first multiple of $11$ greater than $100$ is $110$ $(11 	imes 10)$.The last multiple of $11$ less than $300$ is $286$ $(11 	imes 26)$.This forms an arithmetic progression: $110, 121, 132, \dots, 286$.Using the formula for the $n^{th}$ term of an arithmetic progression: $a_n = a + (n - 1)d$,where $a = 110$,$d = 11$,and $a_n = 286$.$286 = 110 + (n - 1)11$$176 = (n - 1)11$$n - 1 = 16$$n = 17$.Alternatively,the number of multiples of $k$ up to $N$ is given by $\lfloor N/k floor$.The number of multiples of $11$ up to $300$ is $\lfloor 300/11 floor = 27$.The number of multiples of $11$ up to $100$ is $\lfloor 100/11 floor = 9$.The number of multiples between $100$ and $300$ is $27 - 9 = 18$.

How many numbers between $100$ and $300$ are divisible by $11$?

Similar Questions

$\sqrt[3]{6 \frac{35}{216}}$ is equal to........

In a college,$\frac{1}{5}$ of the girls and $\frac{1}{8}$ of the boys took part in a social camp. The fraction of the total students in the college who took part in the camp is:

The sum of three numbers is $68$. If the ratio between the first and second is $2:3$ and that between the second and third is $5:3$,then the second number is

The sum of the digits of a two-digit number is $8$. If the digits are reversed,the number is increased by $54$. Find the number.

$21.9 \%$ of $(511.987 - 42.49) = \frac{?}{5.5}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module