How many numbers between 100 and 300 are divi | vedclass

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(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

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$18$

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(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 $11$?

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