Question

Odd number between 150 and 350 are divisible by neither 9 nor 11

Answer 1

Please see the attachment

Answer 2

81 Odd numbers between 150 and 350 are neither divisible by 9 nor 11

Given:

Odd number between 150 and 350

To Find:

Count of Odd number between 150 and 350 which are neither divisible by 9 nor 11

Solution:

Formula for nth term in a AP

aₙ = a + (n - 1)d

aₙ = nth term

a = first term

n = number of terms

d = common difference

Odd number between 150 and 350

151 , 153 , ...      , 349

This is an AP with a = 151 , d = 2 , aₙ = 349

349 = 151 + (n - 1)2

=> 198 = (n - 1)2

=> 99 = n - 1

=> n = 100

Odd number divisible by 9 between 150 and 350

153 , 171 , ... . 333

This is an AP with a = 153 , d = 18 , aₙ = 333

333 = 153 + (n - 1)18

=> n = 11

Odd number divisible by 11 between 150 and 350

165 , 187 , ... . 341

This is an AP with a = 165 , d = 22 , aₙ = 341

341 = 165 + (n - 1)22

=> n = 9

Odd number divisible by both 9 and 11 => divisible b 99 between 150 and 350 is only 297  hence 1

So Odd number between 150 and 350 which are neither divisible by 9 nor 11

=  odd numbers - Divisible by 9 - divisible by 11 +  Divisible by 99( 9 & 11 both)

= 100 - 11 - 9  + 1

= 81

81 Odd numbers between 150 and 350 are neither divisible by 9 nor 11

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