Numbers 1 to 1000 which are divisible by 60 but not by 24 is

Question

Numbers 1 to 1000 which are divisible by 60 but not by 24 is (A) 16 (B) 41 (C) 8 (D) 12

Tardigrade Admin · Accepted Answer

Let n(A)= Number of divisible by 60 =(60,120, ldots . ., 960)=16 n(B)= Number of divisible by 24=(24,48 m ldots ., 984) =41 n(A ∩ B)= Number divisible by both =120+240+ ldots .+960=8 Hence, n(A ∩ barB)=n(A)-n(A ∩ B) =16-8=8

Q. Numbers $1$ to $1000$ which are divisible by $60$ but not by $24$ is

16

41

8

12

Let $n (A) =$ Number of divisible by 60
$= (60, 120, \dots .., 960) = 16$
$n (B) =$ Number of divisible by $24 = (24, 48 m \dots ., 984)$
$= 41$
$n (A \cap B) =$ Number divisible by both
$= 120 + 240 + \dots . + 960 = 8$
Hence, $n (A \cap \overset{ˉ}{B}) = n (A) - n (A \cap B)$
$= 16 - 8 = 8$

Q. Numbers 1 to 1000 which are divisible by 60 but not by 24 is

16

41

8

12

Let n(A)= Number of divisible by 60 =(60,120,…..,960)=16 n(B)= Number of divisible by 24=(24,48m….,984) =41 n(A∩B)= Number divisible by both =120+240+….+960=8 Hence, n(A∩Bˉ)=n(A)−n(A∩B) =16−8=8

Q. Numbers $1$ to $1000$ which are divisible by $60$ but not by $24$ is

Let $n (A) =$ Number of divisible by 60
$= (60, 120, \dots .., 960) = 16$
$n (B) =$ Number of divisible by $24 = (24, 48 m \dots ., 984)$
$= 41$
$n (A \cap B) =$ Number divisible by both
$= 120 + 240 + \dots . + 960 = 8$
Hence, $n (A \cap \overset{ˉ}{B}) = n (A) - n (A \cap B)$
$= 16 - 8 = 8$