How many numbers from 1 to 1000 are divisible by 60 but not by 24?

Question

How many numbers from 1 to 1000 are divisible by 60 but not by 24? (A) 8 (B) 12 (C) 16 (D) 24

Tardigrade Admin · Accepted Answer

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

Q. How many numbers from 1 to 1000 are divisible by 60 but not by 24?

8

12

16

24

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

Q. How many numbers from 1 to 1000 are divisible by 60 but not by 24?

8

12

16

24

Let n(A)= number divisible by 60=60+120+......+960=16 n(B)= number divisible by 24=24+48+ +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

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