Permutation and CombinationHard
Question
How many divisors of 21600 are divisible by 10 but not by 15?
Options
A.10
B.30
C.40
D.none
Solution
Here 21600 = 25. 33. 52
(2 × 5) × 24 × 33 × 51
Now numbers which are divisible by 10
= (4 + 1)(3 + 1)(1 + 1) = 40
(2 × 3 × 5) × (24 × 32 × 51) now numbers which are
divisible by both 10 and 15
= (4 + 1)(2 + 1)(1 + 1) = 30
So the numbers which are divisible by only 40 - 30 = 10
(2 × 5) × 24 × 33 × 51
Now numbers which are divisible by 10
= (4 + 1)(3 + 1)(1 + 1) = 40
(2 × 3 × 5) × (24 × 32 × 51) now numbers which are
divisible by both 10 and 15
= (4 + 1)(2 + 1)(1 + 1) = 30
So the numbers which are divisible by only 40 - 30 = 10
Create a free account to view solution
View Solution FreeMore Permutation and Combination Questions
All the five digits number in which each successive digit exceeds its predecessor are arranged in the increasing order o...How many 6 digit different number can formed with help of the digits of numbers 121 and 202?...How many 5 digit odd numbers can be formed with the help of digits 0,2,3,4 and 6 (Rept. not allowed) ?...If 28C2r : 24C2 r-4 = 225:11 then the value of r is-...A shelf contains 20 books, of which 4 are single volume and the others are 8,5 and 3 volumes respectively. In how many w...