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
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