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04 Jul 2025, 09:45
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1-600 has 120 multiples of 5.
plus there are 2 way.
the multiple of 5 can be n or n+1
so 240 options
240/600= 2/5
eg. from 1-5. 4 and 5 will work.
from 5-10, 9 and 10 will work and so on.
as long as one of the numbers is a multiple of 5
Same logic
25 has 24 multiples in 1-600.
plus there are 2 way.
the multiple of 25 can be n or n-1
25 or 26
50 or 51.
75 or 76
100 or 101
8 options in each 100 so 8*6=48
48/600= 2/25.
But I feel there is a problem in the question because 601 will not be in the set. we will have only 47 options
and 47/600 is not an option.
plus there are 2 way.
the multiple of 5 can be n or n+1
so 240 options
240/600= 2/5
eg. from 1-5. 4 and 5 will work.
from 5-10, 9 and 10 will work and so on.
as long as one of the numbers is a multiple of 5
Same logic
25 has 24 multiples in 1-600.
plus there are 2 way.
the multiple of 25 can be n or n-1
25 or 26
50 or 51.
75 or 76
100 or 101
8 options in each 100 so 8*6=48
48/600= 2/25.
But I feel there is a problem in the question because 601 will not be in the set. we will have only 47 options
and 47/600 is not an option.
Bunuel
04 Jul 2025, 09:47
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1<=n<=600
2<=n+1<=601
0<=n-1<=599
For probability that n(n + 1) is divisible by 5, we need n to be divisible by 5 or n+1 to be divisible by 5. Both of them together cannot be divisible by 5, so there's no overlap
For 1<=n<=600, we have (600-5)/5+1 = 120
For 2<=n+1<=601, we have (600-5)/5+1 = 120
Total = 240
p=240/600=2/5
For probability that n(n - 1) is divisible by 25, we need n to be divisible by 25 or n+1 to be divisible by 25. Both of them together cannot be divisible by 5 or 25, so there's no overlap
For 1<=n<=600, we have (600-25)/25+1 = 24
For 0<=n-1<=599, we have (575-0)/25+1 = 24
Total = 48
q=48/600=2/25
2<=n+1<=601
0<=n-1<=599
For probability that n(n + 1) is divisible by 5, we need n to be divisible by 5 or n+1 to be divisible by 5. Both of them together cannot be divisible by 5, so there's no overlap
For 1<=n<=600, we have (600-5)/5+1 = 120
For 2<=n+1<=601, we have (600-5)/5+1 = 120
Total = 240
p=240/600=2/5
For probability that n(n - 1) is divisible by 25, we need n to be divisible by 25 or n+1 to be divisible by 25. Both of them together cannot be divisible by 5 or 25, so there's no overlap
For 1<=n<=600, we have (600-25)/25+1 = 24
For 0<=n-1<=599, we have (575-0)/25+1 = 24
Total = 48
q=48/600=2/25
Bunuel
04 Jul 2025, 09:56
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Bunuel
To make it a multiple of 5, either n or n-1 has to be a multiple. So 1...5 we have 2, 6...10, We have 2.
So for every 5 we have 2, So for 600. 2*120/ 600 => 2/5.
Similarly, n or n-1 has to be multiple of 25, So 24*2/600 => 2/25.
Hence IMO p = 2/5, q = 2/25
