Explanation:
did you write all requests without any typos or missing anything ?
I am going to answer what you wrote :
how many numbers between 11 and 60 ?
I assume we mean natural numbers, right ?
how many between 11 and 12 ? right, 0.
how many between 11 and 13 ? right, 1 (12).
and so on.
you notice a pattern ?
it is : high number - low number - 1
so, for 11 and 60 we get
60 - 11 - 1 = 48
there are 48 numbers between 11 and 60.
how many odd (uneven) numbers are between 11 and 60 ?
again, how many between 11 and 12 ? 0.
between 11 and 13 ? 0 (12 is not odd).
between 11 and 14 ? 1 (13).
between 11 and 15 ? 1 (13).
between 11 and 16 ? 2 (13, 15)
between 11 and 20 ? 4 (13, 15, 17, 19)
you see the pattern here ? it is
(high number - low number - 1)/2
so, for 11 and 60 we get
(60 - 11 - 1)/2 = 48/2 = 24
there are 24 odd numbers between 11 and 60.
if that division leads to a fraction, we need to round down to the next natural number.
e.g. between 11 and 59 there are
(59 - 11 - 1)/2 = 47/2 = 23.5 rounded down is 23. as between 11 and 59 there are only 23 odd numbers.
how many perfect square numbers between 11 and 60 ?
1² = 1 no.
2² = 4 no.
3² = 9 no.
4² = 16 yes.
5² = 25 yes.
6² = 36 yes.
7² = 49 yes.
8² = 64 no.
9² and any other larger numbers squared are too large.
so, we have 4 perfect square numbers between 11 and 60 (16, 25, 36, 49).
how many prime numbers less than 20 between 11 and 60 ?
next number after 11 : 12 (not a prime number, divisible by 2, 3, ...).
next number : 13 (yes, prime number).
next number : 14 (not a prime number, divisible by 2, 7).
next number : 15 (not a prime number, divisible by 3, 5).
next number : 16 (not a prime number, divisible by 2, 4, ...)
next number : 17 (yes, prime number).
next number : 18 (not a prime number, divisible by 2, 3 ...)
next number : 19 (yes, prime number)
done.
there are 3 prime numbers less than 20 between 11 and 60.