For how many integers n where 2≤n≤100 is (n2) odd?

n has to be odd because \(odd^2=odd\)

It cannot be even because \(even^2=even\)

So how many integers from 2 to 100 are odd?

The answer would be 49 integers

All odd numbers between 3 and 99 will be odd when squared. So, you have:

 

[99 - 3] / 2 + 1 =

96 / 2 + 1          =

48 + 1                = 49 numbers whose squares will be odd. Eamples: 3^2=9, 5^2=25, 7^2=49 and so on.