professor wrote the following inequalities for N number of students in his lecture. N <10, N>10, N<22, N>22. Turns out only one statement is correct. How many students were in his lecture​

There are N students in the class.

We know that ONLY ONE of the inequalities is true:

N < 10

N > 10

N < 22

N > 22

We want only one of these four inequalities to be true.

Remember that if we have:

x > y

y is not a solution, because:

y > y is false.

Then:

If we take N = 10, then:

N < 22

Is the only true option.

While if we take N = 22

N > 10

is the only true option.

So there are two possible values of N.