The answer is correct.

The numbers 10........31 have squares of 3digit .These are 22 numbers.

32......99 have squares of 4 digit.These are 68 numbers.


So we are comparing, 22/68 and 1/3

So the answer is B.

Two-digit integers are 10 - 99
number of two-digit integers whose squares are three-digit numbers: 22 ( that is 10^2 = 100 and 31^2 = 961, the integers between this two numbers will also have 3-digit number as square)


number of two-digit integers whose squares is a four-digit number: 68 (that is 32^2 = 1024 and 99^2 = 9801, the integers between this two numbers will also have 4-digit number as square)
so,$\frac{22}{68} = \frac{11}{34} < \frac{1}{3}$

Option B is answer.

Carcass, If I select 31 and 32, then 31/32=0.96. It is higher than 0.33 (1/3). Why I cannot select 31 and 32?

But you have to consider the constraints above picking numbers not just two numbers