2 Digits, 5 Divisors

The number of divisors are always in pairs other than for numbers which are in perfect square. Therefore, the number having odd number of divisors could be only perfect squares. Now the possible values are 16, 25, 36, 49, 64, 81.

Now, the square of primes can have only 3 divisors therefore, the remaining numbers are 16, 36, 64, 81.

Now, by checking the number of divisors in these numbers would give us only two values left i.e. 16 & 81

Number of divisors of a number equals the product of multiplicitites+1 of the its prime factors. For example $180 = 2^2\times 3^2\times 5$ , the multiplicities are 2, 2 and 1, the number of divisors of 180 equals $(2+1)\times (2+1)\times (1+1) = 18$ . For our case the product of multiplicities (+1) equals 5, which means we can only have one prime factor, which is set to the power of 4. Only 2 primes to the 4th power are 2 digit numbers` $2^4$ and $3^4$ . The correct answer is 2.