(51 + 52 + 53 + .........+100) is equal to 

Any number which can be expressed as a fraction of two integers like P & Q as P/Q where Q is not equal to zero.

Every integer is a rational number since Q can be 1.

Hence, in the given options, 4 can be expressed as a simple fraction as 4/1. And all other options cannot be expressed as fractions.

Hence, 4 is a rational number in the given options.

The mutiplicative inverse of a number is nothing but a reciprocal of a number.

Now, the product of a number and its multiplicative inverse is always equal to 1.

For example :

Let the number be 15

Multiplicative inverse of 15 = 1/15

The product of a number and its multiplicative inverse is = 15 x 1/15 = 1.

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

Factors of 5 are 1, 5

Factors of 11 are 1, 11

Factors of 21 are 1, 3, 7, 21

Factors of 37 are 1, 37.

Hence, according to the definition of a prime number, 21 is not a prime number as it has more than two factors.

Let the three consecutive odd numbers be x, x+2, x+4

Then,

x + x + 2 + x + 4 = 93

=> 3x + 6 = 93

=> 3x = 87

=> x = 29 => 29, 31, 33 are three consecutive odd numbers.

Therefore, the middle number is 31.