The number properties

[nidhis.1408]

If x is a prime number, what is the value of x?
(1) There are a total of 50 prime numbers between 2 and x, inclusive.
(2) There is no integer n such that x is divisible by nand 1 < n < x.

[eagleeye]

We are told that x is a prime number, and we need to find the value of x.
With that in mind, let's look at

(1) There are a total of 50 prime numbers between 2 and x, inclusive.
There are always a finite number of primes between any two numbers, if we start with 2 and count the next 50 primes, we will get to x. Hence this statement is sufficient.

(2) There is no integer n such that x is divisible by n and 1 < n < x.
This statement simply restates the definition of a prime. Since a prime is divisible by itself and 1, and n lies between 1 and x, therefore this definition holds for any prime. Hence this statement is insufficient.

So the right answer is A.

Let me know if this helps