NP Guide (3rd Ed) - Divisibility & Primes Advanced (pg. 117

[bensonhua]

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 n and 1 < n < x.

The answer is A / 1 only....

I thought this was insufficient as there are a bunch of prime number between 2 and 50? how could you know which one since it could be any of them?

[venkat_yj]

Pl read the question carefully.

(1) is referring to 50 prime numbers between 2 and x; not the number 50. So if you start writing the prime-number sequence starting 2, the value of the 50th prime number is x.

[Ben Ku]

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.

Statement (1) is NOT saying "x is a prime number between 2 and 50." (which is I believe how you interpreted it). Instead, it is saying "between 2 and x, there are 50 prime numbers." What that means is that x is a prime number between the 50th and 51st prime number, including the 50th. If P50 represents the 50th prime number, and P51 represents the 51st prime number, then

P50 <= x < P51

The only prime number in that interval is P50. So (1) is sufficient.