GMAT Prep Prime Number

caramel3536 · Posted: Sat Jul 19, 2008 9:21 am Post subject: GMAT Prep Prime Number

If p is a prime numer greater than 2, what is the value of p/
(1) There are a total of 100 prims btwn 1 and p+1
(2) There are a total of p prime number between 1 and 3912

Ans = D

VP_Tatiana · Posted: Sun Jul 20, 2008 2:16 pm Post subject:

From statement 1, we can see that p must equal the 100th prime number. The range from 1 to p+1 will then include 100 prime numbers. We can find 1 and only one value of p, since we know p is prime. If we make p any smaller, we don't get 100 prime numbers in the range. If we make p any bigger, it has to be the next prime number, and then we will have 101 prime numbers in the range. Thus, statement 1 is sufficient.

From statement 2, we have a defined range. It is thus possible (though it will take a long time) to count all of the prime numbers in that range. That will give us a definite value for p, so statement 2 is sufficient.

Since both statements are sufficient, the answer is D.