Data Sufficiency

on this problem, it's impossible to compute the actual value of p in the given timeframe. but, fortunately, you don't have to!
remember that data sufficiency isn't about solving the problem -- it's about determining whether there's only one solution, or more than one..

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(2) must be sufficient, as there is clearly some fixed number of primes between 1 and 3912. i.e., if you had all the time in the world and counted all the primes, you'd get ... a number.
one number.
we don't care what that number is, because it's clear that the number is unique -- there are exactly so-and-so-many primes in that range, and that's that.

(1) also sufficient.
p is a prime number, so:
if p is the 100th prime, then there are 100 primes - viz., the first 100 primes - between 1 and p + 1.
if p is the 101th prime or later, then there are 101 or more primes, so that's no good.
if p is the 99th prime or earlier, then there are 99 or fewer primes; also no good.
therefore, p is the 100th prime.
again, you don't have to determine the value of p (i.e., there's no reason to bother figuring the actual value of the 100th prime number!) it's good enough to know that p has one value.

by the way, this is a very good problem for testing your understanding of data sufficiency in general.
it should be a very fast problem, because you don't have to (and, in fact, can't) actually calculate the solution -- you just have to think about the fact that there's only going to be one value.

if you are worried about timing here, then you may be overly concerned with calculation, and/or you may not have gotten entirely accustomed to data sufficiency yet.