iil-london wrote:
If p is a prime number greater than 2, what is the value of p ?
(1) There are a total of 100 prime numbers between 1 and p+1
(2) There are a total of p prime numbers between 1 and 3912
Thanks.
wow, this question really showed up on the gmatprep? if so, it's unprecedented: it's honestly the first question i've ever seen on which it's simply
impossible to compute the actual answer choice within the time limit without an absurdly prodigious amount of memorized knowledge (here, knowledge about prime numbers).
there are many, many official problems on which you don't
have to solve for a quantity - and in which solving for the quantity would certainly waste time - but, in all those problems, you
can solve for the quantity well within the 2-minute guideline if you know what you're doing.
--
in any case:
(2) must be sufficient, as there is obviously
some fixed number of primes between 1 and 3912. we don't care what that number is, because it's clear that there's only one such number (the number of primes in a fixed range isn't about to change anytime soon).
(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.
answer = d
incidentally, the actual value of p is 541.