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.
Ron has been teaching various standardized tests for 20 years.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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