Prime # question- GMATPrep

anks17 wrote:Though, could solve it but would like to know what will be the strategy adopted by Geniuses out there.Kindly share.

This question is testing what you know about primes and counting.

Statement 1 talks about 100 primes between 1 and p+1. Since we know that p+1 is not a prime, and we can find the 98 primes between 2 and p, we can just keep on finding the primes, till we get to the 99th one after finding 2. Sufficient.

Statement 2 talks about p primes between 1 and 3912. Again, we can find all the primes starting with 2,3,5,..all the way upto the last prime less than 3912. The number of primes that we would count would equal p. again, sufficient.

Hence D is correct.

can somebody pls elaborate on statement 1 here??

mehaksal wrote:can somebody pls elaborate on statement 1 here??

Well Statement 1 says that there are 100 primes between 1 and p+1.

2 is a prime number and the question states that p is a prime number.

So therefore we need to find the rest of the 98 prime numbers between 1 and p+1. The set of 100 primes between 1 and p+1 is defined. There can be no other values which can contradict or make the statement insufficient. So by counting, we can find the set. All we need to know if we can do the same and we can. Hence the statement is sufficient.


It's the same with Statement 2. The set is defined as p primes between 1 and 3192. If we count, we will be able to find p. The statement is sufficient.

The idea is that we do not necessarily need to solve for p. We just need to confirm that the statement is sufficient and there can be no contradictions to the statement.


I hope that helps.

Regards
Anup

eagleeye wrote:
Statement 1 talks about 100 primes between 1 and p+1. Since we know that p+1 is not a prime, and we can find the 98 primes between 2 and p, we can just keep on finding the primes, till we get to the 99th one after finding 2. Sufficient.

here I disagree with you. actually, the q.stem states that 100 primes BETWEEN 1 and p+1(NOT INCLUSIVE!). So, 2 is the 1st prime and the 100th term(not 99th) will be p.

of course, in this q. this point doesnt matter much, but in other questions it could be crucial.