Hi,
The key to this one is recognizing that it's data sufficiency. So, you don't need to know exactly what "p" is - all you need to do is make sure that you could find it if you had to (which you don't, because it's data sufficiency). Basically, we just want to make sure that there is only one possibility for "p".
Statement 1 tells us that there are 100 prime numbers between 1 and p+1. So, if we wanted to, we could count up 100 prime numbers from 1. But we don't have to. This statement gives us an exact value for "p" because we know it's the 100th prime number, whatever that is (but again, we don't need to know exactly what it is).
Statement 2 works the same way. We could count how many prime numbers there are between 1 and 3,912. But, we don't have to - all we need to know is that this gives us an exact value for "p" once again, whatever it is.
This is a tough one because in most data sufficiency problems, there is a way to solve - even if you don't have to. I don't really see a way here unless you actually count all the prime numbers, and that gets a bit tricky once you're into the bigger numbers that people don't normally memorize.
Hope this helps!
Prime #
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Source: Beat The GMAT — Problem Solving |
