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Prime Numbers

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by GMATGuruNY » Sun Jan 05, 2014 3:55 am
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
Statement 1: There are a total of 100 prime numbers between 1 and p+1
1, 2, 3, 5....p, p+1.
The values in red constitute the prime numbers between 1 and p+1.
Since there are a total of 100 prime numbers between 1 and p+1, p must be the 100th prime number.
Thus, the value of p can be determined.
SUFFICIENT.

Statement 2: There are a total of p prime numbers between 1 and 3912
Here, we can determine the value of p simply by counting the number of prime numbers between 1 and 3912.
SUFFICIENT.

The correct answer is D.
Last edited by GMATGuruNY on Tue Apr 01, 2014 3:04 am, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Jan 05, 2014 7:28 am

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.
Target question: What is the value of p?

Statement 1: There are a total of 100 prime numbers between 1 and p+1
In other words, p is the 100th prime number.
So, if we begin listing primes (2,3, 5, 7, 11, 13,..), the 100th prime on our list will equal p.
Since we could use statement 1 to definitively determine the value of p, statement 1 is SUFFICIENT

Statement 2: There are a total of p prime numbers between 1 and 3912.
Well, we could list every prime number between 1 and 3912, and then count how many primes are in the list. This would give us the value of p.
Since we could use statement 2 to definitively determine the value of p, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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