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GMAT Prep test: Need Explanation for Point 1.

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by tanvis1120 » Tue Aug 05, 2014 10:51 am
If p is a prime number greater than 2, what is the value of P.
1. There are total 100 prime numbers between 1 and p+1.
2. there are total p prime numbers between 1 and 3912.

Now, my answer is B.
I could not solve it for the first option.
Could anyone please explain?

Option1: Total numbers between 1 and p+1 = {(P+1)-1}+1 = p+1
There are 100 prime numbers and p+1-100 composite numbers.
How do we find P from 1st option?
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by Brent@GMATPrepNow » Tue Aug 05, 2014 11:06 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

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Brent
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by GMATinsight » Wed Aug 06, 2014 6:57 pm
tanvis1120 wrote:If p is a prime number greater than 2, what is the value of P.
1. There are total 100 prime numbers between 1 and p+1.
2. there are total p prime numbers between 1 and 3912.

Now, my answer is B.
I could not solve it for the first option.
Could anyone please explain?

Option1: Total numbers between 1 and p+1 = {(P+1)-1}+1 = p+1
There are 100 prime numbers and p+1-100 composite numbers.
How do we find P from 1st option?
POINT TO KEEP IN MIND : You don't have to find the VALUE OF P instead you only have to check whether given information in statement is sufficient to answer the question or not.

Statement 1) There are a total of 100 prime numbers between 1 and p+1.
Which only refers that we will will count first 100 prime number (Which we can if we want to) and (the value of last Prime number+1) will be same as the value of (P+1)
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