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If p is a prime number greater

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If p is a prime number greater

by REINE » Wed Mar 22, 2017 12:02 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

A. Statement 1 alone is sufficient
B. Statement 2 alone is sufficient
C. Both statements are sufficient together but not alone
D. Each statement is sufficient alone
E. Both statement are not sufficient together
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Mar 22, 2017 7:53 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 ceilidh.erickson » Wed Mar 22, 2017 9:53 am
It's worth remembering: with DS, you don't have to come up with the answer to the question yourself! You just need to determine whether the question is answerable at all... perhaps answerable by someone with a calculator.

So on this question, if you were thinking "I don't know the answer to what the 100th prime number is, so I don't know what p is" you're in good company - neither do I! I know the first 20 or so primes, but I don't have any reason to memorize primes beyond that. But a quick google search would yield one and only one answer for the value of p, so that's sufficient!

Here's an example of a similar idea: you can't get the actual answer without a calculator, but you know that it's answerable. This is #240 in OG 2017:
What is the cube root of w ?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.
Also Reine, CITE YOUR SOURCE for the questions you post! It's a copyright violation to post questions without citing the author.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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