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prime numbers

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by parulmahajan89 » Wed Jan 29, 2014 8:48 pm
If P is a prime number greater than 2,what is the value of p?

1) There are total of 100 prime numbers between 1 and p+1
2) There are total of p prime numbers between 1 and 3912

How to approach this problem?
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Source: — Data Sufficiency |
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by sanju09 » Wed Jan 29, 2014 11:00 pm
parulmahajan89 wrote:If P is a prime number greater than 2,what is the value of p?

1) There are total of 100 prime numbers between 1 and p+1
2) There are total of p prime numbers between 1 and 3912

How to approach this problem?
Shear waste of time if we try to figure out what p is actually equal to. Thankfully this strange question appeared on DS, where sufficiency matters more than anything.

(1) If there are total of 100 prime numbers between 1 and p+1, then p must be the 100th prime, which can be caught if we take all the necessary baby steps not required here. [spoiler]Sufficient[/spoiler]

(2) If there are total of p prime numbers between 1 and 3912, then since 3912 is a known quantity, p can be caught if we take all the necessary baby steps not required here. [spoiler]Sufficient

Pick D[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



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by Matt@VeritasPrep » Mon Feb 03, 2014 4:39 pm
parulmahajan89 wrote:If P is a prime number greater than 2,what is the value of p?

1) There are total of 100 prime numbers between 1 and p+1
2) There are total of p prime numbers between 1 and 3912

How to approach this problem?
I'd approach it by remembering that DS doesn't require me to ACTUALLY answer the question, just to state whether I COULD answer the question if I had the time and the desire to do so.

Given Statement 1 and a table of primes, I could tell you exactly what the 100th prime is. (Just looked it up: it's 541.) So we let (p + 1) equal 542 and discover that there are exactly 100 prime numbers between 1 and 542: SUFFICIENT. (If we used any higher integers, they either wouldn't be equal to a prime plus 1 or they'd have an additional prime between themselves and 1.)

Given Statement 2 and a (larger) table of primes, I could tell you how many primes there are between 1 and 3912. That number would be p, and we'd be done: SUFFICIENT again!

This is a dream question to see on the test: once you get past the initial "What the heck!?" reaction, you can solve it pretty quickly without having to find any numbers at all.
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