Another number properties (prime numbers)

[iil-london]

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

Thanks.

[RonPurewal]

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

Thanks.

wow, this question really showed up on the gmatprep? if so, it's unprecedented: it's honestly the first question i've ever seen on which it's simply impossible to compute the actual answer choice within the time limit without an absurdly prodigious amount of memorized knowledge (here, knowledge about prime numbers).

there are many, many official problems on which you don't have to solve for a quantity - and in which solving for the quantity would certainly waste time - but, in all those problems, you can solve for the quantity well within the 2-minute guideline if you know what you're doing.

--

in any case:

(2) must be sufficient, as there is obviously some fixed number of primes between 1 and 3912. we don't care what that number is, because it's clear that there's only one such number (the number of primes in a fixed range isn't about to change anytime soon).

(1) also sufficient: p is a prime number, so:
if p is the 100th prime, then there are 100 primes - viz., the first 100 primes - between 1 and p + 1.
if p is the 101th prime or later, then there are 101 or more primes, so that's no good.
if p is the 99th prime or earlier, then there are 99 or fewer primes; also no good.
therefore, p is the 100th prime.

answer = d

incidentally, the actual value of p is 541.

[StaceyKoprince]

Agree that this is non-GMAT-like. iil-london, can you confirm that you saw this yourself on a GMATPrep test? (That is, you did not just copy this from some other online source that said it was gmatprep - or that this is something else entirely and you just accidentally posted it in the gmatprep folder.) Odd for an official math problem to rely entirely on logic.

[Suyash]

how can i miss this..yes ron and stacey it is cent percent from gprep since i got the same question today...on my 1st gprep...was about to ask until the above post....was completely stumped and had to guess.....

[StaceyKoprince]

Wow - color me surprised!

[RonPurewal]

how can i miss this..yes ron and stacey it is cent percent from gprep since i got the same question today...on my 1st gprep...was about to ask until the above post....was completely stumped and had to guess.....

yeah, wow, that's insane.

we'll have to keep an eye out for similar problems; this could just be a freak occurrence, or it could signal a rising tide of changing priorities.

[Guest]

First ... thanks for your posts. Second, sorry for the delay in responding.
Yes ... ABSOLUTELY ... this was in the GMATPrep test.

But as Ron's response pointed out ... this was in a Data Sufficiency question ... so if you can ascetain that the information provided in the question stem and the statements is sufficient to solve the problem then that is all you need to do. You dont have to try and work out the exact number ... just that there is enough info in the statements and questions stem to do so.
This was the trap that I fell into when encountering this question for the first time !

[StaceyKoprince]

Thanks!

[aagar2003]

(2) There are a total of p prime numbers between 1 and 3912

(2) must be sufficient, as there is obviously some fixed number of primes between 1 and 3912. we don't care what that number is, because it's clear that there's only one such number (the number of primes in a fixed range isn't about to change anytime soon).

We need to make sure that the total number of p prime numbers is prime too. If it is not, (2) cannot answer the question.
Example: The total numer of primes between 1 and 25 is 9 {2, 3, 5, 7, 11, 13, 17, 19, 23}. Now 9 is not prime.
What is the quickest way of calculating the number of primes betwen 1 and 3,912?

[RonPurewal]

We need to make sure that the total number of p prime numbers is prime too. If it is not, (2) cannot answer the question.

these statements reflect a fundamental misunderstanding of how data sufficiency problems are written.
ALL data sufficiency statements will lead to at least one legitimate solution or possibility.

here, statement (2) is guaranteed to lead to a single number, so that's all we need. the problem must be written so that this single number is actually a solution to the problem.

Example: The total numer of primes between 1 and 25 is 9 {2, 3, 5, 7, 11, 13, 17, 19, 23}. Now 9 is not prime.

... and that's why the problem doesn't use 25; if it did, it would contradict itself.

What is the quickest way of calculating the number of primes betwen 1 and 3,912?

if you are really masochistic enough to do this, the only way is to list them and then count them, one by one.
(in fact, if you could figure out any faster way to do this, you would very quickly become the most famous mathematician who has ever lived.)

[harishmullapudi]

I have a question here... Though I answered this question correctly...

"If p is a prime number greater than 2"

Why is the above statement included in the question?
I think in GMAT Quant section... we are not provided with unnecessary data?

[RonPurewal]

I think in GMAT Quant section... we are not provided with unnecessary data?

Well, this is definitely a real gmat prep problem. So I guess it's bye-bye to that hypothesis.

(I've seen quite a few official problems with unnecessary information.)

[harishmullapudi]

Thanks for the reply Ron... even the intention behind my posting is to know whether I can say bye-bye to that hypothesis... So I got the answer... :)

[tim]

It's rare, but sometimes you get information that is unnecessary in math problems.

[I_need_a_700plus]

Is it just me or am I reading way too much into this question?

When I first read the statement "if p is a prime number greater than 2, what is the value of p?" I interpreted it as p has to be a prime number...i.e. either 3, 5, 7, etc.

So if we start with statement 2: "there are a total of p prime numbers between 1 and 3,912" and we decided to list all the prime numbers: 2, 3, 5, 7, 11, 13, etc.. we will get let's say 3,000 prime numbers from 1 to 3,912 (I am just using 3,000 as an example given I did not list every prime #).

If this was the case, then statement 2 will give us the the number / how many primes there are between 1 and 3,912. However, I thought we needed to determine the actual prime number. If so, then this would be insufficient.