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Please need some help with this one ... thanks a lot

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 3,912

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient. 2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient. Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.

Please need some help with this one ... thanks a lot

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 3,912

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient. 2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient. Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.

Using Stmt 1, it's pretty straight forward.

Using Stmt 2, let n = no. of prime numbers between 1 and 3912. How can we be sure that n is a prime number and it is equal to p? Do we have to assume so in questions like these?

D is correct. Both statements are sufficient by itself.

We can find the prime no. using the given information in each statement. But we need not find that number, just need to know the sufficiency !
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Please need some help with this one ... thanks a lot

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 3,912

1: p has to be 100th prime number starting from 2 (1st prime number) sufficient. 2: all the prime numbers between 1 and 3912 can be found and the number of prime number will be what we need. Sufficient. Hence D.

PS: This is a DS question so we do not need to calculate the p till end. calculation will take some time but no need to do.

Using Stmt 1, it's pretty straight forward.

Using Stmt 2, let n = no. of prime numbers between 1 and 3912. How can we be sure that n is a prime number and it is equal to p? Do we have to assume so in questions like these?

Stem and the statements are ALWAYS providing us with correct information.

If it turns out that the quantity of primes between 1 and 3912 is not the prime number itself, this will mean that the question is flawed. GMAT wouldn't give us such question then.

Stem says p is a prime number. Statement (2) says that "there are a total of p prime numbers between 1 and 3912". So yes the # of primes between 1 and 3912 MUST be prime number itself. We don't know what number it is, but we can calculate it, hence we can calculate p, hence (2) is also sufficient.

statement A is not sufficient...consider this: how many prime numbers are between 1 and 14 and between 1 and 16,,,same number..you can not conclude anything from statement like there 100 prime less than p+1... B is sufficient..

statement A is not sufficient...consider this: how many prime numbers are between 1 and 14 and between 1 and 16,,,same number..you can not conclude anything from statement like there 100 prime less than p+1... B is sufficient..

OA for this question is D, not B.

Statement (1) is says that there are 100 primes in the range between 1 and P+1, so this statement basically says that P is the 100th prime --> we can determine the single numerical value of P (we can find 100th prime). As this is DS question no matter what the actual value of P is, the fact that we can find it, is already sufficient.
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If p is a prime number greater than 2, what is the value of p ? [#permalink]

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14 Jul 2015, 10:22

This isn't an algebra problem. It is number properties and the application of them.

We know p is prime so when statement 1 ultimately says that p is the 100th prime number. Whatever that is, we can find it.

We could count all the prime numbers for statement 2, but there is no need.

D
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Re: If p is a prime number greater than 2, what is the value of [#permalink]

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19 Jun 2016, 18:53

Incidentally, Bunuel I ran the wolfram to find the number of primes between 1 & 3912. It said 541.

Not to see if 541 is prime or not. We have the closest square root of 541 less than 25 ( considering 625). Thus, we need to check for 2- No 3-No 5-- No 7- No 9-- No ( sum of digits = 10) 11- No 13- No 17- No 19- No 23- No Hence 541 is prime as predicted by you. ( Ohh. by the way, I did countercheck with wolfram again & its correct)

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