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If p is a prime number greater than 2, what is the value of

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

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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
[Reveal] Spoiler: OA
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Re: dS prime numbers [#permalink]

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aljatar wrote:
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
[Reveal] Spoiler: OA
OA is D

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.
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Re: dS prime numbers [#permalink]

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New post 29 Mar 2010, 02:58
Yes we don't need to calculate for DS question and from both statements individually are sufficient to find the prime numbers
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Re: dS prime numbers [#permalink]

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New post 16 Apr 2010, 11:25
bangalorian2000 wrote:
aljatar wrote:
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
[Reveal] Spoiler: OA
OA is D

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?
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Re: dS prime numbers [#permalink]

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New post 16 Apr 2010, 23:57
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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Re: dS prime numbers [#permalink]

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New post 17 Apr 2010, 05:25
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PhunsukWangdu wrote:
bangalorian2000 wrote:
aljatar wrote:
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
[Reveal] Spoiler: OA
OA is D

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.

Hope it's clear.
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Re: dS prime numbers [#permalink]

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New post 24 Apr 2010, 10:44
bangalorian2000 wrote:
1: p has to be 100th prime number starting from 2 (1st prime number) sufficient.

Why can't p+1 be the 100th prime number ?
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Re: dS prime numbers [#permalink]

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Re: dS prime numbers [#permalink]

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New post 22 Nov 2010, 16:09
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..
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Re: dS prime numbers [#permalink]

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lhich2000 wrote:
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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Re: dS prime numbers [#permalink]

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+1 D

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Re: Data Suff [#permalink]

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New post 20 Dec 2010, 22:10
Each statement on it's own is sufficient to tell you the value of P.
Thus answer should be "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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New post 22 Jan 2013, 22:41
Statement 1:
Listing the first 100 prime numbers and getting the 100th prime will give us p

Statement 2:
Listing all the prime numbers from 1 to 3912 and counting them will give us p

Answer: 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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New post 06 Sep 2014, 04:47
aljatar wrote:
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



pretty straight forward , after writting down info available in question.

p(prime number ) > 2.... (p is always odd).

1. excluding 2 , starting from 3 , 5 .... u could easily get the value of P. (although knowing P is not required)

2. if u count all prime number between 1 & 3912.. u could get the value of P .. but counting is not required as its a DS question. :-D
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If p is a prime number greater than 2, what is the value of p ? [#permalink]

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New post 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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New post 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)

It's good to see the principles in action.

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

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New post 20 Jun 2016, 05:25
D

only 2,3 are consecutive primes.here p and p+1 are co primes

statement 1.100 suff. (p+1 won't be prime coz it co -prime it is divisible by number more than 1)

2) says same.100
Re: If p is a prime number greater than 2, what is the value of   [#permalink] 20 Jun 2016, 05:25
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