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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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28 Mar 2010, 05:56
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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
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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
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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28 Mar 2010, 07:01
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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
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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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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16 Apr 2010, 11:25
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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
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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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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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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24 Apr 2010, 10:47
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msand wrote:
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 ?

As p is prime more than 2 (given), then p+1 is even so it can not be prime.
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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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23 Nov 2010, 05:33
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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: If p is a prime number greater than 2, what is the value of  [#permalink]

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22 Jan 2013, 22:41
2
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

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

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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.
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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)

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

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26 Jan 2017, 07:57
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(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.

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

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30 Jan 2017, 17:48
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

We are given that p is a prime number greater than 2 and we need to determine the value of p.

Note that even though we are asked for the value of p, we actually need to determine whether the value of p is unique. If we can determine from the given statements that p is unique, then the statement(s) will be sufficient. We do not have to actually determine the value of p, even though it would be possible.

Statement One Alone:

There are a total of 100 prime numbers between 1 and p + 1.

If there are exactly 100 prime numbers between 1 and p + 1, then there are exactly 100 prime numbers in the list: 2, 3, 5, 7, 11, 13, …, p. Whatever value p is, p must be unique. It is the 100th number in the list. Statement one alone is sufficient. We can eliminate answer choices B, C, and E.

Statement Two Alone:

There are a total of p prime numbers between 1 and 3,912.

It is a fact that between two distinct positive integers, there must be a unique number of primes. For example, between 1 and 10 inclusive there are exactly 4 primes: 2, 3, 5, 7. There can’t be 3 primes or 5 primes between 1 and 10. Therefore, if there are exactly p prime numbers between 1 and 3,912, p must be unique, even if we don’t know its exact value. Statement two alone is also sufficient.

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

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20 Feb 2017, 12:23
I get the explanations to the correct answer D. However, I am confused on what the question is asking. My interpretation of what the question is asking is...It's asking for a prime number that is greater than 2. There fore according to statement 1 and 2, the answer can be 3, 5, 7, 11,and so on, which doesn't make it unique.

From the answer D and your explanations, it seems that the question is asking for how many prime numbers there are, which is unique when given a set. However my interpretation is it is asking for any prime number greater than 2 as long as it is in the set.
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If p is a prime number greater than 2, what is the value of  [#permalink]

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21 Mar 2018, 08:58
Bunuel chetan2u niks18

Is my below understanding correct for highlighted text?
Quote:
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.

Eg 1: 2 is a prime number, numbers that are prime between 1 and 2 is 0

Eg 2: 3 is a prime number, numbers that are prime between 1 and 3 is 1 (2)

Eg 3: 5 is a prime number, numbers that are prime between 1 and 5 is 2 (1,3)

Does the question ask the value in bracket is UNIQUE ? (2 or 1,3) I did not understand significance of P+1 in St 1
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Re: If p is a prime number greater than 2, what is the value of  [#permalink]

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21 Mar 2018, 09:09
Bunuel chetan2u niks18

Is my below understanding correct for highlighted text?
Quote:
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.

Eg 1: 2 is a prime number, numbers that are prime between 1 and 2 is 0

Eg 2: 3 is a prime number, numbers that are prime between 1 and 3 is 1 (2)

Eg 3: 5 is a prime number, numbers that are prime between 1 and 5 is 2 (1,3)

Does the question ask the value in bracket is UNIQUE ? (2 or 1,3) I did not understand significance of P+1 in St 1

First of all note that 1 is not prime.

let's assume p to be 5, so p+1=6

now I can say that there are 3 prime numbers between 1 & 6 (2,3 & 5), which is same as saying there are 3 prime numbers between 1 & p+1, where p is a prime number.

So in this question, we have 100 prime numbers between 1 & p+1, so you can actually count 100 prime numbers starting with 2. the 100th prime number will be p
Re: If p is a prime number greater than 2, what is the value of   [#permalink] 21 Mar 2018, 09:09

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