Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 14:07

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Dec 2009
Posts: 29
Followers: 0

Kudos [?]: 28 [1] , given: 0

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

### Show Tags

28 Mar 2010, 05:56
1
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

77% (01:29) correct 23% (00:52) wrong based on 504 sessions

### HideShow timer Statistics

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
Senior Manager
Joined: 01 Feb 2010
Posts: 264
Followers: 1

Kudos [?]: 58 [0], given: 2

### Show Tags

28 Mar 2010, 07:01
1
This post was
BOOKMARKED
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.
Manager
Joined: 05 Mar 2010
Posts: 217
Followers: 1

Kudos [?]: 32 [0], given: 8

### Show Tags

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
_________________

Success is my Destiny

Intern
Joined: 14 Jan 2010
Posts: 25
Followers: 0

Kudos [?]: 4 [0], given: 0

### Show Tags

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?
Senior Manager
Joined: 19 Nov 2009
Posts: 322
Followers: 5

Kudos [?]: 92 [0], given: 44

### Show Tags

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 !
_________________

"Success is going from failure to failure without a loss of enthusiam." - Winston Churchill

As vs Like - Check this link : http://www.grammar-quizzes.com/like-as.html.

Math Expert
Joined: 02 Sep 2009
Posts: 38839
Followers: 7718

Kudos [?]: 105915 [0], given: 11593

### Show Tags

17 Apr 2010, 05:25
Expert's post
3
This post was
BOOKMARKED
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.
_________________
Manager
Joined: 27 Dec 2009
Posts: 167
Followers: 2

Kudos [?]: 104 [0], given: 3

### Show Tags

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 ?
Math Expert
Joined: 02 Sep 2009
Posts: 38839
Followers: 7718

Kudos [?]: 105915 [1] , given: 11593

### Show Tags

24 Apr 2010, 10:47
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________
Intern
Joined: 03 Nov 2010
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 0

### Show Tags

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..
Math Expert
Joined: 02 Sep 2009
Posts: 38839
Followers: 7718

Kudos [?]: 105915 [1] , given: 11593

### Show Tags

23 Nov 2010, 05:33
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1672
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 103

Kudos [?]: 992 [1] , given: 109

### Show Tags

23 Nov 2010, 15:34
1
KUDOS
+1 D

Remember that you only need to know whether it is possible to find the answer with the information they provide.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Director
Joined: 03 Sep 2006
Posts: 875
Followers: 7

Kudos [?]: 891 [0], given: 33

### Show Tags

20 Dec 2010, 22:10
Each statement on it's own is sufficient to tell you the value of P.
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23
Followers: 26

Kudos [?]: 466 [0], given: 11

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

### Show Tags

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

_________________

Impossible is nothing to God.

Manager
Joined: 07 Apr 2014
Posts: 141
Followers: 1

Kudos [?]: 24 [0], given: 81

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

### Show Tags

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.
Manager
Status: Helping People Ace the GMAT
Joined: 16 Jan 2013
Posts: 184
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 770 Q50 V46
GPA: 3.1
WE: Consulting (Consulting)
Followers: 11

Kudos [?]: 51 [0], given: 4

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

### Show Tags

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
_________________

Want to Ace the GMAT with 1 button? Start Here:
GMAT Answers is an adaptive learning platform that will help you understand exactly what you need to do to get the score that you want.

Manager
Joined: 21 Jul 2014
Posts: 71
Location: United States
WE: Project Management (Non-Profit and Government)
Followers: 0

Kudos [?]: 11 [0], given: 58

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

### Show Tags

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.
Senior Manager
Joined: 02 Mar 2012
Posts: 368
Schools: Schulich '16
Followers: 4

Kudos [?]: 67 [0], given: 4

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

### Show Tags

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
Senior Manager
Joined: 26 Oct 2016
Posts: 460
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Followers: 25

Kudos [?]: 62 [0], given: 823

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

### Show Tags

26 Jan 2017, 07:57
(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.

_________________

Thanks & Regards,
Anaira Mitch

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1026
Location: United States (CA)
Followers: 33

Kudos [?]: 535 [0], given: 2

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

### Show Tags

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.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 19 Feb 2017
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

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

### Show Tags

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.
Re: If p is a prime number greater than 2, what is the value of   [#permalink] 20 Feb 2017, 12:23
Similar topics Replies Last post
Similar
Topics:
21 What is the value of prime number p ? (1) p+8 is prime. 8 09 Feb 2017, 14:05
1 If p is an integer greater than 1, is p a prime number? 1 21 Dec 2015, 18:56
2 Given that p and q are positive, prime numbers greater than 2 23 Jun 2016, 09:27
8 If p, s, and t are positive prime numbers, what is the value 9 25 Aug 2016, 00:44
5 If p is a prime number greater than 2, what is the value of 9 07 Oct 2014, 04:13
Display posts from previous: Sort by