Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 08 Dec 2009
Posts: 29

If p is a prime number greater than 2, what is the value of [#permalink]
Show Tags
28 Mar 2010, 05:56
Question Stats:
77% (00:27) correct 23% (00:43) wrong based on 658 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
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 01 Feb 2010
Posts: 241

Re: dS prime numbers [#permalink]
Show Tags
28 Mar 2010, 07:01
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 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: 182

Re: dS prime numbers [#permalink]
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: 17

Re: dS prime numbers [#permalink]
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 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: 269

Re: dS prime numbers [#permalink]
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.grammarquizzes.com/likeas.html.



Math Expert
Joined: 02 Sep 2009
Posts: 46207

Re: dS prime numbers [#permalink]
Show Tags
17 Apr 2010, 05:25
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 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 27 Dec 2009
Posts: 149

Re: dS prime numbers [#permalink]
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: 46207

Re: dS prime numbers [#permalink]
Show Tags
24 Apr 2010, 10:47



Intern
Joined: 03 Nov 2010
Posts: 2

Re: dS prime numbers [#permalink]
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: 46207

Re: dS prime numbers [#permalink]
Show Tags
23 Nov 2010, 05:33
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 13 Aug 2012
Posts: 443
Concentration: Marketing, Finance
GPA: 3.23

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 Answer: D
_________________
Impossible is nothing to God.



Manager
Joined: 07 Apr 2014
Posts: 119

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
Affiliations: GMAT Answers
Joined: 16 Jan 2013
Posts: 183
Location: United States
Concentration: Finance, Entrepreneurship
GPA: 3.1
WE: Consulting (Consulting)

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: 72
Location: United States
Schools: HBS '16, Stanford '16, Kellogg '16, CBS '16, Ross '17, Haas '16, Haas EWMBA '18, Tuck '17, Stern '18, Yale '17, Anderson '17, Darden '16, Johnson '16, Tepper '18 (D), LBS '17, Insead '14, IMD '16, IE Nov'15, Booth, LBS MiM'17
WE: Project Management (NonProfit and Government)

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 3No 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: 337

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



Director
Joined: 26 Oct 2016
Posts: 666
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

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. answer = d
_________________
Thanks & Regards, Anaira Mitch



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2738
Location: United States (CA)

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. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 19 Feb 2017
Posts: 1

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.



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1016
Location: India
WE: Engineering (Other)

If p is a prime number greater than 2, what is the value of [#permalink]
Show Tags
21 Mar 2018, 08:58
Bunuel chetan2u niks18Is 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
_________________
It's the journey that brings us happiness not the destination.



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82

Re: If p is a prime number greater than 2, what is the value of [#permalink]
Show Tags
21 Mar 2018, 09:09
adkikani wrote: Bunuel chetan2u niks18Is 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 Hi adkikaniFirst 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






