Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 13 Jun 2013
Posts: 277

Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
Updated on: 19 Nov 2014, 05:25
Question Stats:
47% (01:47) correct 53% (01:38) wrong based on 165 sessions
HideShow timer Statistics
Does P have a factor X where 1 < X < P, and X and P are positive integers? (1) GCD (P^2, k) = k, where k is a prime number (2) 36*20 + 2 < P < 36*20+6
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by manpreetsingh86 on 19 Nov 2014, 05:24.
Last edited by Bunuel on 19 Nov 2014, 05:25, edited 1 time in total.
Edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 49272

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
19 Nov 2014, 05:37
Does P have a factor X where 1 < X < P, and X and P are positive integers?The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number). (1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient. (2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient. Answer: B.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 49272

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
19 Nov 2014, 05:38
Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Similar questions to practice: ifxisanintegerdoesxhaveafactornsuchthat100670.htmldoestheintegerkhaveafactorpsuchthat1pk126735.htmlforanyintegerngreaterthan1ndenotestheproductof168575.htmldoesintegernhave2factorsxysuchthat1xyn165983.htmlifzisanintegeriszprime128732.htmlHope this helps.
_________________
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



Intern
Joined: 01 Oct 2015
Posts: 1

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
15 Nov 2015, 10:37
Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. but what about X itself. for example, if X=721 and in this case it is not a factor of P?



Math Expert
Joined: 02 Sep 2009
Posts: 49272

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
15 Nov 2015, 23:59
vadam wrote: Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. but what about X itself. for example, if X=721 and in this case it is not a factor of P? Your question is not clear. First of all the question asks "Does P have a factor X where 1 < X < P..." plus, an integer is a factor of itself. For example, 721 is a factor of 721.
_________________
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



Board of Directors
Joined: 17 Jul 2014
Posts: 2692
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
09 Feb 2016, 19:34
manpreetsingh86 wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers? (1) GCD (P^2, k) = k, where k is a prime number from this, we know that k is a factor of p^2. but we don't know whether k is a factor of P or not. what if k=p? what if k=p=1? p^2=1. since we need integers, there might be no x at all here. suppose we have p=9 k=3. then yes. it might be a number x that is a factor of p. (2) 36*20 + 2 < P < 36*20+6 722 < P < 726 p can be 723, 724, 725. 724 is even, so it is divisible 725 ends in 5 so is divisible by 5 7+2+3=12, so divisible by 3 we see that all possible options of P have other factors. we can give a definite answer. B.



Current Student
Joined: 12 Aug 2015
Posts: 2651

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
16 Mar 2016, 05:05
Here all the values between 36*20+2 and 36*20+6 are non primes as it it possible to obtain the factors. Hence B is sufficient statement 2 can be discarded as p can be 3 and p can be 81 (for k=3) thus B is sufficient
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Manager
Joined: 19 Aug 2016
Posts: 87

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
08 Oct 2017, 17:47
Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Hi Bunuel.. How did u conclude that P is a prime number? Pls help..thanks in advance



Math Expert
Joined: 02 Sep 2009
Posts: 49272

Re: Does P have a factor X where 1<X<P , and X and P are positive integers
[#permalink]
Show Tags
08 Oct 2017, 21:01
zanaik89 wrote: Bunuel wrote: Does P have a factor X where 1 < X < P, and X and P are positive integers?
The question basically asks whether p is a prime number. If it is, then it won't have a factor x such that 1 < x < p (definition of a prime number).
(1) GCD (P^2, k) = k, where k is a prime number. Can p be a prime? Yes, consider p = k = 2. Can p be a nonprime? Yes, consider p = 4 and k = 2. Not sufficient.
(2) 36*20 + 2 < P < 36*20+6 > p could be 36*20 + 3 = 723, 36*20 + 4 = 724, or 36*20 + 5 = 725. None of these numbers is prime: 723 is a multiple of 3 (sum of its digits is a multiple of 3), 724 is even and 725 is a multiple of 5. So, we can give a definite answer that p is not a prime number, therefore it must have a factor which is greater than 1 and less than p itself. Sufficient.
Answer: B. Hi Bunuel.. How did u conclude that P is a prime number? The question asks whether p is prime. If p is prime it won't have a factor x such that 1 < x < p, if p is NOT prime it will have a factor x such that 1 < x < p. For example, prime number 7, does not have a factor x such that 1 < x < 7. Pls help..thanks in advance Where does it say that p is a prime?
_________________
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




Re: Does P have a factor X where 1<X<P , and X and P are positive integers &nbs
[#permalink]
08 Oct 2017, 21:01






