Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Jan 2013
Posts: 2

If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
25 Jan 2013, 03:43
Question Stats:
51% (01:49) correct 49% (01:05) wrong based on 379 sessions
HideShow timer Statistics
If x is a positive integer, is x a prime integer? (1) x+1 is a prime number. (2) x5 is a prime number. Can't figure it out.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49208

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
25 Jan 2013, 04:47
If x is a positive integer, is x a prime integer?(1) x+1 is a prime number. Notice that x cannot be an odd prime, because in this case (odd prime) + 1 = (even number), and the only even prime is 2, but in this case x=1, which is not prime. So, if x=prime, then it must be 2: 2+1=3=prime. Of course, x can be a nonprime, for example 1. Not sufficient. (2) x5 is a prime number. If x=7, then the answer is YES but if x=8, then the answer is NO. Not sufficient. (1)+(2) From (1) we have that if x IS a prime, then it must be 2. But if x=2, them x5=3, which is not a prime. Thus x=prime=2 contradicts the second statement. Therefore x cannot be a prime number. Sufficient. Answer: C. 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
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 87
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
20 May 2013, 03:15
suprememodelrus wrote: If x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
Hi Bunuel, My approach does not look standard. Is it correct? From statement 1: X= 1,2,4,6,10,12,16,18........ From statement 2: X= 7,8,10,12,16,22........ common from the both statements are 10,12,16..... Thus X is not a prime integer. Kindly provide algebric approach if possible. Thanks in advance
_________________
Do not forget to hit the Kudos button on your left if you find my post helpful.



Retired Moderator
Joined: 05 Jul 2006
Posts: 1731

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
20 May 2013, 09:41
f x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
I think this is a bad question , however ...
from 1
x , x+1 are 2 successive integers ....... if x is prime and since the only 2 prime that are successive are 2,3 therefore if x is prime it is 2 , however x could be 4 as well .... insuff
from 2
The only 2 primes 5 units apart are 7 and 2 , (since all primes > 3 end in 1,3,7,9) if x were to be prime it is 7 , however x could be 8 and (x5) could be 3 ... insuff
both together
for x to be prime according to the above 2 statements then it has be less than a prime by 1 and larger than another by 5 .... there exist no such a prime
thus sure x is not a prime ( integers if not prime are composite)



Math Expert
Joined: 02 Sep 2009
Posts: 49208

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
21 May 2013, 01:05
atalpanditgmat wrote: suprememodelrus wrote: If x is a positive integer, is x a prime integer?
(1) x+1 is a prime number. (2) x5 is a prime number.
Hi Bunuel, My approach does not look standard. Is it correct? From statement 1: X= 1,2,4,6,10,12,16,18........ From statement 2: X= 7,8,10,12,16,22........ common from the both statements are 0,12,16..... Thus X is not a prime integer. Kindly provide algebric approach if possible. Thanks in advance Yes, that's correct. From both statements x must be even (10, 12, 16, ...), but it cannot be 2. So, x is not a prime number.
_________________
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



SVP
Joined: 06 Sep 2013
Posts: 1821
Concentration: Finance

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
29 Jan 2014, 08:01
Correct. From both statements together:
X must be higher than 5 because no prime can be negative. All primes higher than 5 are odd. So x+1 will be an even number. There is only one even number that is prime which is 2. Given that x>5 then we know that X cannot be a prime
C



Manager
Joined: 02 Aug 2017
Posts: 70
Concentration: Strategy, Nonprofit
GPA: 3.71

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
29 Aug 2018, 08:57
If x is a positive integer, is x a prime integer? (1) x+1 is a prime number. x+1 can be either of 2,3,5,7,11,13,17,19,... etc Hence, X can be either of 1,2,4,6,10,12,16,18,...etc Here X=2 is prime, while other values are nonprime NOT SUFFICIENT(2) x5 is a prime number. x5 can be either of 2,3,5,7,11,13,17,19,... etc Hence, X can be either of 7,8,10,12,16,18,22,24,...etc Here X=7 is prime, while other values are nonprime NOT SUFFICIENTConsidering (1) and (2) together, X can be 10,12,16,18...etc all of this values are even values greater than 2 hence, X cannot be prime SUFFICIENT
_________________
Everything is in flux, nothing stays still
MGMAT1 :590 Q42 V30 (07/07/18) VERITAS :660 Q48 V33 (16/07/18) GMATPREP1 :690 Q46 V36 (22/07/18) GMATPREP2 :740 Q51 V39 (06/08/18) ECONOMIST :740 Q49 V44 (11/08/18) KAPLAN :690 Q49 V36 (17/08/18) PRINCETON :690 Q48 V38 (26/08/18) MGMAT2 :720 Q43 V45 (02/09/18)



Intern
Joined: 26 Jun 2018
Posts: 3

Re: If x is a positive integer, is x a prime integer?
[#permalink]
Show Tags
30 Aug 2018, 23:53
Statement 1x+1 is prime when x =2, both x+1 and x are prime numbers However when x= 4,6,10…, while x+1 is prime, x is not prime Therefore, Statement 1 is insufficient Statement 2x5 is prime when x= 7 both x5 and x are prime numbers However when x= 8,10,12…, while x5 is prime, x is not Therefore Statement 2 is insufficient Statement 1+2Now for x to be prime it has to be equal to 2,3,5,7,11… coming back to the question: is x a prime integer? if both x+1 and x5 are prime numbers: then x cannot be equal to 2, the only prime number which makes x+1 a prime also x cannot be equal to 7, the only prime number which makes x5 a prime for both statements to be true x has to be a non prime value Hence 1+2 is sufficient




Re: If x is a positive integer, is x a prime integer? &nbs
[#permalink]
30 Aug 2018, 23:53






