Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC
Author 
Message 
TAGS:

Hide Tags

eGMAT Representative
Joined: 04 Jan 2015
Posts: 2943

If N is a positive integer
[#permalink]
Show Tags
Updated on: 13 Aug 2018, 02:27
Question Stats:
68% (01:58) correct 32% (01:45) wrong based on 189 sessions
HideShow timer Statistics
eGMAT Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
This is Question 10 of The eGMAT Number Properties Marathon Go to Question 11 of the Marathon
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Retired Moderator
Joined: 07 Jan 2016
Posts: 1090
Location: India

Re: If N is a positive integer
[#permalink]
Show Tags
28 Feb 2018, 03:36
EgmatQuantExpert wrote: Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
we need to know if n is a multiple of 2 1) n^2 + 3 is prime if n =1 n=2 the statement is true for both but n^3/4 is not a integer if n=1 and an integer when n=2 2) n= number of odd factors of 6 6 = 3x2 i.e factors = 1,2,3,6 1 is odd and 3 is odd n=2 2^3/4= 2(integer) sufficient (B) imo



SVP
Joined: 26 Mar 2013
Posts: 2284

Re: If N is a positive integer
[#permalink]
Show Tags
28 Feb 2018, 07:19
Hatakekakashi wrote: EgmatQuantExpert wrote: Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
we need to know if n is a multiple of 2 1) n^2 + 3 is prime if n =1 n=2 the statement is true for both but n^3/4 is not a integer if n=1 and an integer when n=2 2) n= number of odd factors of 6 6 = 3x2 i.e factors = 1,2,3,6 1 is odd and 3 is odd n=2 2^3/4= 2(integer) sufficient (B) imo Hi HatakekakashiPleasse review highlighted If n=1 ....then 1+3 = 4 s it is NOT prime number as statement states.



Retired Moderator
Joined: 07 Jan 2016
Posts: 1090
Location: India

Re: If N is a positive integer
[#permalink]
Show Tags
28 Feb 2018, 11:24
Mo2men wrote: Hatakekakashi wrote: EgmatQuantExpert wrote: Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
we need to know if n is a multiple of 2 1) n^2 + 3 is prime if n =1 n=2 the statement is true for both but n^3/4 is not a integer if n=1 and an integer when n=2 2) n= number of odd factors of 6 6 = 3x2 i.e factors = 1,2,3,6 1 is odd and 3 is odd n=2 2^3/4= 2(integer) sufficient (B) imo Hi HatakekakashiPleasse review highlighted If n=1 ....then 1+3 = 4 s it is NOT prime number as statement states. my bad..was at work thanks for pointing out :D i guess (D) then n^2+ 3 is prime n can't be odd as odd+odd =even and not prime as value >2 n=2 value 7 n=4 value 19 n=6 39 (not prime) n=8 67 prime n=10 103 (prime) we can see that n^2 + 3 is prime n^3/4 will most likely be an integer



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2943

Re: If N is a positive integer
[#permalink]
Show Tags
28 Feb 2018, 12:35
Solution: We need to find, whether \(N^3/4\) is an integer or not? Now, \(N^3/4\) is an integer only when \(N\) is even number. Thus, we only need to find, whether \(N\) is an even number or not? Statement 1:"\(N^2+3\) is a prime number.” Since \(N\) is a positive integer, therefore, \(N^2+3\) is always greater than \(3\). We know, all Prime numbers greater than \(3\) are odd. Thus, \(N^2+3\) = \(odd\) \(N^2\)+ \(odd=odd\) \(N^2\)= \(even\) Therefore, \(N^2+3\) is a prime number when \(N\) is an even number. Thus, \(N^3/4\) is an integer. Therefore, Statement 1 alone is sufficient to answer the question. Statement 2:“\(N\) is the number of odd factors of \(6\).” To calculate odd factors of a number, we do not consider the even prime number. Therefore, Odd factors of \(6\)= power of \(3+1\) Odd factors of\(6\)= \(1+1\) Odd factors of \(6=2\) Thus, \(N=2\). Therefore, \(N^3/4\) is an integer. Therefore, Statement 2 alone is sufficient to answer the question. Therefore, we can find the answer by EACH of the statement alone. Answer: Option D
_________________



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7612
GPA: 3.82

Re: If N is a positive integer
[#permalink]
Show Tags
03 Mar 2018, 13:40
EgmatQuantExpert wrote: Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. We can modify the original condition and question as follows. The question that \(N^3/4\) is an integer is equivalent to \(N\) is an even integer. Condition 1) In order for \(N^2 + 3\) to an prime number, \(N^2\) and \(N\) must be an even integer. The condition 1) is sufficient. Condition 2) \(N = 1\) or \(N = 3\). For both cases, \(N^3/4\) is \(1/4\) or \(27/4\). They are not integers. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, the condition 2) is sufficient. Therefore, D is the answer.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 20 Sep 2018
Posts: 2

Re: If N is a positive integer
[#permalink]
Show Tags
03 Mar 2019, 10:58
MathRevolution wrote: EgmatQuantExpert wrote: Question: If \(N\)\(\) is a positive integer, is \(N^3/4\) an integer? 1. \(N^2+3\) is a prime number. 2. \(N\) is the number of odd factors of \(6\). A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient. B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient. C) Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D) EACH statement ALONE is sufficient. E) Statement (1) and (2) TOGETHER are NOT sufficient.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. We can modify the original condition and question as follows. The question that \(N^3/4\) is an integer is equivalent to \(N\) is an even integer. Condition 1) In order for \(N^2 + 3\) to an prime number, \(N^2\) and \(N\) must be an even integer. The condition 1) is sufficient. Condition 2) \(N = 1\) or \(N = 3\). For both cases, \(N^3/4\) is \(1/4\) or \(27/4\). They are not integers. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, the condition 2) is sufficient. Therefore, D is the answer. For condition 2, why did you state that N=1 or N=3? Condition 2 says N is the number of odd factors of 6. The number of odd factors of 6 is 2 (3 and 1).



Manager
Joined: 03 Sep 2018
Posts: 63

Re: If N is a positive integer
[#permalink]
Show Tags
05 Apr 2019, 01:23
Alternative approach to statement I: any prime >3 can be expressed as 6n+1, hence, N^2+3=6n+1=6n2, now, 6n2= 2(3n1), hence N^2 will always be divisible by 2^2 Please give kudos if you consider this post helpful. Thanks
_________________
Please consider giving Kudos if my post contained a helpful reply or question.




Re: If N is a positive integer
[#permalink]
05 Apr 2019, 01:23






