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

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

If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
06 Feb 2018, 01:23
Question Stats:
84% (01:06) correct 16% (01:44) wrong based on 75 sessions
HideShow timer Statistics
[GMAT math practice question] If \(n\) is a positive integer, is \(91\) a factor of \(n\)? 1) \(91\) is a factor of \(n^2\) 2) \(91\) is a factor of \(2n\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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"



Senior Manager
Joined: 07 Jul 2012
Posts: 372
Location: India
Concentration: Finance, Accounting
GPA: 3.5

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
06 Feb 2018, 03:24
(1) 91 is a factor of \(n^2\) It means \(n^2\) is divisible by 91. It means if \(n^2\) is divisible by 91, then n must be divisible by 91. In other words, 91 is a factor of n [Suff] (2) 91 is a factor of 2n It means 2n is divisible by 91. But 91 is not divisible by 2. So n must be divisible by 91. In other words, 91 is a factor of n [Suff] Answer: D.
_________________
Kindly hit kudos if my post helps!



Senior Manager
Joined: 31 May 2017
Posts: 348

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
06 Feb 2018, 22:04
If n is a positive integer, is 91 a factor of n? 1) 91 is a factor of n^2 If 91 is a factor of n * n, then 91 is a factor of n as well  Sufficient 2) 91 is a factor of 2n If 91 is a factor of 2 * n, , then 91 is a factor of n as well  Sufficient Both option sufficient. Ans  Option D
_________________



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

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
08 Feb 2018, 01:09
=> 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. Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Condition 1) Since \(91 = 7*13\), \(n^2\) is a multiple of both \(7\) and \(13\). Since \(7\) and \(13\) are prime numbers, \(n\) must be a multiple of both \(7\) and \(13\). Condition 1) is sufficient. Condition 2) If \(91\) is a factor of \(2n\), then \(91k = 2n\) for some integer \(k\). Since \(91\) is odd, \(k\) must be an even integer. Write \(k = 2a\), for some integer \(a\). Then \(2n = 91*2a\). It follows that \(n = 91*a\). Thus, \(n\) is a multiple of \(91\). Condition 2) is sufficient. This is a CMT(Common Mistake Type) 4(B) question. Condition 2) is easy to understand and condition 1) is difficult to figure out. If you are unable to figure out condition 2), you should choose D as the answer. Therefore, the answer is D. If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C or E. Answer: D
_________________
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"



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
12 Feb 2018, 17:14
MathRevolution wrote: [GMAT math practice question]
If \(n\) is a positive integer, is \(91\) a factor of \(n\)?
1) \(91\) is a factor of \(n^2\) 2) \(91\) is a factor of \(2n\) Notice that 91 = 7 x 13. So if 91 is a factor of n, n must be divisible by both 7 and 13. Statement One Alone: 91 is a factor of n^2 Since n^2/91 = integer, we see that n must have factors of 7 and 13 and thus n/91 or n/(7*13) = integer. Statement one alone is sufficient to answer the question. Statement Two Alone: 91 is a factor of 2n Since neither 7 nor 13 divides into 2, it must be true that 7 and 13 both divide into n. In other words, their LCM, which is 91, divides into n also. So 91 is a factor of n. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 01 Feb 2018
Posts: 17

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
25 Mar 2018, 14:26
Hey guys,
I got stuck on this question...I chose E because of the following reasoning:
1. e.g. 25 is a factor of 5^2 but 25 is not a factor of 5, but 5 is a factor of 5^2 and of 5, hence insuff
2. e.g. 42 is a factor of 21*2 but 41 is not a factor of 21, but 21 is a factor of 21*2 and of 21, hence insuff
Where is the flaw?



Math Expert
Joined: 02 Sep 2009
Posts: 56307

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
25 Mar 2018, 21:05
truongvu31 wrote: Hey guys,
I got stuck on this question...I chose E because of the following reasoning:
1. e.g. 25 is a factor of 5^2 but 25 is not a factor of 5, but 5 is a factor of 5^2 and of 5, hence insuff
2. e.g. 42 is a factor of 21*2 but 41 is not a factor of 21, but 21 is a factor of 21*2 and of 21, hence insuff
Where is the flaw? Why are you choosing 25 and 42 when the question asks about 91? You cannot arbitrarily change numbers in a question and expect that they will behave the same way original numbers would. 1. 25 is itself a perfect square. So, if 25 = 5^2 is a factor of n^2, it's not necessary 25 to be a factor of n. But 91 is NOT a perfect square: 91 = 7*13. For 91 = 7*13 to be a factor of n^2, it should be a factor of n because how else 7 and 13 would appear in n^2? Exponentiation does not produce primes, meaning that x^2, where x is a positive integer, has as many different prime factors as x itself. 2. Here again, you chose an even number, 42 and the factor that it's a factor of 2n does not necessarily mean that 42 is a factor of n. But 91 is NOT even. For 91 to be a factor of 2n, it should be a factor of n because how else 7 and 13 would appear in 2n?
_________________



Intern
Joined: 01 Feb 2018
Posts: 17

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
26 Mar 2018, 04:31
Bunuel wrote: truongvu31 wrote: Hey guys,
I got stuck on this question...I chose E because of the following reasoning:
1. e.g. 25 is a factor of 5^2 but 25 is not a factor of 5, but 5 is a factor of 5^2 and of 5, hence insuff
2. e.g. 42 is a factor of 21*2 but 41 is not a factor of 21, but 21 is a factor of 21*2 and of 21, hence insuff
Where is the flaw? Why are you choosing 25 and 42 when the question asks about 91? You cannot arbitrarily change numbers in a question and expect that they will behave the same way original numbers would. 1. 25 is itself a perfect square. So, if 25 = 5^2 is a factor of n^2, it's not necessary 25 to be a factor of n. But 91 is NOT a perfect square: 91 = 7*13. For 91 = 7*13 to be a factor of n^2, it should be a factor of n because how else 7 and 13 would appear in n^2? Exponentiation does not produce primes, meaning that x^2, where x is a positive integer, has as many different prime factors as x itself. 2. Here again, you chose an even number, 42 and the factor that it's a factor of 2n does not necessarily mean that 42 is a factor of n. But 91 is NOT even. For 91 to be a factor of 2n, it should be a factor of n because how else 7 and 13 would appear in 2n? I got it, thanks for the explanation!



Senior Manager
Joined: 03 Jun 2019
Posts: 415
Location: India

Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
Show Tags
21 Jul 2019, 03:54
MathRevolution wrote: [GMAT math practice question]
If \(n\) is a positive integer, is \(91\) a factor of \(n\)?
1) \(91\) is a factor of \(n^2\) 2) \(91\) is a factor of \(2n\) Given: \(n\) is a positive integer, Asked: Is \(91\) a factor of \(n\)? 1) \(91\) is a factor of \(n^2\) 91 = 13*7 Since \(91\) is a factor of \(n^2\) 91 is a factor of n since 13 & 7 are prime numbers SUFFICIENT 2) \(91\) is a factor of \(2n\)[/quote] 13*7 = 91 is a factor of 2n => 91 is a factor of n since 2 is not a common factor SUFFICIENT IMO D
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."
Please provide kudos if you like my post.




Re: If n is a positive integer, is 91 a factor of n?
[#permalink]
21 Jul 2019, 03:54






