Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 60647

If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
25 Jun 2018, 20:29
Question Stats:
71% (01:22) correct 29% (01:31) wrong based on 1137 sessions
HideShow timer Statistics
If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. NEW question from GMAT® Official Guide 2019 (DS05377)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Veritas Prep GMAT Instructor
Joined: 01 Jul 2017
Posts: 81
Location: United States
Concentration: Leadership, Organizational Behavior

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
06 Oct 2018, 07:04
Don't fall for the trap of this question. It isn't about the math. Many explanations of Quantitative questions focus blindly on the math, but remember: the GMAT is a criticalthinking test. For those of you studying for the GMAT, you will want to internalize strategies that actually minimize the amount of math that needs to be done, making it easier to manage your time (giving you more time for harder questions.) The tactics I will show you here will be useful for numerous questions, not just this one. My solution is going to walk through not just what the answer is, but how to strategically think about it. Ready? Let's talk strategy here. Here is the full "GMAT Jujitsu" for this question: The first thing we need to understand is the concept of a greatest common divisor (often called the greatest common factor or \(GCF\).) The GCF is the largest factor that is shared between two integers. And yet, once we know this, the fundamental trap of this problem is getting you to think that you actually need to solve for the GCF, instead of stopping as soon as you know you CAN solve. Many people spend too much time on Data Sufficiency questions because they think they need to get to the bitter end. We don’t. As soon as we have enough information to conclude that a statement is either sufficient or insufficient, we can move on. For example, let’s evaluate statement #1. It states that the “ product of \(12\) and \(n\) is \(432\).” Immediately, you should recognize that you can solve for \(n\), since \(12n = 432\). One equation. One variable. No weirdness. No possibility of multiple values. You don’t have to do the long division here  actually solving for n  to determine that statement #1 is sufficient. After all, if you can solve for \(n\), you can obviously determine what the factors of \(n\) are, and thereby determine what the GCF of \(12\) and \(n\) are. Case closed. Statement #1 is sufficient. Notice that you don't even need to know the answer to the question "what is the greatest common divisor?" Statement #2 is similarly deceptive, but in a different way. Here, you can’t solve for a specific value of \(n\). However, if the “ greatest common factor of \(24\) and \(n\) is \(12\)”, then \(12\) is clearly a factor of \(n\). And we also know that \(12\) is the greatest factor of \(12\) (after all, you can’t have an integer factor of a number greater than the number itself.) So, no matter how you look at it, we know that the greatest common factor of \(n\) and \(12\) must be \(12\). Statement #2 is also sufficient. With both the statements individually sufficient, the answer is D.Now, let’s look back at this problem from the perspective of strategy. This problem can teach us several patterns seen throughout the GMAT. First, minimize your math. I have met many engineers who think the Quantitative portion of the test is all about the math, and they end up doing pretty poorly on the GMAT because they fail to realize the test is actually measuring something besides their math skills: criticalthinking. This is especially true with Data Sufficiency. You only need to do "sufficient" math to prove that there must be only one answer to the question. (And this problem requires almost zero math if you think about it.) Second, statements in Data Sufficiency questions often bait you into thinking that you solve each statement in the same way. But the GMAT rewards flexiblethinking, not linearthinking. With Statement #1, we can solve for \(n\). With Statement #2, it is impossible to know what \(n\) is. But the question isn't asking what \(n\) is. It is basically asking, "is there enough information here to calculate the GCF of two numbers?" On GMAT questions, you must always focus on exactly what the actual question is asking. For this question, we can arrive at an answer by leveraging the information in the problem. And that is how you think like the GMAT.
_________________
Aaron PondVeritas Prep Teacher of the YearVisit me at https://www.veritasprep.com/gmat/aaronpond/ if you would like to learn even more "GMAT Jujitsu"!



Director
Joined: 04 Aug 2010
Posts: 514
Schools: Dartmouth College

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
05 Jul 2018, 03:05
Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ?
(1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. Statement 1: 12n = 432. Since we can solve for n, the GCF of 12 and n can be determined. SUFFICIENT. Statement 2: 24 = 2* 2*2*3. Since the GCF of n and 24 is the blue product (12) without the red factor (2), n must be a multiple of 12 that does NOT include an additional factor of 2. In other words: n = 12a, where a is an ODD positive integer. Options for n: 12*1, 12*3, 12*5, 12*7, 12*9... In every case, the GCF of n and 12 is the value in green (12). SUFFICIENT.
_________________
GMAT and GRE Tutor New York, NY
Available for tutoring in NYC and longdistance. For more information, please email me at GMATGuruNY@gmail.com.



Math Expert
Joined: 02 Aug 2009
Posts: 8336

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
25 Jun 2018, 21:10
Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. NEW question from GMAT® Official Guide 2019 (DS05377) GCD means the largest number which has both 12 and n as its multiple.. So you require to know the value of n or some relationship between 12 and n or some property of n.. 1) 12 * n =432... n can be found and GCD of 12 and n can also be found.. Sufficient 2) GCD of 24 and n is 12. This tells us that n is multiple of 12... Let n =12x, where X is an integer So GCD of 12 and 12x has to be 12 itself Sufficient D
_________________




Manager
Joined: 07 Feb 2017
Posts: 173

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
25 Jun 2018, 20:47
(1) n=36 gcd=12 (2) 12 divides n gcd=12
It must be D. Each statement alone is sufficient



Manager
Joined: 25 Jul 2017
Posts: 92

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
25 Jun 2018, 20:51
Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. NEW question from GMAT® Official Guide 2019 (DS05377) From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36. So Greatest common divisor of 12, 36 can be derived.  SufficientFrom Statement 2: "The greatest common divisor of 24 and n is 12.". that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12.  Sufficient.D is the answer.



eGMAT Representative
Joined: 04 Jan 2015
Posts: 3222

If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
25 Jun 2018, 21:55
Solution Given:To find:• The greatest common divisor of 12 and n Analysing Statement 1• As per the information given in statement 1, the product of 12 and n is 432
o Therefore, we can find the value of n = \(\frac{432}{12}\) • As we can find n, we can also find the greatest common divisor of 12 and n Hence, statement 1 is sufficient to answer the question Analysing Statement 2• As per the information given in statement 2, the greatest common divisor of 24 and n is 12
o So, the number n must be a multiple of 12 o Therefore, the greatest common divisor of 12 and n will be 12 Hence, statement 2 is sufficient to answer the question Hence, the correct answer is option D. Answer: D
_________________



VP
Joined: 09 Mar 2016
Posts: 1223

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
07 Jul 2018, 05:10
anuj04 wrote: Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. NEW question from GMAT® Official Guide 2019 (DS05377) From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36. So Greatest common divisor of 12, 36 can be derived.  SufficientFrom Statement 2: "The greatest common divisor of 24 and n is 12.". that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12.  Sufficient.D is the answer.hey pushpitkc, i dont get if the product of 12 and n is 432" it means n = 36 and the question asks: If n is an integer, what is the greatest common divisor of 12 and n ? how can 36 be divisor of 12 Also From Statement 2: "The greatest common divisor of 24 and n is 12.". i dont get how greatest common divisor of 24 can be 12, 36, 60, 84 ? any ideas ? thanks and have a great day



Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3286
Location: India
GPA: 3.12

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
07 Jul 2018, 05:34
dave13 wrote: anuj04 wrote: Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ? (1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. NEW question from GMAT® Official Guide 2019 (DS05377) From Statement 1: "The product of 12 and n is 432" i.e. n=432/12= 36. So Greatest common divisor of 12, 36 can be derived.  SufficientFrom Statement 2: "The greatest common divisor of 24 and n is 12.". that is n could be, 12, 36, 60, 84.... and so on. And, in each case, the Greatest common divisor for 12 & n will be 12.  Sufficient.D is the answer.hey pushpitkc, i dont get if the product of 12 and n is 432" it means n = 36 and the question asks: If n is an integer, what is the greatest common divisor of 12 and n ? how can 36 be divisor of 12 Also From Statement 2: "The greatest common divisor of 24 and n is 12.". i dont get how greatest common divisor of 24 can be 12, 36, 60, 84 ? any ideas ? thanks and have a great day Hey dave13For the first statement, it says which is the greatest divisor the two integers, n and 12. The greatest common divisor (GCD) of a set of integers is the largest integer that divides each integer in the set. So, if n=36, the greatest common divisor is 12. As for the second statement, the number n and 24 have a greatest common divisor of 12. So, n can be any multiple of 12  12,12*2 = 24,12*3 = 36, and so on. This link should help you understand what the Greatest Common divisor is. Hope this helps you!
_________________
You've got what it takes, but it will take everything you've got



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2806

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
13 Jul 2018, 14:26
Bunuel wrote: If n is an integer, what is the greatest common divisor of 12 and n ?
(1) The product of 12 and n is 432. (2) The greatest common divisor of 24 and n is 12. We need to determine the greatest common divisor or the greatest common factor (GCF) of 12 and n. If we can determine the value of n, then we can determine the GCF of 12 and n. Statement One Alone: The product of 12 and n is 432 Since 12n = 432, n = 432/12 = 36. So the GCF of 12 and 36 is 12. Statement one alone is sufficient. Statement Two Alone: The greatest common divisor of 24 and n is 12. Since the GCF of 24 and n is 12, that means n itself is a multiple of 12. Therefore, the GCF of 12 and n must be also 12. Statement two is sufficient. 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.



Manager
Joined: 24 Dec 2011
Posts: 59
Location: India
GPA: 4
WE: General Management (Health Care)

Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
Show Tags
22 Mar 2019, 10:36
given n is an integer
we need to find the HCF of 12 and n. remember that we need to find the HCF, not the "n".
Statement 1 gives straight answer 1) 12 * n =432 n can be found and HCF of 12 and n can also be found. there ends the matter Sufficient
Statement 2 says the HCF of 24 and n is 12. means that n is a multiple of 12
Let n =12p, where p is an integer So HCF of 12 and 12p has to be 12 itself Sufficient




Re: If n is an integer, what is the greatest common divisor of 12 and n ?
[#permalink]
22 Mar 2019, 10:36






