December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST. December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51082

If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
14 Sep 2015, 04:19
Question Stats:
57% (02:22) correct 43% (02:31) wrong based on 332 sessions
HideShow timer Statistics



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2710
Location: India
GMAT: INSIGHT
WE: Education (Education)

If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
Updated on: 25 Aug 2016, 20:58
Bunuel wrote: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24 II. 32 III. 96
A. None B. I only C. II only D. I and II only E. I, II, and III Given : n is a multiple of 2 but not a multiple of 3 or 4Possible values of n = 2, 10, 14, 22..... @n= 2 : (n + 6)(n + 8)(n + 10) = 8*10*12 i.e. Divisible by 24, 32 and 96 all @n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all @n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all @n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all Answer: Option E
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Originally posted by GMATinsight on 14 Sep 2015, 04:54.
Last edited by GMATinsight on 25 Aug 2016, 20:58, edited 1 time in total.



Current Student
Joined: 07 Jan 2015
Posts: 82
Location: Thailand
GMAT 1: 540 Q41 V23 GMAT 2: 570 Q44 V24 GMAT 3: 550 Q44 V21 GMAT 4: 660 Q48 V33
GPA: 3.31
WE: Science (Other)

If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
14 Sep 2015, 18:55
GMATinsight wrote: Bunuel wrote: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24 II. 32 III. 96
A. None B. I only C. II only D. I and II only E. I, II, and III Given : n is a multiple of 2 but not a multiple of 3 or 4Possible values of n = 10, 14, 22..... @n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all @n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all @n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all Answer: Option E Why does not your possible values include 2? since 2 is also a multiple of 2.



Manager
Joined: 13 Mar 2013
Posts: 164
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
14 Sep 2015, 19:14
If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following? I. 24 II. 32 III. 96 A. None B. I only C. II only D. I and II only E. I, II, and III Ans is E. even multiple of 3  6,12,18,24 and so on multiple of 4  4,8,12,16 and so on There is n not a multiple of 3(even) and 4 hence n possible value is 2,10,14,22 Taking the n=2 and putting the value in equation (n + 6)(n + 8)(n + 10) we get = 8*10*12 check option 1,2,3 all can divide 8*10*12 Hence ans is E
_________________
Regards ,



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2710
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
14 Sep 2015, 20:43
Aves wrote: GMATinsight wrote: Bunuel wrote: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24 II. 32 III. 96
A. None B. I only C. II only D. I and II only E. I, II, and III Given : n is a multiple of 2 but not a multiple of 3 or 4Possible values of n = 10, 14, 22..... @n=10 : (n + 6)(n + 8)(n + 10) = 16*18*20 i.e. Divisible by 24, 32 and 96 all @n=14 : (n + 6)(n + 8)(n + 10) = 20*22*24 i.e. Divisible by 24, 32 and 96 all @n=22 : (n + 6)(n + 8)(n + 10) = 28*30*32 i.e. Divisible by 24, 32 and 96 all Answer: Option E Why does not your possible values include 2? since 2 is also a multiple of 2. 2 also is a possible value and with value 2, the expression become 8*10*12 which is again divisible by all (I.e.24, 32 and 96) hence answer remains same. However I wish to thank you here and want to admit that not mentioning 2 was a mistake done on my part which made me use bigger values to check the divisibility expression. Smaller the values you check, easier it is for you to solve the question. So never miss smallest possible values and never check values randomly. I hope this helps!!!
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Sep 2009
Posts: 51082

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
20 Sep 2015, 08:13
Bunuel wrote: If a positive even number n is not divisible by 3 or 4, then the product (n + 6)(n + 8)(n + 10) must be divisible by which of the following?
I. 24 II. 32 III. 96
A. None B. I only C. II only D. I and II only E. I, II, and III VERITAS PREP OFFICIAL SOLUTION:This question offers several constraints for the possible values of n, and missing any one of those key traits will likely cost you the question. N must be: * Positive * Even * Not divisible by 3 * Not divisible by 4 As this question was discussed by aspiring MBA students in a forum thread earlier this week, the most common reason for someone to miss it was that they missed that small word “even”; they’d plug in a number like 1 or 5 for n – numbers that ARE NOT possible given the constraints – and incorrectly believe that the answer is E. In actuality, however, these constraints taken together mean that the only possible values for n are numbers like: 2, 10, 14, 22, 34… And for these numbers, the product of (n+6)(n+8)(n+10) is divisible by all of the above. We are assured that, if n is even but not divisible by 4, then n + 6 and n + 10 WILL BE divisible by 4 (try it: 2, 6, 10, 14…all of these numbers are even but not divisible by 4; add 6 and you get 8, 12, 16, 20 —> all divisible by 4). So the product will give us: (n + 6)(n + 8)(n + 10) which is equivalent to: Divisible by 4 * Even * Divisible by 4 Providing prime factors of (at minimum): (2*2)(2)(2*2) –> the product must be divisible by 2^5. And because we have three consecutive even integers, exactly one will be divisible by 3 (try it: 2, 4, 6, 8, 10, 12, 14, 16, 18… – every third value is divisible by 3). So we know that the product is divisible by 3*2^5, and to be divisible by I, II, and III we need: 24: 3*2^3 (check!) 32: 2^5 (check!) 96: 3*2^5 (check!)
_________________
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



Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
28 Oct 2016, 05:05
Let’s focus on one restriction. N is not divisible by 4. That means N has only one factor of 2. Now let’s represent N as 2x (where x is any prime factor except 3 and 2). We have (2x+6)(2x+8)(2x+10). Now take common factor 2. We’ll have: 2^3(x+3)(x+4)(x+5)=8(x+3)(x+4)(x+5) Now we know that this product is divisible by 8. Let’s check the divisibility of the remaining part (x+3)(x+4)(x+5) Also notice that because we have factored out 2s all remaining Xs are now odd. In this case odd+3 and odd+5 are both even, and we know that this product is also divisible by 4. Now, because we have 3 consecutive numbers, one of these numbers in any case will be a multiple of 3 (you can check this by yourself by plugging in any values). So this product is also divisible by 3. Now let’s check available options. 24=8*3. After cancelling 8 the remaining part is divisible by 3. 32=8*4. Remaining part is divisible by 4. 96=8*4*3. Same logic. Divisible by 8, 3 and 4. Answer E



Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 505
Location: India

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
01 Mar 2017, 01:59
We cross check few of the numbers like 0, 2, 10, 14….. We can see that the outcome for the product is divisible by 24,32,96. Hence Option E is the answer
_________________
GMAT Mentors



Senior Manager
Joined: 04 Oct 2015
Posts: 259
Location: Viet Nam
Concentration: Finance, Economics
GPA: 3.56

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
13 Apr 2017, 17:05
Let n = 2k, n is not divisible by 3 and 4 > k is not divisible by 3 and 2 > k is odd (n+6)(n+8)(n+10) = (2k+6) (2k+8)(2k+10) = 2^3(k+3)(k+4)(k+5) We have (k+3)(k+4)(k+5) is the product of 3 consecutive integers > (k+3)(k+4)(k+5) is divisible by 3. Futhermore, k is odd > (k+3) and (k+5) are even > (k+3)(k+4)(k+5) is divisible by 2^2. In sum, (n+6)(n+8)(n+10) is divisible by 2^5 and 3 > (n+6)(n+8)(n+10) is divisible by 24, 32 and 96 Hence, E
_________________
Do not pray for an easy life, pray for the strength to endure a difficult one  Bruce Lee



Intern
Joined: 03 Jun 2012
Posts: 1

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
13 Apr 2017, 19:34
When you first look at this question, you must identify the numbers which are positive, even and not multiple of 4 or 3 which are 2, 10, 14, and 22 and so on. Looking at these numbers you will recognize that each number can have exactly one 2 when being factorized. For example 2>2, 10>2*5, 14>2*7 and so on. There is a number property that whenever a number which exactly have one 2 adds into any other number which also exactly have one 2, their sum have at least two 2s. So based on this property look at (n+6) >implies it will have at least two 2 (prime factorize n you will have one 2 and prime factorize 6 you will have one 2 so property applies over it that sum of n and 6 will have at least two 2s when factorized) (n+10) >implies it will have at least two 2 (n+8)>Property does not apply over this as 8 have more than one 2 when factorized. However you can imply that (n+8) at lease have one 2 as this is an even number anyway. (n+6)(n+8)(n+10) >this combine expression indicates three consecutive even numbers. So this means this will have at least one 3. Now you have everything just put into it (n+6)(n+8)(n+10) >(2^2) 2 (2^2) 3 so it implies you can have 3*2^5 at maximum in answer choices. So when factories you will find no number in denominator exceeds than this.



NonHuman User
Joined: 09 Sep 2013
Posts: 9102

Re: If a positive even number n is not divisible by 3 or 4, then the produ
[#permalink]
Show Tags
24 Aug 2018, 10:08
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a positive even number n is not divisible by 3 or 4, then the produ &nbs
[#permalink]
24 Aug 2018, 10:08






