Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59075

If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
21 Oct 2014, 08:35
Question Stats:
75% (01:08) correct 25% (00:52) wrong based on 433 sessions
HideShow timer Statistics
Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1729
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
21 Oct 2014, 19:33
1 + 2 + 3 + 4 + 5 + 6 = 21 = Divisible by 3 2 + 3 + 4 + 5 + 6 + 7 = 20 + 7 = 27 = Divisible by 3 3 + 4 + 5 + 6 + 7 + 8 = 25 + 8 = 33 = Divisible by 3 The consecutive addition will just increase by 6 each time Answer = A One more method:Addition of six consecutive integers = odd + even + odd + even + odd + even = (odd + odd) + (even + even + even) + odd = even + even + odd = even + odd = odd The result will ALWAYS be ODD. So it cannot be divisible by 4 & 6. Answer = 3 = A
_________________
Kindly press "+1 Kudos" to appreciate




Senior Manager
Joined: 13 Jun 2013
Posts: 259

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
21 Oct 2014, 10:32
Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III let the six numbers be k2, k1, k, k+1, k+2, k+3 then, there sum will be 6k+3 3(2k+1),which is clearly a multiple of 3. Also, 2k+1 will always be odd. thus the sum will never be divisible by 2. hence option A



Manager
Joined: 21 Jan 2014
Posts: 61
WE: General Management (NonProfit and Government)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
21 Oct 2014, 23:11
Sum of six consecutive integers = 6y + 15 =3(2y+5) =x
Clearly, there are two important observations from above information : 1) x is a multiple of 3 2) (2y + 5) is an odd term
Therefore, the most relevant option to the question is option A.



Manager
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 121
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23 GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
01 Sep 2015, 07:16
Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III 3,2,1,0,1,2 or 2,1,0,1,2,3 Only option A



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15454
Location: United States (CA)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
03 Sep 2015, 22:41
Hi All, On Test Day, the answers to Roman Numeral questions are almost always written in a way so that you can avoid some of the 'work.' Here, you should notice that at least 1 of the Roman Numerals appears in each answer, so we can use that to our advantage. We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by.... Let's TEST VALUES.... IF we use the 6 consecutive integers: 1, 2, 3, 4, 5 and 6, then the sum = 21. 21 is divisible by 3 21 is NOT divisible by 4 21 is NOT divisible by 6 There's only one answer that 'fits' with these facts, so there's no additional work required... Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Intern
Joined: 12 Mar 2016
Posts: 9

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
28 Nov 2016, 09:29
Sum of six consecutive numbers = 6 (6 + 1 ) \ 2 = 21 21 is divided by 3, not by 4 and 6 Answer : A



Manager
Joined: 02 Jan 2017
Posts: 67
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
11 Dec 2017, 04:02
I understand this can be done by picking numbers and testing them out.
But can someone clarify this concept. It is said every 2 numbers, atleast one number is divisible by 2, for every 3 number atleast one number is divisble by 3. and so on so forth . Using this concept. Should the answer not be E?
It says consecutive six integers? so by the concept the factors should include 6 ,4 and 3.
I am sure i am making a very stupid mistake here. Kindly correct me where i am wrong.



Math Expert
Joined: 02 Sep 2009
Posts: 59075

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
11 Dec 2017, 05:03
mtk10 wrote: I understand this can be done by picking numbers and testing them out.
But can someone clarify this concept. It is said every 2 numbers, atleast one number is divisible by 2, for every 3 number atleast one number is divisble by 3. and so on so forth . Using this concept. Should the answer not be E?
It says consecutive six integers? so by the concept the factors should include 6 ,4 and 3.
I am sure i am making a very stupid mistake here. Kindly correct me where i am wrong. You should consider the sum of the numbers. What I mean that, yes from two consecutive integers one must be divisible by 2 (even) but does is mean that the sum of two consecutive integers is divisible by 2? No, for example, 1 + 2 = 3, which is not divisible by 2. If x is the sum of six consecutive integers, then x is divisible by which of the following:I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III (n  2) + (n  1) + n + (n + 1) + (n + 2) + (n + 3) = 6n + 3 = 3(2n + 1) = 3*odd. So, the sum of six consecutive integers, is an odd multiple of 3: ..., 9, 3, 3, 9, 15, ... It will always be divisible by 3 but not by 2 or any other multiple of 2. Answer: A. Hope it's clear.
_________________



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15454
Location: United States (CA)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
11 Dec 2017, 15:20
mtk10 wrote: I understand this can be done by picking numbers and testing them out.
But can someone clarify this concept. It is said every 2 numbers, atleast one number is divisible by 2, for every 3 number atleast one number is divisble by 3. and so on so forth . Using this concept. Should the answer not be E?
It says consecutive six integers? so by the concept the factors should include 6 ,4 and 3.
I am sure i am making a very stupid mistake here. Kindly correct me where i am wrong. Hi mtk10, You're "mixing" two different ideas that are NOT logically linked. When dealing with 2 consecutive integers, ONE of the integers will be evenly divisible by 2. When dealing with 3 consecutive integers, ONE of the integers will be evenly divisible by 3 and AT LEAST ONE will be evenly divisible by 2. When dealing with 4 consecutive integers, ONE of the integers will be evenly divisible by 4, TWO of the integers will be evenly divisible by 2 and AT LEAST ONE of the integers will be evenly divisible by 3. Etc. However, this question is asking about the SUM of six consecutive integers  and that is a different concept entirely. The concept involved here is "the SUM of ANY 3 consecutive integers will be evenly divisible by 3", so since we're dealing with six consecutive integers, we're dealing with two 'groups' of 3 consecutive integers  so that SUM will also be evenly divisible by 3. GMAT assassins aren't born, they're made, Rich
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



Veritas Prep GMAT Instructor
Joined: 15 Jul 2015
Posts: 110
GPA: 3.62
WE: Corporate Finance (Consulting)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
11 Dec 2017, 16:07
mtk10 wrote: I understand this can be done by picking numbers and testing them out.
But can someone clarify this concept. It is said every 2 numbers, atleast one number is divisible by 2, for every 3 number atleast one number is divisble by 3. and so on so forth . Using this concept. Should the answer not be E?
It says consecutive six integers? so by the concept the factors should include 6 ,4 and 3.
I am sure i am making a very stupid mistake here. Kindly correct me where i am wrong. I tihnk you are mistakenly inferring that you can "factor" these numbers out of the SUM. You would be correct if the question said the "product of six consecutive integers". But, when adding the integeres, instead of multiplying them, you cannot simply factor out each individual integers.
_________________



Manager
Joined: 02 Jan 2017
Posts: 67
Location: Pakistan
Concentration: Finance, Technology
GPA: 3.41
WE: Business Development (Accounting)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
12 Dec 2017, 03:43
EMPOWERgmatRichC wrote: mtk10 wrote: I understand this can be done by picking numbers and testing them out.
But can someone clarify this concept. It is said every 2 numbers, atleast one number is divisible by 2, for every 3 number atleast one number is divisble by 3. and so on so forth . Using this concept. Should the answer not be E?
It says consecutive six integers? so by the concept the factors should include 6 ,4 and 3.
I am sure i am making a very stupid mistake here. Kindly correct me where i am wrong. Hi mtk10, You're "mixing" two different ideas that are NOT logically linked. When dealing with 2 consecutive integers, ONE of the integers will be evenly divisible by 2. When dealing with 3 consecutive integers, ONE of the integers will be evenly divisible by 3 and AT LEAST ONE will be evenly divisible by 2. When dealing with 4 consecutive integers, ONE of the integers will be evenly divisible by 4, TWO of the integers will be evenly divisible by 2 and AT LEAST ONE of the integers will be evenly divisible by 3. Etc. However, this question is asking about the SUM of six consecutive integers  and that is a different concept entirely. The concept involved here is "the SUM of ANY 3 consecutive integers will be evenly divisible by 3", so since we're dealing with six consecutive integers, we're dealing with two 'groups' of 3 consecutive integers  so that SUM will also be evenly divisible by 3. GMAT assassins aren't born, they're made, Rich Thank you and all other experts for such prompt replies And yes i got to this conclusion the second i made the post lol. That its asking about SUM not the integers. Thankyou again.



SC Moderator
Status: GMAT  Pulling Quant and Verbal together
Joined: 04 Sep 2017
Posts: 240
Location: United States (OH)
Concentration: Technology, Leadership
GPA: 3.6
WE: Sales (Computer Software)

If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
13 Apr 2018, 17:26
Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III I did not use this solution to find the answer, but I should have. Very fast if the principle is memorized and fresh on your mind. As a GMAT Club Math Book Principle:  If n is even, the sum of consecutive integers is never divisible by n. Given {9,10,11,12}, we have n=4 consecutive integers. Sum is 9+10+11+12=42, which is not divisible by 4. For this problem, if the above principle was memorized, we could immediately rule out III. Then realize that 6 consecutive integers will lead to an odd number, so rule out II. Only possible answer left would be I.
_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me. How to sort questions by Topic, Difficulty, and Source: https://gmatclub.com/forum/search.php?view=search_tags



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2812

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
18 Aug 2018, 19:42
Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III If we let the six consecutive integers be 1, 2, 3, 4, 5, and 6, then x = 21. We see that x is divisible only by 3, which eliminates Roman numerals II and III. Since there is no other option that excludes both II and III, the answer must be I only. Answer: A
_________________
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.



Director
Joined: 18 Dec 2017
Posts: 684
Location: United States (KS)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
15 Oct 2019, 13:11
Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III Even if we take the least possible consecutive integers (positive) we get 1+2+3+4+5+6 as 21. 21 is only divisible by 3. So A.
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Software Tester currently in USA ( ) Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topicYou are missing on great learning if you don't know what this is: Project SC Butler



Intern
Joined: 15 May 2017
Posts: 23

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
15 Oct 2019, 15:22
TheNightKing wrote: Bunuel wrote: Tough and Tricky questions: properties of numbers. If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 3 II. 4 III. 6 A. I only B. II only C. III only D. I and III E. I, II, and III Even if we take the least possible consecutive integers (positive) we get 1+2+3+4+5+6 as 21. 21 is only divisible by 3. So A. I am confused. The given information does not say that whether this is an even consecutive, multiple of 3 consecutive, or so on... Then 0 2 4 6 8 10 should also divided by 6. Right? Am I doing any thing wrong here?



Director
Joined: 18 Dec 2017
Posts: 684
Location: United States (KS)

If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
15 Oct 2019, 16:27
Quote: I am confused. The given information does not say that whether this is an even consecutive, multiple of 3 consecutive, or so on... Then 0 2 4 6 8 10 should also divided by 6. Right? Am I doing any thing wrong here? Well, consecutive integers are consecutive. Why do you need to assume more than that? If they were even consecutive then the question will mention that.!
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Software Tester currently in USA ( ) Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topicYou are missing on great learning if you don't know what this is: Project SC Butler



Intern
Joined: 15 May 2017
Posts: 23

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
15 Oct 2019, 16:38
TheNightKing wrote: Quote: I am confused. The given information does not say that whether this is an even consecutive, multiple of 3 consecutive, or so on... Then 0 2 4 6 8 10 should also divided by 6. Right? Am I doing any thing wrong here? Well, consecutive integers are consecutive. Why do you need to assume more than that? If they were even consecutive then the question will mention that.! Please correct me If I am wrong. In data sufficiency, If a given piece of information is not given, then possibility is there. Doesn’t it apply here as well? Posted from my mobile device



Director
Joined: 18 Dec 2017
Posts: 684
Location: United States (KS)

Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
Show Tags
15 Oct 2019, 16:44
Quote: Please correct me If I am wrong. In data sufficiency, If a given piece of information is not given, then possibility is there. Doesn’t it apply here as well?
What you are saying is very broad in nature. I will take an example and try to explain. Problem Solving reads : M is the sum of 6 consecutive odd integers. That means M cannot be sum of consecutive even integers or consecutive primes. Though it can be any set of 6 consecutive odd integers (positive, negative) but cannot be other than that. Data Sufficiency question : Is M>6? Then you can fairly assume M can be anything in the world. Positive/Negative/Real/Even/Odd. But again if Let's say Statement 1 reads : M is a prime number. Then you know M is prime for a fact and nothing else. {2,3,5,7,11.......}
_________________
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long Software Tester currently in USA ( ) Learn from the Legend himself: All GMAT Ninja LIVE YouTube videos by topicYou are missing on great learning if you don't know what this is: Project SC Butler




Re: If x is the sum of six consecutive integers, then x is divisible by wh
[#permalink]
15 Oct 2019, 16:44






