May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th. Jun 01 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

Manager
Joined: 12 Dec 2012
Posts: 217
Concentration: Leadership, Marketing
GMAT 1: 540 Q36 V28 GMAT 2: 550 Q39 V27 GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)

Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
Updated on: 26 Mar 2013, 02:14
Question Stats:
46% (02:02) correct 54% (02:10) wrong based on 377 sessions
HideShow timer Statistics
Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1I got this wrong ... Can anybody please explain?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Originally posted by TheNona on 25 Mar 2013, 10:00.
Last edited by Bunuel on 26 Mar 2013, 02:14, edited 1 time in total.
Renamed the topic and edited the question.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9238
Location: Pune, India

Re: Challenge Problem from MGMAT: Consecutive Positive Madness
[#permalink]
Show Tags
25 Mar 2013, 21:45
TheNona wrote: This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 I got this wrong ... Can anybody please explain? There are lots of properties of numbers and GMAT does not expect you to know them. So a question that appears of GMAT must be solvable without knowing the properties. So think hard about what you know and what you can apply. Use pattern recognition. Try some numbers to start off: 1+2 = 3 2+3 = 5 3+4 = 7 ok, so is there a pattern here? We are getting all odd numbers. 3, 5, 7, 9, 11 etc. Every odd number can be written as sum of two consecutive numbers. Why? Say an odd number is N. When you divide it by 2, you get half of it which has a .5. You take the integer above it and below it and they will add up to give N e.g. N = 11. 11/2 = 5.5 so take numbers 5 and 6 and they will add to give 11. Why? because 5.5 is the arithmetic mean of 2 consecutive numbers:5 and 6. Takeaway: Every odd number can be written as sum of two consecutive integers. So rule out (A), (C) and (E). Now, try to sum up three consecutive numbers. 1+2+3 = 6 2+3 +4 = 9 (ignore odd numbers so we have already dealt with them) 3+4+5 = 12 4+5+6 = 15 5+6+7 = 18 6+7+8 = 21 7+8+9 = 24 You are getting all multiples of 3. The important thing is that no multiple of 3 is getting skipped. You are getting all of them. Hence we can represent all multiples of 3 as sum of 3 numbers. Hence (D) is also out since it is a multiple of 3. Now think why? Sum of three consecutive integers is given by (n1) + n + (n + 1) = 3n Takeaway: Sum of any three consecutive numbers will be a multiple of 3. Hence answer must be (B) i.e. 4^6
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Manager
Joined: 12 Mar 2012
Posts: 80
Location: India
Concentration: Technology, Strategy
GPA: 3.2
WE: Information Technology (Computer Software)

Re: Challenge Problem from MGMAT: Consecutive Positive Madness
[#permalink]
Show Tags
25 Mar 2013, 10:32
Every natural number not of the form 2^k for some natural number k can be written as the sum of two or more consecutive positive integers. Hence answer is B. I solved this question manually but later found on internet that numbers which can be expressed as 2^n, n is a natural number, cannot be represented as sum of 2 or more consecutive numbers.
Please give a kudo if you like my explanation.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: Challenge Problem from MGMAT: Consecutive Positive Madness
[#permalink]
Show Tags
25 Mar 2013, 22:23
TheNona wrote: This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 We know that the sum of consecutive integers is :S = n/2(f+l) > Here n is the number of terms and f and l are the first and last terms respectively. Now, we have been told that n>=2. We can have only the following cases : f = odd, l = odd, n = (oddodd)+1 = odd. Thus, S = odd*even/2. f = odd, l = even, n = (evenodd)+1 = even. S = odd.even/2. Similarly, for the other two combinations also, the sum S = odd*even/2. Now, out of the given options, all the options can be in this pattern except 4^6 = 2^12. B.
_________________



Intern
Joined: 16 Jan 2013
Posts: 20

Re: Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
04 Apr 2013, 08:44
jbisht wrote: TheNona wrote: Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1I got this wrong ... Can anybody please explain? Is this a 700 level question ? answer simply depends upon logic of even and odd number 4^(any Number) = will never be odd



Manager
Status: single
Joined: 19 Jan 2015
Posts: 85
Location: India
GPA: 3.2
WE: Sales (Pharmaceuticals and Biotech)

Re: Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
13 Sep 2015, 18:13
whenever if you sum two consecutive positive integers, one is odd another one is even, sum always will be odd. so we can easily take away options A ,C and E beacuse all are odd numbers . Whenever if we power odd numbers how many times sum is odd.
Now remaining is 4^6and 6^4. both are even numbers if you power it , its sum always even.
Now if you sum two numbers is odd.if you sum three numbers sum can be even or odd. But here sum of even power numbers is even. any sum of three numbers is divisible by 3.
Take sum of 4^6 and 6^4.
first take 6^4 is 36*36. both numbers are divisible by3.
Now look 4^6. sum is 16*16*16. all three numbers not divisibly by 3.
So option B is not a sum of consecutive numbers..



Senior Manager
Joined: 01 Nov 2013
Posts: 289
WE: General Management (Energy and Utilities)

Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
03 Apr 2016, 08:47
Any sum of any number of consecutive integers will always have an odd factor other 1 . Hence, B is the answer. because B does not have any odd factor other than 1.
_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.
I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.Mohammad Ali



Manager
Joined: 01 Sep 2016
Posts: 192

Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
24 Sep 2017, 00:44
OFFICIAL SOLUTIONF FROM MANHATTANThe problem seeks a quantity that cannot be a sum of the type described. Process of elimination, then, will likely be an efficient solution method. Specifically, if an answer choice can be shown to be the sum of two or more consecutive positive integers, then that answer can be eliminated. One approach: Test Cases The problem specifically discusses the sum of two or more consecutive positive integers. Start with the simplest possibility: the sum of two consecutive positive integers. 1 + 2 = 3 2 + 3 = 5 3 + 4 = 7 What’s the pattern? First, any two consecutive positive integers will sum to an add number. Second, any odd sum greater than 1 can be created (the sums will continue to increase in this manner – 3, 5, 7, 9, 11, … – forever). Therefore, any odd number greater than 1 can be created by adding together two consecutive positive integers. Answers A, C, and E all represent odd numbers; eliminate them. Try the next simplest case: the sum of three consecutive positive integers. 1 + 2 + 3 = 6 2 + 3 + 4 = 9 3 + 4 + 5 = 12 What’s the pattern here? The sums can be odd or even – no apparent pattern there. Hmm. All three are multiples of 3… is that an actual pattern, though? Yes, it is! The sum of any set of three consecutive integers can also be calculated by taking the average and multiplying by the number of terms – that is, multiplying by 3. So any sum of three consecutive integers will be a multiple of 3. As a result, any multiple of 3 (starting with 6) can be created by finding the sum of the appropriate set of three consecutive positive integers. Answer D represents a multiple of 3; eliminate it. By process of elimination, the only remaining answer is B. The correct answer is B.
_________________
we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender!



Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
15 Dec 2017, 21:06
TheNona wrote: Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1I got this wrong ... Can anybody please explain? Let, the 2 consecutive integers be a, a +d and 3 consecutive integers be ad, a , a+d Now, \(3^7 , 5^5 & 7^3\) can be sum of 2 Consecutive Integers for d =1 in 2a + d equation. The confusion here will be for \(4^6 & 6^4\)as we cant decide with 2a+d equation. Lets take 3 consecutive integers ad, a, a+d 3a = \(4^6 & 6^4\) .. In this only \(6^4\) is divisible. Hi Bunuel & chetan2u, Can you please confirm if the above approach is correct to solve the problem or am I missing something??
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Math Expert
Joined: 02 Aug 2009
Posts: 7686

Re: Which of the following cannot be the sum of two or more cons
[#permalink]
Show Tags
16 Dec 2017, 06:13
rahul16singh28 wrote: TheNona wrote: Which of the following cannot be the sum of two or more consecutive positive integers? (A) 3^7 (B) 4^6 (C) 5^5 (D) 6^4 (E) 7^3 This Week's Challenge Problem from MGMAT : "Consecutive Positive Madness" https://www.manhattangmat.com/challenge_thisweek.cfm?submitted=1I got this wrong ... Can anybody please explain? Let, the 2 consecutive integers be a, a +d and 3 consecutive integers be ad, a , a+d Now, \(3^7 , 5^5 & 7^3\) can be sum of 2 Consecutive Integers for d =1 in 2a + d equation. The confusion here will be for \(4^6 & 6^4\)as we cant decide with 2a+d equation. Lets take 3 consecutive integers ad, a, a+d 3a = \(4^6 & 6^4\) .. In this only \(6^4\) is divisible. Hi Bunuel & chetan2u, Can you please confirm if the above approach is correct to solve the problem or am I missing something?? Hi.. You are absolutely correct in your approach.. Why 4^6 cannot be put as SUM of two consecutive integers.. Because you cannot add 2 or more integers to get any pure power of 2.. check 2, 4, 8 , 16 ...and so on
_________________




Re: Which of the following cannot be the sum of two or more cons
[#permalink]
16 Dec 2017, 06:13






