May 19 07:00 PM EDT  08:00 PM EDT Some of what you'll gain: Strategies and techniques for approaching featured GMAT topics. Sunday May 19th at 7 PM ET May 19 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Sunday, May 19th at 7 AM PT May 20 10:00 PM PDT  11:00 PM PDT Practice the one most important Quant section  Integer Properties, and rapidly improve your skills. 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.
Author 
Message 
Manager
Joined: 29 Nov 2011
Posts: 76

For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
Updated on: 04 Nov 2017, 09:00
Question Stats:
54% (02:17) correct 46% (02:15) wrong based on 124 sessions
HideShow timer Statistics
For positive integer m, the mth heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the nth triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal? (A) 33 ≤ k ≤ 40 (B) 41 ≤ k ≤ 48 (C) 49 ≤ k ≤ 56 (D) 57 ≤ k ≤ 64 (E) 65 ≤ k ≤ 72 Bunuel, can you please help with this one? Edit: This question was moved to an archive because this concept is NOT tested on the GMAT Original tags were MGMAT, Algebra, Too hard, and 700+ == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Smita04 on 24 Apr 2012, 07:20.
Last edited by bb on 04 Nov 2017, 09:00, edited 2 times in total.
Added the OA.



Math Expert
Joined: 02 Sep 2009
Posts: 55150

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
24 Apr 2012, 08:09
Smita04 wrote: For positive integer m, the mth heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the nth triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal?
(A) 33 ≤ k ≤ 40 (B) 41 ≤ k ≤ 48 (C) 49 ≤ k ≤ 56 (D) 57 ≤ k ≤ 64 (E) 65 ≤ k ≤ 72
Bunuel, can you please help with this one? It's been a long time since I've last heard about heptagonal and triangular numbers. Anyway, probably the best way would be to write down the numbers. Since the nth triangular number is the sum of the first n positive integers, then nth triangular number is given by the formulas n(n+1)/2. For example: The 1st triangular number is 1(1+1)/2=1; The 2nd triangular number is 2(2+1)/2=3=1+ 2; The 3rd triangular number is 3(3+1)/2=6=3+ 3; The 4th triangular number is 6+ 4=10; The 5th triangular number is 10+ 5=15; ... So, triangular numbers are: 1, 1+ 2=3, 3+ 3=6, 6+ 4=10, 10+ 5=15, 15+ 6=21, 21+ 7=28, 28+ 8=36, 36+ 9=45, 45+ 10= 55, 55+ 11=66, ... On the other hand, heptagonal numbers are: 1, 7, 18, 34, 55, 81, ... using (5m^2 – 3m)/2. So, as you can see the smallest triangular number that is also heptagonal is 1. Since it's not among answer choices I guess they don't consider 1, so the next one is 55. Answer: C.
_________________



Manager
Joined: 07 Sep 2011
Posts: 60
Location: United States
Concentration: Strategy, International Business
WE: General Management (Real Estate)

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
29 Apr 2012, 05:44
Hi Bunuel
Do you think this particular concept is tested on GMAT?



Math Expert
Joined: 02 Sep 2009
Posts: 55150

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
29 Apr 2012, 05:46
manjeet1972 wrote: Hi Bunuel
Do you think this particular concept is tested on GMAT? No, this concept is not tested on the GMAT.
_________________



Intern
Joined: 05 Apr 2010
Posts: 12

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
20 Apr 2013, 01:27
The triangular number = n(n+1)/2 [Sum of positive numbers].
The 1st triangular number is 1(1+1)/2=1; The 2nd triangular number is 2(2+1)/2=3=1+2; The 3rd triangular number is 3(3+1)/2=6=3+3; The 4th triangular number is 6+4=10; The 5th triangular number is 10+5=15;
So, triangular numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66......
On the other hand, heptagonal numbers are: 1, 7, 18, 34, 55, 81, ... using (5m^2 – 3m)/2.
So, the smallest triangular number that is also heptagonal is 1 which is not present in any choice. Hence, look for the next one. So the next one is 55. Only C satisfied the equation.
Answer: C.



Manager
Joined: 27 Feb 2012
Posts: 118

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
20 Apr 2013, 01:57
emmak wrote: For positive integer m, the mth heptagonal number is given by the formula (5m2 – 3m)/2. For positive integer n, the nth triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal? (A) 33 ≤ k ≤ 40 (B) 41 ≤ k ≤ 48 (C) 49 ≤ k ≤ 56 (D) 57 ≤ k ≤ 64 (E) 65 ≤ k ≤ 72
Express appreciation by pressing KUDOS. If m = 1, then the heptagonal number is (5*1^2 – 3×1)/2 = (5 – 3)/2 = 1. If m = 2, then the heptagonal number is (5*2^2 – 3×2)/2 = (20 – 6)/2 = 14/2 = 7. If m = 3, then the heptagonal number is (5*3^2 – 3×3)/2 = (45 – 9)/2 = 36/2 = 18. If m = 4, then the heptagonal number is (5*4^2 – 3×4)/2 = (80 – 12)/2 = 68/2 = 34. If m = 5, then the heptagonal number is (5*5^2 – 3×5)/2 = (125 – 15)/2 = 110/2 = 55. If m = 6, then the heptagonal number is (5*6^2 – 3×6)/2 = (180 – 18)/2 = 162/2 = 81. Using n*(n+1)/2 if n =1, triangle number is 1 if n =2, triangle number is 3 if n =3 triangle number is 6 if n =4, triangle number is 10 if n =5, triangle number is 15 if n =6 triangle number is 21 if n=7, triangle number is 28 if n = 8, triangle number is 36 if n =9, triangle number is 45 if n = 10 triangle is 55.....stop... We have 55 as the answer. the target number must be 34 or 55, A or C now. Now we need to find the smallest value which will exist for both triangle and heptagonal
_________________

Please +1 KUDO if my post helps. Thank you.



Manager
Joined: 04 Mar 2013
Posts: 66
Location: India
Concentration: General Management, Marketing
GPA: 3.49
WE: Web Development (Computer Software)

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
06 Jul 2013, 08:00
Smita04 wrote: For positive integer m, the mth heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the nth triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal? m (A) 33 ≤ k ≤ 40 (B) 41 ≤ k ≤ 48 (C) 49 ≤ k ≤ 56 (D) 57 ≤ k ≤ 64 (E) 65 ≤ k ≤ 72
Bunuel, can you please help with this one? hey thanks for the beautiful question i dont know about questions of this kind till date.. thanks again a here's my approach : heptagonal numbers : 5m^2 3m from choices we can see the total range is only till 72 so first wirte down these by substituting values of k = 1,2, 3 we get 1,7, 18, 34, 5x 22/2 = 55, 27x3 we have reached till 72 out limit so we can't exceed from here now get to 2nd one (nx n+1)/2 so u can easly get 55 by keeping n = 10 and our answer is C hope this helps, please PM for any queries



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

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
21 Mar 2015, 12:45
Smita04 wrote: For positive integer m, the mth heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the nth triangular number is the sum of the first n positive integers. Which of the following is true for k, the smallest triangular number that is also heptagonal?
(A) 33 ≤ k ≤ 40 (B) 41 ≤ k ≤ 48 (C) 49 ≤ k ≤ 56 (D) 57 ≤ k ≤ 64 (E) 65 ≤ k ≤ 72
Bunuel, can you please help with this one? Another approach....though I think that solution by calculating individual series is a faster method. the mth heptagonal number = nth triangular number= k (5m^2 – 3m)/2 = n ( n+1) /2 = k (5m^2 – 3m) = n ( n+1) = 2 k n ( n+1) = 2K = Product of two consecutive integers.33 ≤ k ≤ 40 So 66 ≤2 k ≤ 80 so 8 x 9 = 72 41 ≤ k ≤ 48 So 82 ≤2 k ≤ 96 so 9 x10 = 90 49 ≤ k ≤ 56 So 98 ≤2 k ≤ 112 so 10 x 11 =110 57 ≤ k ≤ 64 So 114≤ 2k ≤ 128 nothing lies in between.... 65 ≤ k ≤ 72 So 130≤ 2k ≤ 144 so 11 x 12 =132 so now we have to check ( cumbersome ... but easy.) 5m^2 – 3m 2 k = 0 The only value of 2k that satisfies the above equation is 110. So K= 55 Hence, C.
_________________
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



Senior Manager
Joined: 24 Nov 2015
Posts: 498
Location: United States (LA)

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
14 May 2016, 14:31
What do you mean exactly by the terms ' heptagonal number ' and ' triangular number ' ?



NonHuman User
Joined: 09 Sep 2013
Posts: 10949

Re: For positive integer m, the mth heptagonal number is given
[#permalink]
Show Tags
11 Sep 2017, 04:19
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. == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
_________________




Re: For positive integer m, the mth heptagonal number is given
[#permalink]
11 Sep 2017, 04:19






