For positive integer m, the m-th heptagonal number is given : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 16:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For positive integer m, the m-th heptagonal number is given

Author Message
TAGS:

### Hide Tags

Manager
Joined: 29 Nov 2011
Posts: 81
Followers: 1

Kudos [?]: 282 [3] , given: 37

For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

24 Apr 2012, 06:20
3
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

59% (03:10) correct 41% (02:17) wrong based on 107 sessions

### HideShow timer Statistics

For positive integer m, the m-th heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the n-th 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

[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2014, 00:54, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93033 [2] , given: 10541

### Show Tags

24 Apr 2012, 07:09
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
Smita04 wrote:
For positive integer m, the m-th heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the n-th 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

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 n-th triangular number is the sum of the first n positive integers, then n-th 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.

_________________
Manager
Joined: 07 Sep 2011
Posts: 64
Location: United States
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 6

Kudos [?]: 38 [0], given: 3

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

29 Apr 2012, 04:44
Hi Bunuel

Do you think this particular concept is tested on GMAT?
Math Expert
Joined: 02 Sep 2009
Posts: 36540
Followers: 7072

Kudos [?]: 93033 [0], given: 10541

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

29 Apr 2012, 04:46
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: 15
Followers: 0

Kudos [?]: 9 [0], given: 4

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

20 Apr 2013, 00:27
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.

Manager
Joined: 27 Feb 2012
Posts: 137
Followers: 1

Kudos [?]: 49 [0], given: 22

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

20 Apr 2013, 00:57
emmak wrote:
For positive integer m, the m-th heptagonal number is given by the formula (5m2 – 3m)/2. For positive integer n, the n-th 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: 03 Mar 2013
Posts: 91
Location: India
Concentration: General Management, Marketing
GPA: 3.49
WE: Web Development (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 6

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

06 Jul 2013, 07:00
Smita04 wrote:
For positive integer m, the m-th heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the n-th 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

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

hope this helps, please PM for any queries
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13430
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

08 Feb 2015, 14:44
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.
_________________
Senior Manager
Joined: 01 Nov 2013
Posts: 357
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
Followers: 6

Kudos [?]: 165 [0], given: 403

For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

21 Mar 2015, 11:45
Smita04 wrote:
For positive integer m, the m-th heptagonal number is given by the formula (5m^2 – 3m)/2. For positive integer n, the n-th 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

Another approach....though I think that solution by calculating individual series is a faster method.

the m-th heptagonal number = n-th 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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13430
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

03 Apr 2016, 08:15
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.
_________________
Director
Joined: 24 Nov 2015
Posts: 564
Location: United States (LA)
Concentration: General Management, Marketing
GMAT 1: 700 Q49 V36
GRE 1: 328 Q167 V161
Followers: 11

Kudos [?]: 25 [0], given: 222

Re: For positive integer m, the m-th heptagonal number is given [#permalink]

### Show Tags

14 May 2016, 13:31
What do you mean exactly by the terms ' heptagonal number ' and ' triangular number ' ?
Re: For positive integer m, the m-th heptagonal number is given   [#permalink] 14 May 2016, 13:31
Similar topics Replies Last post
Similar
Topics:
Given two positive numbers that the sum of two numbers is 5 times 1 12 Dec 2016, 07:05
3 m and n are positive integers. 2 09 Dec 2016, 00:54
The numbers m, n, and K are all positive integers. Given that m is a 3 27 Apr 2016, 11:00
9 If m is a positive integer, is m/24 also an integer ? 4 23 Feb 2015, 19:08
16 For every integer m from 1 to 100, inclusive, the mth term 11 04 Mar 2012, 15:18
Display posts from previous: Sort by