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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

24 Apr 2012, 07:20

3

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

59% (03:12) correct
41% (02:20) wrong based on 115 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

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

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 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; ...

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.

Re: For positive integer m, the m-th 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;

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.

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

Show Tags

20 Apr 2013, 01:57

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
_________________

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

Show Tags

06 Jul 2013, 08:00

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

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

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

Show Tags

08 Feb 2015, 15:44

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.
_________________

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

Show Tags

21 Mar 2015, 12:45

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

Bunuel, can you please help with this one?

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 ≤ 80so 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 ≤ 128nothing lies in between.... 65 ≤ k ≤ 72 So 130≤ 2k ≤ 144so 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

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

Show Tags

03 Apr 2016, 09:15

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.
_________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...