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:

A marching band of 240 musicians are to march in a [#permalink]

Show Tags

20 Nov 2005, 20:36

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

56% (02:09) correct 44% (02:08) wrong based on 162 sessions

HideShow timer Statistics

A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

20 Nov 2005, 20:57

TeHCM wrote:

A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

(1) 3 (2) 4 (3) 5 (4) 6 (5) 8

8<=t<=30 and t must be a factor of 240. There're 8 possible values of t: 8,10,12,15,16,20,24,30 ---> 8 possible rectangular formations.

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

20 Nov 2005, 21:15

TeHCM wrote:

A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

(1) 3 (2) 4 (3) 5 (4) 6 (5) 8

find the exact multiple of integers greater than 8 but smaller than 30.
240 = 8x30
240 = 10x24
240 = 12x20
240 = 15x16
240 = just revers the above multiples ony by one = 16x15
240 = 20x12
240 = 24x10
240 = 30x8

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

21 Nov 2005, 00:38

The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

23 Nov 2005, 05:22

krisrini wrote:

The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)} Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with. {(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)} Hence 8.

Kristrini> you get an A+ for the extra effort!

Agreed that the total # combinations are 8: (8X30) (10X24) (12X20) (15X16) and their four inverses.

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

25 Oct 2015, 05:03

I also did factor approach and got right.

However, OA also writes this :-

Straightforward Math is the best route to take to solve this question. Since s × t must equal 240, s and t must be factors of 240. Find the prime factors that make up 240:

240 = 2×2×2×2×3×5.

Now find the combinations of these factors that give you s × t = 240, where 8≤t ≤30: 8×30, 10×24, 12×20, 15×16, 16×15, 20×12, 24×10 and 30×8, a total of 8 combinations.

Note: if you are still wondering how we found these factors using the prime factors, think about it this way. 8×30 = (2×2×2) × (2×3×5). 10×24 = (2×5) × (2×2×2×3). Thus, all of these combinations use all six prime factors. It's just a matter of how you can arrange them.

SO, can it be done via some permutation and combination approach. I need to select some or none from all these factors I guess. Any clue ?

Straightforward Math is the best route to take to solve this question. Since s × t must equal 240, s and t must be factors of 240. Find the prime factors that make up 240:

240 = 2×2×2×2×3×5.

Now find the combinations of these factors that give you s × t = 240, where 8≤t ≤30: 8×30, 10×24, 12×20, 15×16, 16×15, 20×12, 24×10 and 30×8, a total of 8 combinations.

Note: if you are still wondering how we found these factors using the prime factors, think about it this way. 8×30 = (2×2×2) × (2×3×5). 10×24 = (2×5) × (2×2×2×3). Thus, all of these combinations use all six prime factors. It's just a matter of how you can arrange them.

SO, can it be done via some permutation and combination approach. I need to select some or none from all these factors I guess. Any clue ?

They use the terms "combinations" and "arrange" in a very generic manner. You cannot use any permutation and combination formulas as such. Since t has to be between 8 and 30, some brute force will be required.
_________________

Re: A marching band of 240 musicians are to march in a [#permalink]

Show Tags

22 Dec 2017, 14:47

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.
_________________