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:

Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

03 Dec 2007, 09:01

5

This post received KUDOS

21

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

58% (02:30) correct
42% (01:57) wrong based on 593 sessions

HideShow timer Statistics

Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?

for 14 size of carton: 14=12+2(empty), 4*3+2(empty)
for 16 size of carton: 16=12+4(empty), 4*4+0(empty) for 20 size of carton: 20=12+8(empty), 4*5+0(empty)

Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?

a) 12 b) 15 c) 20 d) 24 e) 40

I tried solving this by dividing the volume of this box by the volume of this cylinder, however, it didn't work cause i got roughly 30, while the OA is C. Can anyone show me how? would really appreciate it!

Diameter of can = 4
We can fill max. cans when the height is 14 and the base is 20 by 16.
This is because:
if base is 14 by 16 then we can fit a max of 14/4 * 16/4 = 12 cans.
if base is 14 by 20 then we can fit a max of 14/4 * 20/4 = 15 cans.
if base is 20 by 16 or 16 by 20 then we can fit a max of 20/4 * 16/4 = 20 cans.

Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?

a) 12 b) 15 c) 20 d) 24 e) 40

I tried solving this by dividing the volume of this box by the volume of this cylinder, however, it didn't work cause i got roughly 30, while the OA is C. Can anyone show me how? would really appreciate it!

Never try doing these by solving for volume, it doesnt really work that way. Heres why.

We want the most cans so want to fit as many cans in the length and width as possible.

So we have 16x20 which are both divisible by 4. (diameter of the can is 4).

so we can have 4 one way and 5 another so 20 total.

And 12 inches is the height of each can so they all fit.

i drew a table: hope its correct: 14 16 20 1 4 5 3 4 1 3 1 5

the height will fit only 1 time in every dimension (12 apears only once in 14/16/20) and the 4=d will apear 3 times in 14 and 4 times in 16 and 5 times in 20

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

26 Aug 2012, 23:45

2

This post received KUDOS

Experts, one clarification - If I modify the question little bit and let the new dimensions be 16* 20 * 16 then we can obviously place 20 cylinders as above on the 16*20 base. Now, there will be 4 inches left in the height of the cuboid and we can place more cylinders in horizontal position over the vertical ones.

Please clarify that shall we consider these extra ones - y/n _________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ MGMAT 6 650 (51,31) on 31/8/11 MGMAT 1 670 (48,33) on 04/9/11 MGMAT 2 670 (47,34) on 07/9/11 MGMAT 3 680 (47,35) on 18/9/11 GMAT Prep1 680 ( 50, 31) on 10/11/11

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

27 Aug 2012, 12:00

1

This post received KUDOS

catfreak wrote:

Experts, one clarification - If I modify the question little bit and let the new dimensions be 16* 20 * 16 then we can obviously place 20 cylinders as above on the 16*20 base. Now, there will be 4 inches left in the height of the cuboid and we can place more cylinders in horizontal position over the vertical ones.

Please clarify that shall we consider these extra ones - y/n

I agree with you. There will be room for 6 cans I think. However, you have to consider that there are some industrial and safety restrictions _________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

for 14 size of carton: 14=12+2(empty), 4*3+2(empty) for 16 size of carton: 16=12+4(empty), 4*4+0(empty) for 20 size of carton: 20=12+8(empty), 4*5+0(empty)

You have to find the side of the box with the biggest area. In that side you will place the bottoms of the cans.

Is it true always that selecting the face with biggest area will result in max cans fit inside the carton?

Jaisri wrote:

walker wrote:

C.

for 14 size of carton: 14=12+2(empty), 4*3+2(empty) for 16 size of carton: 16=12+4(empty), 4*4+0(empty) for 20 size of carton: 20=12+8(empty), 4*5+0(empty)

Can you please explain the above calculation?

Answer to your question is that it depends on the situation represented in the question. In case of cuboid, we have to keep all its dimensions(length, breadth and height) in mind. It is suggested that we visualize the situation given, when the question is about solid geometry.

E.g. In present question since it is give that height of the tennis-ball cans is 12 inches. Even if we insert the 4*5 = 20 cans inside the carton there would be some space that will remain empty. Because the height of can is only 12 inches and 2 inches of empty space will be remaining out of 14 inches height of carton. Since a can of 4 inches diameter can not be inserted in 2 inches space.

Now Visualize that you are trying to stand some cans on 20x16 carpet area and the condition is that diameter of each can is 4 inches. So for 20 inches length we can consider standing only 20/4 = 5 cans(rows). And for 16 inches breadth we can stand only 16/4 = 4 cans(columns). So total no of cans that can stand in 20x16 area is 5x4 = 20 cans. You can see the diagram below for the calculation of 20. 0 represents tennis - ball cans - 5 rows x 4 columns

0000 0000 0000 0000 0000 _________________

Thanks & Regards Yodee

‘A good plan violently executed now is better than a perfect plan executed next week.’ - General Georg S. Patton

Last edited by yodeepak on 30 Sep 2013, 01:10, edited 1 time in total.

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

27 Sep 2013, 04:33

Expert's post

6

This post was BOOKMARKED

tarek99 wrote:

Cylindrical tennis-ball cans are being packed into cartons. If each can has a radius of 2 inches and a height of 12 inches, and the dimensions of each carton are 14 inches by 16 inches by 20 inches, what is the maximum number of tennis-ball cans that can fit in each carton?

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

30 Sep 2013, 22:55

Dimensions of can = 4 inches * 12 inches. Dimensions of carton = 14 * 16 * 20 inches.

Since 16*20 will be the plane where we can get the maximum occupancy, lets fit in 4*5 cans.The height of each can is 12 inches leaving 2 inches on the top as clearance , so C

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

09 Oct 2014, 19:42

if the cylinders are fit along 16 axis, 20 will also be placed in the canton if the cans are oriented on vertical directions. So 15 cylinders along 16 and then on top of that 5 cans can be placed horizontally. same thing if we put them along 20 axis, the canton can also hold 20 cylinders.

Re: Cylindrical tennis-ball cans are being packed into cartons. [#permalink]

Show Tags

23 Jun 2015, 05:26

Jaisri wrote:

metallicafan wrote:

+1 C

You have to find the side of the box with the biggest area. In that side you will place the bottoms of the cans.

Is it true always that selecting the face with biggest area will result in max cans fit inside the carton?

No, not always true.

PareshGmat wrote:

Height of Cylindrical can = 12. This gets aligned with dimension "14" of the carton (refer it as height of the box. This will give minimum wastage)

This is NOT always true.

In this case, no matter how you orient the box, you will be able to fit 20 in the box.

If you put them vertical on the 14x16 plane, then you can fit 12, but then you can fit 8 on top = 20. If you put them vertical on the 14x20 plane, then you can fit 15, but then you can fit 5 on top = 20. If you put them vertical on the 16x20 plane, then you can fit 20, and none on top = 20.

In other scenarios it's not always equal, but it's erroneous to state that one way will give minimum wastage all the time, simply not true.

gmatclubot

Re: Cylindrical tennis-ball cans are being packed into cartons.
[#permalink]
23 Jun 2015, 05:26

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

I’m a little delirious because I’m a little sleep deprived. But whatever. I have to write this post because... I’M IN! Funnily enough, I actually missed the acceptance phone...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...