GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Dec 2018, 01:42

Close

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
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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Happy Christmas 20% Sale! Math Revolution All-In-One Products!

     December 20, 2018

     December 20, 2018

     10:00 PM PST

     11:00 PM PST

    This is the most inexpensive and attractive price in the market. Get the course now!
  • Key Strategies to Master GMAT SC

     December 22, 2018

     December 22, 2018

     07:00 AM PST

     09:00 AM PST

    Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

Four cylindrical cans each with a radius of 2 inches are placed on th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51301
Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 21:54
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

29% (01:36) correct 71% (01:40) wrong based on 64 sessions

HideShow timer Statistics

Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches?

(A) 64

(B) 32

(C) 30

(D) 20

(E) 16

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 842
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 22:37
Bunuel wrote:
Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches?

(A) 64

(B) 32

(C) 30

(D) 20

(E) 16


'the four sides of the box bulge slightly' means that the cans take up a slightly larger area than that of the box.
So, we'll look at the extreme of the range - a Logical approach.

4 cans arranged in a box on their base would be arranged in 2 rows of 2
(if they were arranged in 1 row of 4 or another non-symmetrical arrangement then there would be one side that didn't 'bulge').
Since each can has a radius of 2, this means that the cans takes up (2 cans * diameter of 4) = 8 inches.
Then, if the cans fit perfectly, the perimeter of the box would be 8*4 =32 inches.
But we know that the cans don't quite fit (the sides 'bulge') and therefore our answer is a bit less than 32.

(C), 30, is our answer.

Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required.
_________________

Image
Sign up for 7-day free trial
Image

Image

Claim your offer here.

Happy holidays!

BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:02
Bunuel wrote:
Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches?

(A) 64

(B) 32

(C) 30

(D) 20

(E) 16


diameter of can = 4

so if side of the box buiges there is one can at the end of each of the box/facing each side and for it to bulge the box should be able to accommodate 8 inches in length atleast

imo 8 is the side of the square and perimeter = 32

(B) looks good

but considering bulge of the box i.e takes more area

a side of 7.5 can suffice


ps - considering the bulge is caused by the exterior of a can went it C
at first i thought it'd be B
BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:03
DavidTutorexamPAL wrote:
Bunuel wrote:
Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches?

(A) 64

(B) 32

(C) 30

(D) 20

(E) 16


'the four sides of the box bulge slightly' means that the cans take up a slightly larger area than that of the box.
So, we'll look at the extreme of the range - a Logical approach.

4 cans arranged in a box on their base would be arranged in 2 rows of 2
(if they were arranged in 1 row of 4 or another non-symmetrical arrangement then there would be one side that didn't 'bulge').
Since each can has a radius of 2, this means that the cans takes up (2 cans * diameter of 4) = 8 inches.
Then, if the cans fit perfectly, the perimeter of the box would be 8*4 =32 inches.
But we know that the cans don't quite fit (the sides 'bulge') and therefore our answer is a bit less than 32.

(C), 30, is our answer.

Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required.


I went with C as well initially .. but does the bulge definitetly mean it's going to take more area?
BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:06
DavidTutorexamPAL wrote:
Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required.


even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 842
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:08
Hatakekakashi wrote:

I went with C as well initially .. but does the bulge definitetly mean it's going to take more area?


I think so... if the sides 'bulge' e.g are pressed outward it is implied that the cans need more space then they have.
To be fair this question is more about English than about math, not a standard question IMO
_________________

Image
Sign up for 7-day free trial
Image

Image

Claim your offer here.

Happy holidays!

BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:15
1
DavidTutorexamPAL wrote:
Hatakekakashi wrote:

I went with C as well initially .. but does the bulge definitetly mean it's going to take more area?


I think so... if the sides 'bulge' e.g are pressed outward it is implied that the cans need more space then they have.
To be fair this question is more about English than about math, not a standard question IMO


I understand.. I think the word bulge makes all the difference


Regards,
HK
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 842
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 18 Feb 2018, 23:47
1
Hatakekakashi wrote:
DavidTutorexamPAL wrote:
Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required.


even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge


So I did the math and actually you would lose very little height by arranging in a triangle, the answer would still be (C).
Basically if you put two cans on the base of the box = the base of the triangle they still need 8 inches of space for width.
And if you put the third right above them in the middle then you lose about 0.54 inches in total length giving a length of about 7.46.
So a 30-inch-perimeter box with a side of 7.5 inches would still likely bulge on all sides and at any rate is the only relevant answer.

Since we're on the topic, consider an arrangement where two cans are in opposite corners and are tangent to each other.
The other two cans are on top of them.
We have no information on the total height of the box vs. height of the cans so this could work.
Then the side of the minimal square is 4 + 2*sqrt(2) and the perimieter is about 27.3 inches
This could also be made to bulge on 4 sides quite easily by decreasing the perimeter slightly (but there is no relevant answer).

Anyways, for anyone reading please note that the above is not really relevant for your exam, feel free to skip over it :)
_________________

Image
Sign up for 7-day free trial
Image

Image

Claim your offer here.

Happy holidays!

BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 19 Feb 2018, 00:51
DavidTutorexamPAL wrote:
Hatakekakashi wrote:
DavidTutorexamPAL wrote:
Bunuel, just for the sake of nitpicking, why can't the cans be arranged in a triangle with another one on top? They would still all be 'on their bases', as required.


even though the question is not directed towards me I think if it's a triangle all 4 sides of the box won't bulge


So I did the math and actually you would lose very little height by arranging in a triangle, the answer would still be (C).
Basically if you put two cans on the base of the box = the base of the triangle they still need 8 inches of space for width.
And if you put the third right above them in the middle then you lose about 0.54 inches in total length giving a length of about 7.46.
So a 30-inch-perimeter box with a side of 7.5 inches would still likely bulge on all sides and at any rate is the only relevant answer.

Since we're on the topic, consider an arrangement where two cans are in opposite corners and are tangent to each other.
The other two cans are on top of them.
We have no information on the total height of the box vs. height of the cans so this could work.
Then the side of the minimal square is 4 + 2*sqrt(2) and the perimieter is about 27.3 inches
This could also be made to bulge on 4 sides quite easily by decreasing the perimeter slightly (but there is no relevant answer).

Anyways, for anyone reading please note that the above is not really relevant for your exam, feel free to skip over it :)



Thanks for taking your time out to do the math. in any case 30 should be fine then

but as you've mentioned that the height of the can is not mentioned and considering the cans resting on the lateral surface i.e like this - instead of | then the answer could also not be determined ( discussion not related to the question)

don't you think so?
examPAL Representative
User avatar
G
Joined: 07 Dec 2017
Posts: 842
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 19 Feb 2018, 01:00
Hatakekakashi wrote:
Thanks for taking your time out to do the math. in any case 30 should be fine then

but as you've mentioned that the height of the can is not mentioned and considering the cans resting on the lateral surface i.e like this - instead of | then the answer could also not be determined ( discussion not related to the question)

don't you think so?


WRT to the question then the cans are placed on their bases so I don't think they can be placed on their lateral surface.
In general I agree with you, without information on the can's height the problem is unsolvable.
There are potentially all kinds of different solutions including a mix of 'on the side' and 'on the base'

If any of you are incredibly bored, consider this a spare time project to try at home!
Take a bunch of cans and play around with them, see how many you can cram into a box.
_________________

Image
Sign up for 7-day free trial
Image

Image

Claim your offer here.

Happy holidays!

BSchool Forum Moderator
User avatar
P
Joined: 07 Jan 2016
Posts: 832
Location: India
GMAT 1: 710 Q49 V36
Reviews Badge
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 19 Feb 2018, 01:08
DavidTutorexamPAL wrote:

If any of you are incredibly bored, consider this a spare time project to try at home!
Take a bunch of cans and play around with them, see how many you can cram into a box.


hahaha :D I weigh 270 pounds so i guess can cram a lot of them ;)

Regards,
HK
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Four cylindrical cans each with a radius of 2 inches are placed on th  [#permalink]

Show Tags

New post 21 Feb 2018, 13:21
Bunuel wrote:
Four cylindrical cans each with a radius of 2 inches are placed on their bases inside an open square pasteboard box. If the four sides of the box bulge slightly, which of the following could be the internal perimeter of the base of the box, expressed in inches?

(A) 64

(B) 32

(C) 30

(D) 20

(E) 16


The 4 cans will be placed on the square base of the box in the 2-by-2 formation. Since the total length of the diameters of 2 cans is 4 + 4 = 8, the cans would fit in a square with perimeter 8 x 4 = 32 without any bulging. Since all the sides of the box bulge slightly, the perimeter of the base of the box should be slightly less than 32. A possible value is 30.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: Four cylindrical cans each with a radius of 2 inches are placed on th &nbs [#permalink] 21 Feb 2018, 13:21
Display posts from previous: Sort by

Four cylindrical cans each with a radius of 2 inches are placed on th

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.