It is currently 19 Nov 2017, 19:24

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

Events & Promotions in June
Open Detailed Calendar

A cube of side 5cm is painted on all its side. If it is sliced into 1

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

Hide Tags

2 KUDOS received
Director
Director
User avatar
Joined: 16 May 2007
Posts: 547

Kudos [?]: 76 [2], given: 0

A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 09 Jul 2007, 07:26
2
This post received
KUDOS
14
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:16) correct 35% (01:45) wrong based on 445 sessions

HideShow timer Statistics

A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64
[Reveal] Spoiler: OA

Kudos [?]: 76 [2], given: 0

Manager
Manager
User avatar
Joined: 07 Feb 2007
Posts: 212

Kudos [?]: 15 [0], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 09 Jul 2007, 07:31
trahul4 wrote:
A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


D. 6*9=54. A cube has 6 sides, each of which has 9 cubes with one sides painted.
32223
21112
21112
21112
32223

Kudos [?]: 15 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 04 Jun 2007
Posts: 344

Kudos [?]: 35 [0], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 09 Jul 2007, 07:33
trahul4 wrote:
A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


9 such cubes for each of the 6 surfaces = 9 * 6 = 54 cubes. (D)

Kudos [?]: 35 [0], given: 0

Intern
Intern
avatar
Joined: 05 Apr 2007
Posts: 16

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

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 09 Jul 2007, 08:26
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

Thank you in advance.

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

Senior Manager
Senior Manager
avatar
Joined: 04 Jun 2007
Posts: 364

Kudos [?]: 110 [0], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Jul 2007, 09:49
trahul4 wrote:
A 5 cubic centimeter cube is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


are you sure it's a 5 cubic centimeter cube or is it a 5 cubic metre cube?? there should be five 1 cubic centimeter cubes when a 5 cubic centimeter cube is cut up

Kudos [?]: 110 [0], given: 0

Manager
Manager
User avatar
Joined: 07 Feb 2007
Posts: 212

Kudos [?]: 15 [0], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Jul 2007, 10:38
Andrey2010 wrote:
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

Thank you in advance.


Well. I though the cube is 5*5*5 centimeter, or the question does not make sense-- how a 5 cubic centimeter cube is divided into 1 cubic centimeter cube?

The number listed above is how many faces painted for each 1cm*1cm cube on a surface.
32223
21112
21112
21112
32223

Kudos [?]: 15 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 04 Jun 2007
Posts: 344

Kudos [?]: 35 [0], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Jul 2007, 10:46
wudy wrote:
Andrey2010 wrote:
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

Thank you in advance.


Well. I though the cube is 5*5*5 centimeter, or the question does not make sense-- how a 5 cubic centimeter cube is divided into 1 cubic centimeter cube?

The number listed above is how many faces painted for each 1cm*1cm cube on a surface.
32223
21112
21112
21112
32223


My assumption was exactly the same. I didn't think that a cube of side 5^(1/3) cm being divided into 1 cubic centimeter cubes makes sense. So, I assumed that each of the sides of the cube was 5 cm (a 5 cm cube as opposed to 5 cubic centimeter).

Kudos [?]: 35 [0], given: 0

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 27 Jul 2006
Posts: 292

Kudos [?]: 18 [2], given: 0

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Jul 2007, 22:19
2
This post received
KUDOS
There is another way to do this problem. We know that all of the squares on each side have 2 sides (or 3 sides) painted. we want to remove them.

Make a new square which represents all of these squares. 5-2(one inch from each edge)=3

3.3=9 squares on each side.

9.6 sides is 54 squares

Kudos [?]: 18 [2], given: 0

Manager
Manager
avatar
Joined: 30 Jul 2011
Posts: 113

Kudos [?]: 29 [0], given: 24

Location: United States (NJ)
Concentration: General Management, Finance
GMAT 1: 520 Q40 V21
GPA: 2.95
GMAT ToolKit User
A cube of side 5cm is painted on all of its sides. If it is [#permalink]

Show Tags

New post 01 Aug 2011, 08:23
1
This post was
BOOKMARKED
A cube of side 5cm is painted on all of its sides. If it is sliced into 1 cubic cm cubes, how many 1 cubic cm cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64

[Reveal] Spoiler:
D. This came straight from the GMAT club math review, but I'm a bit tripped up on the explanation

Kudos [?]: 29 [0], given: 24

2 KUDOS received
Manager
Manager
avatar
Joined: 14 Oct 2009
Posts: 57

Kudos [?]: 11 [2], given: 1

Location: India
Re: 3-D Cube Question [#permalink]

Show Tags

New post 01 Aug 2011, 08:30
2
This post received
KUDOS
The answer is 'D'.

A 5 cm^3 cube divided in 1cm^3 cubes = 125 cubes in total. A cube has 6 faces.
On each face, all the cubes surrounding the boundary will have more than 1 side painted, which makes total of 5+5+3+3 = 16 cubes.

So we are left with 25-16 = 9 cubes on each face (which has only 1 side painted) totaling to 9*6=54 cubes.

Kudos [?]: 11 [2], given: 1

5 KUDOS received
BSchool Thread Master
avatar
Joined: 19 Feb 2010
Posts: 390

Kudos [?]: 201 [5], given: 76

Re: 3-D Cube Question [#permalink]

Show Tags

New post 01 Aug 2011, 09:16
5
This post received
KUDOS
2
This post was
BOOKMARKED
I think the quickest way is to imagine in your mind 1 side of the cube. Understand that the border cubes will have more than one side painted, so the ones with only one side are the ones in the middle, in this case 3x3=9. Then multiply that by 6 sides. If you will make a diagram, make only one side and then multiply by 6. Don't waste the little precious time that you have.
See the picture below to understand it better. The green squares have adjacent surfaces painted. Only the blue ones have 1 side only painted.
Attachments

5cm cube.jpg
5cm cube.jpg [ 3.96 KiB | Viewed 7713 times ]

Kudos [?]: 201 [5], given: 76

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 725

Kudos [?]: 146 [0], given: 42

Re: 3-D Cube Question [#permalink]

Show Tags

New post 01 Aug 2011, 11:46
all the boundary cubes will have more than one face painted. only the center ones on each side of the larger cube, will have paint on just one side.

if we observer one face, there are 9 such cubes which have only one face painted.

so this times 6 faces we will have 9*6 = 54 such small cubes .

Answer is D.

Kudos [?]: 146 [0], given: 42

Intern
Intern
avatar
Joined: 27 Feb 2011
Posts: 45

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

Re: 3-D Cube Question [#permalink]

Show Tags

New post 01 Aug 2011, 13:50
the smaller cubes which will share an edge will have more than 2 faces painted.. so only the center cubes will have to be considered.. so .. 3*3 on each face.. 6 faces = 54

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

Intern
Intern
avatar
Joined: 09 Sep 2012
Posts: 32

Kudos [?]: 41 [0], given: 33

Location: United States
Re: 3-D Cube Question [#permalink]

Show Tags

New post 23 Sep 2012, 03:04
puneet478 wrote:
The answer is 'D'.

A 5 cm^3 cube divided in 1cm^3 cubes = 125 cubes in total. A cube has 6 faces.
On each face, all the cubes surrounding the boundary will have more than 1 side painted, which makes total of 5+5+3+3 = 16 cubes.

So we are left with 25-16 = 9 cubes on each face (which has only 1 side painted) totaling to 9*6=54 cubes.


Hi.. is there any formula to calculate total number of cubes after division.
Let say a 6cm cube is divided into 2cm cubes ?

Kudos [?]: 41 [0], given: 33

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1852

Kudos [?]: 2713 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A cube of side 5cm is painted on all of its sides. If it is [#permalink]

Show Tags

New post 21 Feb 2013, 01:00
Yes there is
it will be 6^3 / 2 ^3 = 27 cubes made
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2713 [0], given: 193

Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1387 [0], given: 136

Premium Member
Re: 3-D Cube Question [#permalink]

Show Tags

New post 21 Feb 2013, 05:41
cano wrote:
I think the quickest way is to imagine in your mind 1 side of the cube. Understand that the border cubes will have more than one side painted, so the ones with only one side are the ones in the middle, in this case 3x3=9. Then multiply that by 6 sides. If you will make a diagram, make only one side and then multiply by 6. Don't waste the little precious time that you have.
See the picture below to understand it better. The green squares have adjacent surfaces painted. Only the blue ones have 1 side only painted.


For those who have a problem in visualising they can atleast come to a conlusion that such cubes will be present on all the six sides. Now, whatever be this number(9 in this case), the answer will be a multiple of 6. Thus, just choose an option which is a multiple of 6.
However, GMAT can give 2 options where in more than 1 option is a multiple of 6. In this question, luckily we have only one such option.

D.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1387 [0], given: 136

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42259

Kudos [?]: 132730 [3], given: 12335

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 01 Sep 2014, 01:55
3
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
trahul4 wrote:
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


Look at the image below:
Image
Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Answer: D.

Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html
_________________

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

Kudos [?]: 132730 [3], given: 12335

Intern
Intern
avatar
Joined: 29 Sep 2012
Posts: 12

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

GMAT ToolKit User
A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Sep 2014, 21:14
Bunuel wrote:
trahul4 wrote:
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


Look at the image below:
Image
Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Answer: D.


Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html




Hi Bunuel, When u show the image then i can quickly make out the answer and it gets very easy but this kind of 3-D accurate figure cant be drawn on paper and difficult to be thought in mind within 2 minutes. What should be done??

What is the best way to solve such questions?

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

3 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1852

Kudos [?]: 2713 [3], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 10 Sep 2014, 22:43
3
This post received
KUDOS
snehamd1309 wrote:
Bunuel wrote:
trahul4 wrote:
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64


Look at the image below:
Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Answer: D.



Hi Bunuel, When u show the image then i can quickly make out the answer and it gets very easy but this kind of 3-D accurate figure cant be drawn on paper and difficult to be thought in mind within 2 minutes. What should be done??

What is the best way to solve such questions?


Not Bunuel, but lets try.. :)

Refer diagram below; just imagine one side of the cube
Attachment:
cube.png
cube.png [ 1010 Bytes | Viewed 12712 times ]

It will have 5 * 5 = 25 squares of 1 units

The border (the corner squares) will always be 2 side painted, so remaining are the pink shaded squares

There calculation per side = (5-2) * (5-2) = 3*3 = 9
(Two rows & two Columns are to be subtracted)

Total 6 sides = 9*6 = 54

Answer = 54
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2713 [3], given: 193

Intern
Intern
avatar
Joined: 08 Aug 2014
Posts: 1

Kudos [?]: [0], given: 2

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

Show Tags

New post 15 Sep 2014, 03:14
Shouldn't it ask " A cube of side 5cm is painted on all its faces"

Kudos [?]: [0], given: 2

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1   [#permalink] 15 Sep 2014, 03:14

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

A cube of side 5cm is painted on all its side. If it is sliced into 1

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


GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.