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

It is currently 07 Dec 2019, 19:32

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

A large cube consists of 125 identical small cubes, how

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 103
A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 02 Mar 2011, 03:23
5
35
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (01:23) correct 38% (02:01) wrong based on 660 sessions

HideShow timer Statistics

A large cube consists of 125 identical small cubes, how many of the small cubes are exposed in air?

(A) 64
(B) 72
(C) 98
(D) 100
(E) 116
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59588
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 02 Mar 2011, 03:29
5
1
10
banksy wrote:
226. A large cube consists of 125 identical small cubes, how many of the small cubes are exposed in air?
(A) 64
(B) 72
(C) 98
(D) 100
(E) 116


As the cube consists of 125=5^3 identical small cubes then its sides are built with 5 small cubes. The sides of the inner cube are built with 3 small cube (5 - 2 small edge cubes), thus there are 125-3^3=98 cubes exposed.

Answer: C.
_________________
Most Helpful Community Reply
Manager
Manager
avatar
Joined: 14 Feb 2011
Posts: 143
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 02 Mar 2011, 23:31
5
4
OK - let me try and explain this.

The question says that a large cube is actually made up of 125 smaller cubes.

Since 125 = \(5^3\), it implies that each side of the large cube is actually made up of 5 cubes. For simplicity, if large cube has side 5 cm, then small cube has side one cm and hence large cube with volume 125 cu. cm. is actually 125 cubes of 1 cu. cm. each.

Now, the question is how many cubes are exposed, which simply means that how many of such small cubes constitute outer surface (which is exposed to air)?

So, we can work this out by finding those cubes that do not have any of the surfaces exposed to air.

Lets visualise the cube as 5 squares of 25 cubes each placed over one another, Now top and bottom square are clearly the ones with all cubes exposed to air.

For squares 2, 3 and 4, 16 cubes that make the four sides are exposed to air, but 9 cubes that are enclosed within these sides are not exposed. So total of 9*3 = 27 cubes are not exposed to air.

Hence, 125 - 27 = 98 cubes are exposed to air.

You can quickly visualise that except a 3x3 cube within the larger cube, everything else is exposed, so you can quickly do \(5^3\) - \(3^3\) and derive the answer, as Bunuel has done.
General Discussion
Intern
Intern
avatar
Joined: 17 Nov 2010
Posts: 2
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 02 Mar 2011, 23:00
Bunuel wrote:
banksy wrote:
226. A large cube consists of 125 identical small cubes, how many of the small cubes are exposed in air?
(A) 64
(B) 72
(C) 98
(D) 100
(E) 116


As the cube consists of 125=5^3 identical small cubes then its sides are built with 5 small cubes. The sides of the inner cube are built with 3 small cube (5 - 2 small edge cubes), thus there are 125-3^3=98 cubes exposed.

Answer: C.


Haven't understood the solution. Can you please explain further?

Thanks
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 61
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 02 Mar 2011, 23:12
i understand neither the mathematic question and its solution. can you please explain?
Intern
Intern
avatar
Joined: 22 Feb 2010
Posts: 34
GMAT ToolKit User
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 18 May 2013, 04:21
2
beyondgmatscore wrote:
OK - let me try and explain this.

The question says that a large cube is actually made up of 125 smaller cubes.

Since 125 = \(5^3\), it implies that each side of the large cube is actually made up of 5 cubes. For simplicity, if large cube has side 5 cm, then small cube has side one cm and hence large cube with volume 125 cu. cm. is actually 125 cubes of 1 cu. cm. each.

Now, the question is how many cubes are exposed, which simply means that how many of such small cubes constitute outer surface (which is exposed to air)?

So, we can work this out by finding those cubes that do not have any of the surfaces exposed to air.

Lets visualise the cube as 5 squares of 25 cubes each placed over one another, Now top and bottom square are clearly the ones with all cubes exposed to air.

For squares 2, 3 and 4, 16 cubes that make the four sides are exposed to air, but 9 cubes that are enclosed within these sides are not exposed. So total of 9*3 = 27 cubes are not exposed to air.

Hence, 125 - 27 = 98 cubes are exposed to air.

You can quickly visualise that except a 3x3 cube within the larger cube, everything else is exposed, so you can quickly do \(5^3\) - \(3^3\) and derive the answer, as Bunuel has done.


A very good explanation indeed. I tried a different approach and ended up with incorrect answer. Please help me correct with my mistake here.
Let us consider that there are five individual small cubes that make up the edge of the cube. I have added one picture for representation.
Assume that the cube is made up of 5 small individual cubes as shown in the picture. This is only one face of the 6 faces of the cube. We consider the outer cubes as below:
Blue Cubes - The 3X3=9 blue faces have no corners common and repeat at each of the faces of the cube. Thus, there are in total 3X3X6 = 54 blue cubes in total
Green Cubes - We have 12 (3X4) Green cubes on one face that share their edges with other cubes. We will have similar 12 Green cubes on the other side. Thus, we have 24 Green cubes.
Orange Cubes - We have 4 such cubes that are at corners and share their edges with cubes at other sides. We will have 4X2=8 such orange cubes.
Total cubes facing the air = Blue + Green + Orange = 54+24+8=86
Please tell me my mistake. Thanks.
Attachments

cube.JPG
cube.JPG [ 5.07 KiB | Viewed 60679 times ]

Manager
Manager
User avatar
Joined: 25 Sep 2012
Posts: 228
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 20 May 2014, 02:48
holidevil wrote:
beyondgmatscore wrote:
OK - let me try and explain this.

The question says that a large cube is actually made up of 125 smaller cubes.

Since 125 = \(5^3\), it implies that each side of the large cube is actually made up of 5 cubes. For simplicity, if large cube has side 5 cm, then small cube has side one cm......


A very good explanation indeed. I tried a different approach and ended up with incorrect answer. Please help me correct with my mistake here.
Let us consider that there are five individual small cubes that make up the edge of the cube. I have added one picture for representation.
Assume that the cube is made up of 5 small individual cubes as shown in the picture. This is only one face of the 6 faces of the cube. We consider the outer cubes as below:
Blue Cubes - The 3X3=9 blue faces have no corners common and repeat at each of the faces of the cube. Thus, there are in total 3X3X6 = 54 blue cubes in total
Green Cubes - We have 12 (3X4) Green cubes on one face that share their edges with other cubes. We will have similar 12 Green cubes on the other side. Thus, we have 24 Green cubes.
Orange Cubes - We have 4 such cubes that are at corners and share their edges with cubes at other sides. We will have 4X2=8 such orange cubes.
Total cubes facing the air = Blue + Green + Orange = 54+24+8=86
Please tell me my mistake. Thanks.



if anyone is facing the same problem...

In this case we are not counting 3 small cubes which are between the bottom and top orange cubes (for each orange cube). We can clearly understand that counting by above method can lead to an error and Bunuel's method is way much better. If you understand the logic behind Bunuel's method, this question will be a cakewalk.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59588
Re: 226. A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 20 May 2014, 02:59
Bunuel wrote:
banksy wrote:
226. A large cube consists of 125 identical small cubes, how many of the small cubes are exposed in air?
(A) 64
(B) 72
(C) 98
(D) 100
(E) 116


As the cube consists of 125=5^3 identical small cubes then its sides are built with 5 small cubes. The sides of the inner cube are built with 3 small cube (5 - 2 small edge cubes), thus there are 125-3^3=98 cubes exposed.

Answer: C.


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

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html
_________________
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: A large cube consists of 125 identical small cubes, how  [#permalink]

Show Tags

New post 06 Nov 2018, 05:40
3
banksy wrote:
A large cube consists of 125 identical small cubes, how many of the small cubes are exposed in air?

(A) 64
(B) 72
(C) 98
(D) 100
(E) 116


The detailed solution with more learning is right here...



Exposed in air = 125 - 27 = 98

Answer: Option C
Attachments

File comment: www.GMATinsight.com
Answer 5.jpg
Answer 5.jpg [ 154.93 KiB | Viewed 12951 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
GMAT Club Bot
Re: A large cube consists of 125 identical small cubes, how   [#permalink] 06 Nov 2018, 05:40
Display posts from previous: Sort by

A large cube consists of 125 identical small cubes, how

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





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