Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 27 May 2008
Posts: 126

A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
19 Aug 2010, 04:41
15
This post received KUDOS
50
This post was BOOKMARKED
Question Stats:
35% (03:30) correct
65% (02:42) wrong based on 1385 sessions
HideShow timer Statistics
A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is : A. 25.9% B. 44.44% C. 35% D. 61% E. None of these
Official Answer and Stats are available only to registered users. Register/ Login.



Senior Manager
Joined: 25 Jun 2009
Posts: 302

Re: Cube prob [#permalink]
Show Tags
19 Aug 2010, 06:13
1
This post was BOOKMARKED
mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these 200 cubes will be exposed outside and 16 cubes will be inside which will not be exposed at all. To minimise the coloured area 16 coloured cubes will be used inside and rest outside. So total 144 coloured cubes + 56 noncoloured cubes will be used outside. The percentage of exposed area to the coloured\(= \frac{200}{144} *100=139 % ( approx)\) Can you please confirm the OA for this one ? Cheers,



Math Expert
Joined: 02 Sep 2009
Posts: 39579

Re: Cube prob [#permalink]
Show Tags
19 Aug 2010, 06:48
20
This post received KUDOS
Expert's post
27
This post was BOOKMARKED
mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area THAT is coloured is:
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these Good question, +1. Though I think there is a little typo, the question should be: "The percentage of exposed area THAT is coloured is:" We have 160+56=216=6^3 big cube. Non exposed will be 4^3 little cubes, which will be "inside" the big cube, so exposed will be 2164^3=152 little cubes out of which there will be 15256=96 colored cube (as colored cubes are minimized on the surface). Now surface area of big cube is 6*36=216 (exposed area) out of which the area of 96 is colored, so the percentage of exposed area THAT is coloured is > \(\frac{96}{216}\approx(0.4444)=44.44%\). Answer: B.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 25 Jun 2009
Posts: 302

Re: Cube prob [#permalink]
Show Tags
19 Aug 2010, 07:19
1
This post was BOOKMARKED
Bunuel wrote: mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area THAT is coloured is:
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these Good question, +1. Though I think there is a little typo, the question should be: "The percentage of exposed area THAT is coloured is:" We have 160+56=216=6^6 big cube. Non exposed will be 4^3 little cubes, which will be "inside" the big cube, so exposed will be 2164^3=152 little cubes out of which there will be 15256=96 colored cube (as colored cubes are minimized on the surface). Now surface area of big cube is 6*36=216 (exposed area) out of which the area of 96 is colored, so the percentage of exposed area THAT is coloured is > \(\frac{96}{216}\approx(0.4444)=44.44%\). Answer: B. Bunuel, Can you please explain how did you get that non exposed cubes will be 4 ^3 cubes? I always tend to get confused with questions like these and try to use the brute force to calculate the number of exposed or non exposed cubes. Cheers,



Math Expert
Joined: 02 Sep 2009
Posts: 39579

Re: Cube prob [#permalink]
Show Tags
19 Aug 2010, 07:32
5
This post received KUDOS
Expert's post
3
This post was BOOKMARKED
nitishmahajan wrote: Bunuel wrote: mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area THAT is coloured is:
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these Good question, +1. Though I think there is a little typo, the question should be: "The percentage of exposed area THAT is coloured is:" We have 160+56=216=6^6 big cube. Non exposed will be 4^3 little cubes, which will be "inside" the big cube, so exposed will be 2164^3=152 little cubes out of which there will be 15256=96 colored cube (as colored cubes are minimized on the surface). Now surface area of big cube is 6*36=216 (exposed area) out of which the area of 96 is colored, so the percentage of exposed area THAT is coloured is > \(\frac{96}{216}\approx(0.4444)=44.44%\). Answer: B. Bunuel, Can you please explain how did you get that non exposed cubes will be 4 ^3 cubes? I always tend to get confused with questions like these and try to use the brute force to calculate the number of exposed or non exposed cubes. Cheers, Well the big cube which has the side built with 6 little cubes (6^3) will have "inside" the cube which has the side built with 4 little cubes (62 edges), so 4^3... Similarly, the cube which has the side built with 4 little cubes (4^3) will have "inside" the cube which has the side built with 2 little cubes, (42 edges), so 2^3...
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 25 Jun 2009
Posts: 302

Re: Cube prob [#permalink]
Show Tags
19 Aug 2010, 07:41
Quote: Well the big cube which has the side built with 6 little cubes (6^3) will have "inside" the cube which has the side built with 4 little cubes (62 edges), so 4^3... Similarly, the cube which has the side built with 4 little cubes (4^3) will have "inside" the cube which has the side built with 2 little cubes, (42 edges), so 2^3... Thanks a lot Bunuel...!



Manager
Joined: 27 May 2008
Posts: 126

Re: Cube prob [#permalink]
Show Tags
20 Aug 2010, 03:54
Well the big cube which has the side built with 6 little cubes (6^3) will have "inside" the cube which has the side built with 4 little cubes (62 edges), so 4^3... Similarly, the cube which has the side built with 4 little cubes (4^3) will have "inside" the cube which has the side built with 2 little cubes, (42 edges), so 2^3...
Nice explanation "Bunuel", you got it absolutely correct. It took me lot of time to get the concept and the answer.



Intern
Joined: 11 May 2010
Posts: 3

Re: Cube prob [#permalink]
Show Tags
21 Aug 2010, 02:40
2
This post was BOOKMARKED
Bunuel wrote: mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area THAT is coloured is:
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these Good question, +1. Though I think there is a little typo, the question should be: "The percentage of exposed area THAT is coloured is:" We have 160+56=216=6^6 big cube. Non exposed will be 4^3 little cubes, which will be "inside" the big cube, so exposed will be 2164^3=152 little cubes out of which there will be 15256=96 colored cube (as colored cubes are minimized on the surface). Now surface area of big cube is 6*36=216 (exposed area) out of which the area of 96 is colored, so the percentage of exposed area THAT is coloured is > \(\frac{96}{216}\approx(0.4444)=44.44%\). Answer: B. Thanks for an explanation of the "cube" concept but here is a question. Why did you divide the number of outside colored cubes by the number of all small cubes? The questions asks about relationship of exposed area and the coloured cubes.



Math Expert
Joined: 02 Sep 2009
Posts: 39579

Re: Cube prob [#permalink]
Show Tags
21 Aug 2010, 03:15
zsokhan wrote: Bunuel wrote: mission2009 wrote: A big cube is formed by rearranging the 160 coloured and 56 noncoloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area THAT is coloured is:
1) 25.9% 2) 44.44% 3) 35% 4) 61% 5) None of these Good question, +1. Though I think there is a little typo, the question should be: "The percentage of exposed area THAT is coloured is:" We have 160+56=216=6^6 big cube. Non exposed will be 4^3 little cubes, which will be "inside" the big cube, so exposed will be 2164^3=152 little cubes out of which there will be 15256=96 colored cube (as colored cubes are minimized on the surface). Now surface area of big cube is 6*36=216 (exposed area) out of which the area of 96 is colored, so the percentage of exposed area THAT is coloured is > \(\frac{96}{216}\approx(0.4444)=44.44%\). Answer: B. Thanks for an explanation of the "cube" concept but here is a question. Why did you divide the number of outside colored cubes by the number of all small cubes? The questions asks about relationship of exposed area and the coloured cubes. We are asked to find the ratio of colored area to whole surface area. Colored area is 96, as 96 cubes are exposed.Total surface area is: 6 faces * area of one face =6*(6*6)=216. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 11 May 2010
Posts: 3

Re: Cube prob [#permalink]
Show Tags
21 Aug 2010, 09:03
Thanks for answer but it seems I haven't got something. I thought we have 64 cubes inside ( the smaller inside cube, 4x4x4). As I understood they aren't exposed and we have to exlude them from 216.
Posted from my mobile device



Manager
Joined: 20 Apr 2010
Posts: 210
Schools: ISB, HEC, Said

Re: Cube prob [#permalink]
Show Tags
26 Aug 2010, 08:20
Nice Explaination Bunuel



Intern
Joined: 23 Jul 2013
Posts: 4

Re: Cube prob [#permalink]
Show Tags
14 Aug 2013, 09:32
Just a thought... But if the number of non colored cubes was to be 30 and the number of colored cubes 186, then it would have made the problem a whole lot tougher. Assuming that all the sides of the colored cubes are indeed colored, they would need to be placed at the edges and corners first to increase the surface are that is colored. Please correct me if I am wrong



Senior Manager
Joined: 10 Jul 2013
Posts: 334

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
14 Aug 2013, 11:56
17
This post received KUDOS
6
This post was BOOKMARKED
A big cube is formed by rearranging the 160 colored and 56 noncolored similar cubes in such a way that the exposure of the colored cubes to the outside is minimum. The percentage of exposed area that is colored: A. 25.9% B. 44.44% C. 35% D. 61% E. None of these ...... My explanation and diagram:
Attachments
cube 44.jpg [ 217.18 KiB  Viewed 18203 times ]
_________________
Asif vai.....



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 613
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
21 Aug 2013, 11:28
1
This post received KUDOS
Asifpirlo wrote: A big cube is formed by rearranging the 160 colored and 56 noncolored similar cubes in such a way that the exposure of the colored cubes to the outside is minimum. The percentage of exposed area that is colored:
A. 25.9% B. 44.44% C. 35% D. 61% E. None of these ...... My explanation and diagram: Mind blowing excellent Figure...
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 39579

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
21 Aug 2013, 11:32
3
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 613
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
22 Aug 2013, 10:58
Thanks Bunuel Your helps are amazing, this is the greatest GMAT portal on earth.
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Senior Manager
Joined: 19 Oct 2012
Posts: 275
Location: India
Concentration: General Management, Operations
GPA: 3.81
WE: Information Technology (Computer Software)

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
23 Aug 2013, 11:31
Bunuel, The percentage of exposed area that is colored will be: Number of colored cubes exposed (96)/Total number of cubes which are exposed(152=21664) Please clarify this. I think the question needs to be worded more specifically such as, The %tage of colored cubes which are exposed or something on similar lines.
_________________
Citius, Altius, Fortius



Intern
Joined: 16 Jun 2013
Posts: 11
Concentration: Technology, Strategy

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
20 Sep 2013, 21:48
vabhs192003 wrote: Bunuel,
The percentage of exposed area that is colored will be: Number of colored cubes exposed (96)/Total number of cubes which are exposed(152=21664)
Please clarify this. I think the question needs to be worded more specifically such as, The %tage of colored cubes which are exposed or something on similar lines. I think this question arose because one small thing in Bunuel's answer is missing. 96 is not only a number of colored сubes exposed, but also the exposed surface area of these сubes. only 1 side of each of 96 colored сubes will be exposed. 216 is the total exposed surface area of all 216 cubes (hope no questions with that). We are asked for "The percentage of exposed area that is coloured", thus, 96/216 = 0.4444. And I totally agree with earlier note of ashivapu, in case the number of colored cubes were more than 160, the questions would be even tougher!



Intern
Joined: 01 Oct 2013
Posts: 4
Concentration: Technology, Sustainability
GPA: 3.02
WE: Project Management (Telecommunications)

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
29 Oct 2013, 10:29
Guys, Pleas read my explanation.
160+56=216=6^3, total number of cubes.
So first inside cube has 4^3=64 and that cube has 2^3=8, leading to 64+8=72 cubes inside, giving 21672=144 cubes will be exposed.



Intern
Joined: 07 Oct 2013
Posts: 5

Re: A big cube is formed by rearranging the 160 coloured and 56 [#permalink]
Show Tags
29 Oct 2013, 11:16
1
This post was BOOKMARKED
Good question
Out of the 216 cubes:
64 (4^3) can be used to create the middle 4by4 cube  use all color cubes for this
152 (216  96) will have at least one face showing on the outside. out of these
96 will have one side showing  use all color cubes (6 sides * 4^2 on each side) 48 will have two sides showing  use all noncolor cubes (12 edges with 4 cubes each) 8 will have three sides showing at the corners  use all noncolor cubes
so the percentage is 96 / (6^3). you could also count the faces for the area 96*1 / (96*1 + 48*2 + 8*3).
Great solution Bunuel




Re: A big cube is formed by rearranging the 160 coloured and 56
[#permalink]
29 Oct 2013, 11:16



Go to page
1 2
Next
[ 40 posts ]




