Find all School-related info fast with the new School-Specific MBA Forum

It is currently 22 Jul 2014, 05:28

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For a display, identical cubic boxes are stacked in square

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 340
Followers: 2

Kudos [?]: 89 [0], given: 136

For a display, identical cubic boxes are stacked in square [#permalink] New post 23 Sep 2013, 04:10
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (low)

Question Stats:

76% (02:27) correct 24% (01:37) wrong based on 80 sessions
For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom of the layer has 81 boxes and the top of the layer has only 1 box, how many boxes are in display?

A. 236
B. 260
C. 269
D. 276
E. 285
[Reveal] Spoiler: OA

_________________

+1 Kudos me, Help me unlocking GMAT Club Tests


Last edited by Bunuel on 23 Sep 2013, 05:02, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
7 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18676
Followers: 3229

Kudos [?]: 22151 [7] , given: 2599

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 23 Sep 2013, 05:23
7
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
imhimanshu wrote:
For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom of the layer has 81 boxes and the top of the layer has only 1 box, how many boxes are in display?

A. 236
B. 260
C. 269
D. 276
E. 285


Basically we have a 9-layer pyramid as shown below:
Attachment:
pyramid_with_corner_cube_from_istock.jpg
pyramid_with_corner_cube_from_istock.jpg [ 9.94 KiB | Viewed 4366 times ]
(Actually this pyramid 8-layer, couldn't find 9-layer one image)

The number of boxes would be: 9^2 + 8^2 + 7^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1 = 285.

You can use the sum of the first n perfect squares formula to calculate: \frac{n(n+1)(2n+1)}{6}=\frac{9*(9+1)(2*9+1)}{6}=285.

Answer: E.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 01 Sep 2012
Posts: 124
Followers: 1

Kudos [?]: 18 [0], given: 19

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 23 Sep 2013, 13:46
Thanks bunuel but how did you manage to understand that?
I read the question again and cannot imagine the picture you uploaded in my head at all.
Thanks! :)
_________________

If my answer helped, dont forget KUDOS! :)


IMPOSSIBLE IS NOTHING

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18676
Followers: 3229

Kudos [?]: 22151 [2] , given: 2599

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 23 Sep 2013, 23:56
2
This post received
KUDOS
Expert's post
roygush wrote:
Thanks bunuel but how did you manage to understand that?
I read the question again and cannot imagine the picture you uploaded in my head at all.
Thanks! :)


I read the stem carefully. We are told that:
Cubic boxes are stacked in square layers --> each layer is a square;
The bottom of the layer has 81 boxes --> the bottom layer has 9 rows and each row has 9 boxes.
Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it --> the second layer has 8 rows and each row has 8 boxes.
...

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 24 Jan 2012
Posts: 10
Followers: 0

Kudos [?]: 13 [0], given: 3

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 24 Sep 2013, 07:58
Bunuel wrote:
roygush wrote:
Thanks bunuel but how did you manage to understand that?
I read the question again and cannot imagine the picture you uploaded in my head at all.
Thanks! :)


I read the stem carefully. We are told that:
Cubic boxes are stacked in square layers --> each layer is a square;
The bottom of the layer has 81 boxes --> the bottom layer has 9 rows and each row has 9 boxes.
Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it --> the second layer has 8 rows and each row has 8 boxes.
...

Hope it helps.



I got confused (and I still am) by the line which says "Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it"

I got that the bottom layer will have 9 x 9 boxes
I also understand that the next level up will have 8 rows of boxes and since this layer also has to form a square hence it needs 8 boxes in the column as well.

What is elusive for me is "and 1 fewer box in each remaining row[/color] than the layer directly below it". Can you please explain again.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18676
Followers: 3229

Kudos [?]: 22151 [1] , given: 2599

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 24 Sep 2013, 14:04
1
This post received
KUDOS
Expert's post
violetsplash wrote:
Bunuel wrote:
roygush wrote:
Thanks bunuel but how did you manage to understand that?
I read the question again and cannot imagine the picture you uploaded in my head at all.
Thanks! :)


I read the stem carefully. We are told that:
Cubic boxes are stacked in square layers --> each layer is a square;
The bottom of the layer has 81 boxes --> the bottom layer has 9 rows and each row has 9 boxes.
Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it --> the second layer has 8 rows and each row has 8 boxes.
...

Hope it helps.



I got confused (and I still am) by the line which says "Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it"

I got that the bottom layer will have 9 x 9 boxes
I also understand that the next level up will have 8 rows of boxes and since this layer also has to form a square hence it needs 8 boxes in the column as well.

What is elusive for me is "and 1 fewer box in each remaining row[/color] than the layer directly below it". Can you please explain again.


Each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it:

1st layer has 9 rows and 9 boxes in each of them. 2nd row has 1 fewer, so 8 rows and each of the remaining 8 rows has 1 fewer box, so 8 boxes in it.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Joined: 14 Jan 2013
Posts: 158
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 2

Kudos [?]: 39 [0], given: 29

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 30 Mar 2014, 15:02
Bunuel,

Do you have more examples like these questions? I am finding it difficult to understand after reading question.

Thanks

~M14
_________________

"Where are my Kudos" ............ Good Question = kudos

"Start enjoying all phases" & all Sections

__________________________________________________________________
http://gmatclub.com/forum/collection-of-articles-on-critical-reasoning-159959.html

percentages-700-800-level-questions-130588.html

700-to-800-level-quant-question-with-detail-soluition-143321.html

Manager
Manager
avatar
Joined: 20 Oct 2013
Posts: 66
Followers: 0

Kudos [?]: 0 [0], given: 27

Re: For a display, identical cubic boxes are stacked in square [#permalink] New post 24 May 2014, 05:30
superb explanation Bunnel! i couldnt understand the qs...
_________________

Hope to clear it this time!!
GMAT 1: 540
Preparing again :(

Re: For a display, identical cubic boxes are stacked in square   [#permalink] 24 May 2014, 05:30
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic A monument is made by stacking identical rectangular blocks goodyear2013 4 05 Feb 2014, 15:39
Experts publish their posts in the topic 5 boxes are placed in a stack by weight from lightest to manulath 3 07 Jun 2012, 08:19
One company is planning to display some boxes, the first johnycute 1 19 Nov 2006, 20:37
In how many ways can a stack of 14 identical cards be ccax 2 06 Apr 2006, 09:04
Cubical blocks in a display are stacked one on top of the chunjuwu 2 26 Jul 2004, 06:53
Display posts from previous: Sort by

For a display, identical cubic boxes are stacked in square

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.