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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

23 Sep 2013, 04:10

5

This post received KUDOS

27

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

75% (02:13) correct
25% (01:20) wrong based on 457 sessions

HideShow timer Statistics

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?

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 [ 9.94 KiB | Viewed 27186 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: \(\frac{n(n+1)(2n+1)}{6}=\frac{9*(9+1)(2*9+1)}{6}=285\).

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

23 Sep 2013, 13:46

2

This post received KUDOS

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!
_________________

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. ...

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

24 Sep 2013, 07:58

1

This post received KUDOS

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.

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.

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

04 Apr 2015, 16:42

1

This post was BOOKMARKED

Bunuel wrote:

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

(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.

Is there any chance you can apply why that 6 is there? I want to make sure I can apply this formula in more complicated cases.

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

11 Oct 2015, 18:42

Here's where non-native speakers could have trouble. By display I kept thinking of a computer display and I tried to visualize boxes arranged within the TV, and jumped into the conclusion that this was similar to a problem in the OG (13th Ed. PS 124). Now, if you don't know the formula for the sum of the first n perfect squares (I actually forgot it on a second attempt), it is just nonsense to sum each square result. plaverbach's approach is the appropriate one. After taking a look at the answers and noticing that only two of them have the same units number, you pray that those are wrong and go ahead and find that unit.

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

03 Jan 2016, 09:17

I liked plaverbach approach, as I couldn't understand the question in the first place and choose random wrong answer. But when I saw the picture posted, I could use the plaverbach approach.

Re: For a display, identical cubic boxes are stacked in square [#permalink]

Show Tags

29 Aug 2016, 12:01

Attachment:

File comment: Visualize the Question this Way

IMG_20160830_012335.jpg [ 1.04 MiB | Viewed 5544 times ]

In the above figures ,small circles are akin to cubic boxes and lines are rows. So bottom most layer has 9*9 = 81 boxes . Now this figure has more layers stacked on top of it and each layer has 1 less box(small circle) and 1 less row( line). If you follow this theory then you will notice that no of rows = no of boxes in each row.

So 2nd layer from the top will have 2 rows with 2 boxes each. Similarly top most layer will have 1 row and 1 box.

So the total no of boxes will be : 9* 9 + 8*8 +.....+ 1*1 = 285 .

For a display, identical cubic boxes are stacked in square layers [#permalink]

Show Tags

16 Jan 2017, 13:21

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 layer has 21 boxes and the top layer has only 1 box, how many boxes are in the display?

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 layer has 21 boxes and the top layer has only 1 box, how many boxes are in the display?

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

Hi, The Q seems to be flawed as 21 cannot be the number of boxes . It is either 81 or 25.

You can imagine this as a huge cube from which steps are made in 2 sides by removing a row of boxes in each layer. In numerical value,all the layers will be square of integers starting from 1 on top to 5 or 9 in lowermost.

When we add these, it becomes \(1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2\) Either add all of them or use formula SUM=\(\frac{n(n+1)(2n+1)}{6}\)=9*(9+1)*(2*9+1)/6=9*10*19/6=15*19=285 E
_________________

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 layer has 21 boxes and the top layer has only 1 box, how many boxes are in the display?

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

Merging topics. Please refer to the discussion above.
_________________

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...