Last visit was: 14 Jul 2025, 18:46 It is currently 14 Jul 2025, 18:46
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
User avatar
TheNightKing
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,139
Own Kudos:
1,226
 [1]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,139
Kudos: 1,226
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Jul 2025
Posts: 102,570
Own Kudos:
Given Kudos: 98,182
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,570
Kudos: 741,420
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
TheNightKing
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,139
Own Kudos:
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,139
Kudos: 1,226
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 14 Jul 2025
Posts: 21,095
Own Kudos:
26,163
 [1]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,095
Kudos: 26,163
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
imhimanshu
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

We see that the bottommost layer has 9 x 9 = 81 boxes and the topmost layer is 1 x 1 = 1 box. Therefore, each layer must be a perfect square number of boxes from 1 to 81, inclusive. That is, if we count the layers from top to bottom, they have 1, 4, 9, 16, 25, 36, 49, 64, and 81 boxes. Therefore, the total number of boxes is:

1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81

Instead of adding the actual numbers, let’s add their units digits:

1 + 4 + 9 + 6 + 5 + 6 + 9 + 4 + 1 = 5 + 15 + 5 + 15 + 5 = 45

We see the sum must have a units digit of 5; therefore, choice E is the correct answer.

Answer: E
avatar
PayelRB
Joined: 02 Jun 2020
Last visit: 13 Nov 2023
Posts: 23
Own Kudos:
Given Kudos: 173
Location: India
Posts: 23
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
why divide the sum by 6?
User avatar
Paras96
Joined: 11 Sep 2022
Last visit: 30 Dec 2023
Posts: 488
Own Kudos:
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
GMAT 3: 700 Q49 V35
Posts: 488
Kudos: 279
Kudos
Add Kudos
Bookmarks
Bookmark this Post
As per the given scenario,

No. of boxes in the bottom-most layer = 81 = 9^2
For the layer just above the bottom-most layer, No. of boxes = (9-1)*(9-1)=8^2
Similarly, for the next layer, No. of boxes = 7^2
.
.
.
.
No. of boxes in the Top-most layer = 1^2

Total No. of boxes = 1^2 +2^2 + 3^2 + 4^2 + ...............+9^2 = 285

Hence E
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,400
Own Kudos:
Posts: 37,400
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
   1   2 
Moderators:
Math Expert
102570 posts
PS Forum Moderator
691 posts