Last visit was: 29 Apr 2026, 14:51 It is currently 29 Apr 2026, 14:51
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ (Hard)|   Word Problems|      
User avatar
LMP
User avatar
Joined: 29 Jun 2018
Last visit: 15 Mar 2022
Posts: 49
Own Kudos:
235
 [13]
Given Kudos: 62
Location: India
Schools: Johnson '20 HEC Montreal '21
GPA: 4
Schools: Johnson '20 HEC Montreal '21
Posts: 49
Kudos: 235
 [13]
A rectangular floor is fully covered with square tiles of identical si Updated on: 09 Aug 2018, 10:36
Originally posted by LMP on 09 Aug 2018, 07:52.
Last edited by chetan2u on 09 Aug 2018, 10:36, edited 1 time in total.
Updated topic name
Kudos
Add Kudos
13
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

40% (02:58) correct 60% (02:40) wrong based on 91 sessions

History

Date
Time
Result
Not Attempted Yet
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
ShowHide Answer
Official Answer
B
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 29 Apr 2026
Posts: 11,234
Own Kudos:
45,047
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,234
Kudos: 45,047
 [1]
A rectangular floor is fully covered with square tiles of identical si 09 Aug 2018, 10:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bulusuchaitanya
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
Show more

Let the inner rectangle have x tiles in column and y tiles in row that is rectangle of x*y, so red tiles =xy
The white tiles=(x+2)*1*2+y*1*2)=2x+4+2y
So 2x+2y+4=xy.........
2x+4=xy-2y=y(x-2)..........
\(y=\frac{2x+4}{x-2}\)..
Now x will be 2 less than the value we are looking for and y should be an integer..
Let us see..
A) 10......X=8, so y=(2*8+4)/(8-2)=20/6...NO
B) 12.....x=10, so y=(2*10+4)/(10-2)=24/8=3....YES
C) 14....y=28/10...NO
D) 16...y=32/12...NO
E) 18....y=40/16...NO

B
Attachments

PicsArt_08-10-01.24.15.jpg
PicsArt_08-10-01.24.15.jpg [ 44.88 KiB | Viewed 21122 times ]

User avatar
LMP
User avatar
Joined: 29 Jun 2018
Last visit: 15 Mar 2022
Posts: 49
Own Kudos:
235
Given Kudos: 62
Location: India
Schools: Johnson '20 HEC Montreal '21
GPA: 4
Schools: Johnson '20 HEC Montreal '21
Posts: 49
Kudos: 235
A rectangular floor is fully covered with square tiles of identical si 09 Aug 2018, 11:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
Bulusuchaitanya
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) 10
(b) 12
(c) 14
(d) 16
(e) 18

Let the inner rectangle be in column and row x*y, so red tiles =xy
The white tiles=(x+2)*1*2+y*1*2)=2x+4+2y
So 2x+2y+4=xy.........
2x+4=xy-2y=y(x-2)..........
\(y=\frac{2x+4}{x-2}\)..
Now x will be 2 less than the value we are looking for and y should be an integer..
Let us see..
A) 10......X=8, so y=(2*8+4)/(8-2)=20/6...NO
B) 12.....x=10, so y=(2*10+4)/(10-2)=24/8=3....YES
C) 14....y=28/10...NO
D) 16...y=32/12...NO
E) 18....y=40/16...NO

B
Show more
Hi
I lost you here itself : Let the inner rectangle be in column and row x*y, so red tiles =xy
The white tiles=(x+2)*1*2+y*1*2)=2x+4+2y
Please elaborate
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 29 Apr 2026
Posts: 11,234
Own Kudos:
45,047
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,234
Kudos: 45,047
A rectangular floor is fully covered with square tiles of identical si 09 Aug 2018, 18:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bulusuchaitanya
chetan2u
Bulusuchaitanya
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) 10
(b) 12
(c) 14
(d) 16
(e) 18

Let the inner rectangle be in column and row x*y, so red tiles =xy
The white tiles=(x+2)*1*2+y*1*2)=2x+4+2y
So 2x+2y+4=xy.........
2x+4=xy-2y=y(x-2)..........
\(y=\frac{2x+4}{x-2}\)..
Now x will be 2 less than the value we are looking for and y should be an integer..
Let us see..
A) 10......X=8, so y=(2*8+4)/(8-2)=20/6...NO
B) 12.....x=10, so y=(2*10+4)/(10-2)=24/8=3....YES
C) 14....y=28/10...NO
D) 16...y=32/12...NO
E) 18....y=40/16...NO

B
Hi
I lost you here itself : Let the inner rectangle be in column and row x*y, so red tiles =xy
The white tiles=(x+2)*1*2+y*1*2)=2x+4+2y
Please elaborate
Show more

I have added a pic and attached a figure.
Since the tiles are square, I take y*X tiles of red colour placed in a rectangular form.
The outer layer will have one more on each side.
User avatar
AdityaHongunti
User avatar
Joined: 20 Sep 2016
Last visit: 31 Mar 2021
Posts: 532
Own Kudos:
1,085
Given Kudos: 632
Location: India
Concentration: Strategy, Operations
Schools: Boston U '22 (S) Smeal "22 (S) Krannert '22 (I) Katz '22 (I) UC Davis '22 (S)
GPA: 3.6
WE:Operations (Consumer Packaged Goods)
Schools: Boston U '22 (S) Smeal "22 (S) Krannert '22 (I) Katz '22 (I) UC Davis '22 (S)
Posts: 532
Kudos: 1,085
A rectangular floor is fully covered with square tiles of identical si 09 Nov 2018, 07:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel could you please explain this? Thank you
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,680
Own Kudos:
1,469
Given Kudos: 607
Location: United States
Posts: 1,680
Kudos: 1,469
A rectangular floor is fully covered with square tiles of identical si 05 Oct 2019, 08:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LMP
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles. A possible value of the number of tiles along one edge of the floor is :

(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
Show more

\(area: xy = white + red\)
\(white: 2(x+y)-corners=2(x+y)-4\)
\(red: xy-white=xy-(2(x+y)-4)=xy-2(x+y)+4\)
\(white=red…2(x+y)-4=xy-2(x+y)+4…4(x+y)-xy-8=0…4x+4y-xy-8=0\)
\((x,y)=intergers…4x+4y-xy-8=0…4x-xy=8-4y…x=(8-4y)/(4-y)=integer\)

\(y=10…(8-4y)/(4-y)=8-40/4-10=-32/-6≠integer\)
\(y=12…(8-4y)/(4-y)=8-48/4-12=-40/-8=integer\)
\(y=14…(8-4y)/(4-y)=8-4(14)/4-14≠integer\)
\(y=16…(8-4y)/(4-y)=8-4(16)/4-16≠integer\)
\(y=18…(8-4y)/(4-y)=8-4(18)/4-18≠integer\)

Answer (B)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,996
Own Kudos:
1,120
Posts: 38,996
Kudos: 1,120
A rectangular floor is fully covered with square tiles of identical si 16 Dec 2024, 06:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109975 posts
Krunaal
Tuck School Moderator
852 posts