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LMP
Joined: 29 Jun 2018
Last visit: 15 Mar 2022
Posts: 49
Given Kudos: 62
Location: India
Schools: Johnson '20 HEC Montreal '21
GPA: 4
B
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62%
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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
(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
09 Aug 2018, 10:23
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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
(a) 10
(b) 12
(c) 14
(d) 16
(e) 18
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
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LMP
Joined: 29 Jun 2018
Last visit: 15 Mar 2022
Posts: 49
Own Kudos:
Given Kudos: 62
Location: India
Schools: Johnson '20 HEC Montreal '21
GPA: 4
09 Aug 2018, 11:29
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Bookmarks
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
(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
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
