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the interior are red

by sanju09 » Mon May 10, 2010 12:10 am
A rectangular floor is 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 the tiles along one edge of the floor is
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
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by kstv » Mon May 10, 2010 3:31 am
Let the no of red tiles laid length wise be = x
and no of red tiles laid breathwise = y
Total no of red tiles = xy
no of white tiles = 2(x+y)+ 4 (the tiles at the edges)
xy = 2(x+y) +4
x(y-2) = 2(y+2) or x = 2(y+2)/(y-2)
Pluggin values
y = 10 x = 3
y = 12 x = 2.8
y = 14 x = 3.2
y = 16 x = 18/7
y = 18 x = 2.5
Option A gives integer values for y
IMO A
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