Latest CAT Aptitude Question SOLUTION: 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 s

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(#M40011020) CAT question Keep an EYE

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

Asked In CAT B.Nagasakthi (11 years ago)

Unsolved Read Solution (4)

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Garima  (11 years ago)

12 tiles.

size of room is 12x5 units and tiles are 1x1 unit.
Total 60 tiles are used.
out of which 30 tiles are red which are used in (12-2)*(5-2) = 10*3 unit area.

Is this solution Helpfull? Yes (4) | No (6)  

Huzefa Chikhly  (11 years ago)

let no of tiles along x axis= x
let no of tiles along y axis= y

then no of tiles on border=2x+2y-4
no of tiles in middle= (x-2)(y-2)
we know that
(x-2)(y-2)=2x+2y-4
put the value of x from options one by one and find the value of y

if y is positive integer then that value of x is ans

we will get y=5 for x=2 so (B) is correct option

Is this solution Helpfull? Yes (4) | No   

Tushar Gupta  (9 years ago)

let the length of rectangle floor be L and breadth be B and X be the size of one tile
and N & M be the no. of the tiles along length L and breadth B than NX = L & MX = B
area of white tiles = area of red tiles = 1/2
now 2NX^2 + 2(M-2)X^2 =1/2(LB) = 1/2(NX) = 1/2(MNX^2)
solving this v get that 4M + 4 N - MN = 8
now looking from the options
only M = 12 gives integer value of N (that is equal to 5)

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Chirag Ranjan Lahiri  (9 years ago)

size of room is 12x5 units and tiles are 1x1 unit.
Total 60 tiles are used.
out of which 30 tiles are red which are used in (12-2)*(5-2) = 10*3 unit area

Is this solution Helpfull? Yes | No (1)  

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