CAT 2005 Question Paper Question 30

Question 30

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

Solution

Let C and R be no. of columns and rows respectively.

The number of red coloured tiles would be given by (R-2)(C-2). This is because two outer rows made of white tiles and the two outer columns made up of outer columns are removed.

Similarly the number of white tiles would be given by R*2 + (C-2)*2. Two tiles are removed from columns because the corner tiles would have already been included while considering the rows.

So according to given condition we have (C-2)*2 + 2*R = (C-2)(R-2).
Now start putting value of c from options into this equation. Only for one option B we get an integer value of R .



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