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CAT-2005-Previous Years Paper

Question
30 out of 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



A 10
B 12
C 14
D 16

Ans. B

Let the rectangle has m and n tiles along its length and breadth respectively.

The number of white tiles

W = 2m + 2 (n−2) = 2 (m + n – 2)

And the number of red tiles = = R = mn – 2 (m + n – 2) Give W = R 4 (m + n – 2) = mn

mn – 4m – 4n = −8

(m − 4) (n − 4) = 8

As m and n are integers so (m − 4) & (n − 4) are both integers. The possibilities are (m – 4, n – 4) = (1, 8) or (2, 4) giving, (m, n) as (5, 12) or (6, 8) so the edges can have 5, 12, 6 or 8 tiles. Answer is (b) only.

CAT-2005-Previous Years Paper Flashcard List

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