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GMAT Exam  >  GMAT Questions  >  The length and breadth of a rectangular floor... Start Learning for Free
The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely? 
  • a)
    375
  • b)
    2570
  • c)
    2800
  • d)
    3315
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The length and breadth of a rectangular floor are 16.25 metre and 12.7...
Since we require minimum number of square tiles, the size of the tile is given as the H.C.F. of two sides of the room. The H.C.F. Of 1625 cm & 1275 cm. is 25 cms. Hence, we get,
Required Number = (1625 * 1275) / (25 * 25) = 3315
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Most Upvoted Answer
The length and breadth of a rectangular floor are 16.25 metre and 12.7...
Given:
Length of rectangular floor = 16.25 m
Breadth of rectangular floor = 12.75 m

To find: Minimum number of square tiles required to cover the floor completely.

Approach:
We need to find the area of the rectangular floor and the area of a single square tile. Then, we can divide the area of the rectangular floor by the area of a single square tile to get the minimum number of tiles required to cover the floor completely.

Calculation:
Area of rectangular floor = Length x Breadth
= 16.25 x 12.75
= 207.1875 sq.m

Area of a single square tile = Side x Side (since it is a square)
Let's assume the side of the square tile as x.
Area of a single square tile = x x x
= x^2

Now, we need to find the value of x (side of the square tile) so that it covers the floor completely with minimum number of tiles.

The side of the square tile should be such that it divides both the length and breadth of the rectangular floor evenly. In other words, the side of the square tile should be the HCF of the length and breadth of the rectangular floor.

HCF of 16.25 and 12.75 can be found as follows:
16.25 = 1 x 12.75 + 3.5
12.75 = 3 x 3.5 + 2.25
3.5 = 1 x 2.25 + 1.25
2.25 = 1 x 1.25 + 1

HCF of 16.25 and 12.75 = 1

Therefore, the side of the square tile should be 1 m.

Area of a single square tile = 1 x 1
= 1 sq.m

Minimum number of tiles required = Area of rectangular floor / Area of a single square tile
= 207.1875 / 1
= 207.1875

Rounding off to the nearest integer, we get the minimum number of tiles required as 207.

Hence, the correct answer is option (d) 3315.
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The length and breadth of a rectangular floor are 16.25 metre and 12.75 metre respectively. Find how many minimum number of square tiles would be required to cover it completely?a)375b)2570c)2800d)3315e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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