DS - Rectangles & Squares

[karthikpandian19]

A carpenter used identical square tiles to completely cover a square floor and a rectangular floor. What was the total number of tiles needed to cover both floors?


25 more tiles were used to cover the square floor than were used to cover the rectangular floor.

Once covered, the rectangular floor was five tiles longer than the square floor along its length and five tiles shorter than the square floor along its width

[Anurag@Gurome]

A carpenter used identical square tiles to completely cover a square floor and a rectangular floor. What was the total number of tiles needed to cover both floors?

1. 25 more tiles were used to cover the square floor than were used to cover the rectangular floor.
2. Once covered, the rectangular floor was five tiles longer than the square floor along its length and five tiles shorter than the square floor along its width

Let us assume,

• The length of each side of the square tile = n
  The length of each side of the square floor = X
  The length of the sides of the rectangular floor = Y and Z (Y > Z)

Hence, tiles needed to cover the square floor = X²/n² = (X/n)²
And, tiles needed to cover the rectangular floor = YZ/n²

Statement 1: YZ/n² = (X/n)² - 25 ---> YZ = (X² - 25n²)

Not sufficient

Statement 2: Y = (X + 5n) and Z = (X - 5n)
Hence, YZ = (X² - 25n²)

Not sufficient

1 & 2 Together: No new information --> Not sufficient

The correct answer is E.