NIMCET 2012 — Reasoning PYQ

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Question

NIMCET 2012 — Reasoning PYQ

NIMCET | Reasoning | 2012

The minimum number of tiles of size 16 by 24 required to form a square by placing them adjacent to one another is

Choose the correct answer:

Explanation

1. Find the side of the smallest square:

The side of the square will be the $LCM(16, 24)$ .

Prime factorization of $16 = 2^4$
Prime factorization of $24 = 2^3 \times 3^1$
$LCM(16, 24) = 2^4 \times 3^1 = 16 \times 3 = 48$

So, the side of the smallest square formed is 48 units.

2. Calculate the number of tiles required:

To find the total number of tiles, we divide the area of the square by the area of one rectangular tile.

\text{Number of tiles} = \frac{\text{Area of Square}}{\text{Area of one Tile}}

\text{Number of tiles} = \frac{48 \times 48}{16 \times 24}

3. Simplify the calculation:

Along the side of 16: $\frac{48}{16} = 3$ tiles
Along the side of 24: $\frac{48}{24} = 2$ tiles

\text{Total tiles} = 3 \times 2 = 6

Correct Option: (a) 6