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The dimensions of a floor are 18 × 24 What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?
  • a)
    6
  • b)
    24
  • c)
    8
  • d)
    12
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The dimensions of a floor are 18 × 24 What is the smallest numbe...
LCM of 18, 24 = 72
Area of the floor = 18 × 24 = 432
the smallest number of identical square tiles that pave the entire floor without the need to break any tile
⇒ (LCM2)/Area 
⇒ (72 × 72)/432 = 12 
We can rather check by the options, the square of which of the options have a multiple in 432.
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Most Upvoted Answer
The dimensions of a floor are 18 × 24 What is the smallest numbe...


Explanation:

Given Dimensions:
- Length of the floor = 18 units
- Width of the floor = 24 units

Finding the dimensions of the square tiles:
To find the dimensions of the square tiles that can perfectly pave the entire floor without the need to break any tile, we need to find the greatest common divisor (GCD) of the given dimensions.

Calculating the GCD:
GCD(18, 24) = 6

Calculating the number of tiles:
To find the number of identical square tiles needed to pave the entire floor, we divide the total area of the floor by the area of each square tile.
- Total area of the floor = 18 * 24 = 432 square units
- Area of each square tile = 6 * 6 = 36 square units

Number of tiles = Total area of the floor / Area of each tile
Number of tiles = 432 / 36 = 12

Therefore, the smallest number of identical square tiles that pave the entire floor without the need to break any tile is 12. Option 'D' is the correct answer.
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Direction: Read the following passage carefully and answer the question. If India has to develop her internal strengths, the nation has to focus on the technological imperatives, keeping in mind three dynamic dimensions: the people, the overall economy and the strategic interests. These technological imperatives also take into account a ‘fourth’ dimension, time, an offshoot of modern-day dynamism in business, trade, and technology that leads to continually shifting targets. We believe that technological strengths are especially crucial in dealing with this fourth dimension underlying continuous change in the aspirations of the people, the economy in the global context, and the strategic interests. The progress of technology lies at the heart of human history. Technological strengths are the key to creating more productive employment in an increasingly competitive market place and to continually upgrade human skills. Without a pervasive use of technologies, we cannot achieve the overall development of our people in the years to come. The direct linkages of technology to the nation’s strategic strengths are becoming more and more clear, especially since the 1990s. India’s own strength in a number of core areas still puts it in a position of reasonable strength in the geopolitical context. Any nation aspiring to become a developed one needs to have strengths in various strategic technologies and also the ability to continually upgrade them through its own creative strengths. For people-oriented actions as well, whether for the creation of large scale productive employment or for ensuring nutritional and health security for people or for better living conditions, technology is the only vital input. The absence of greater technological impetus could lead to lower productivity and wastage of precious natural resources. Activities with low productivity or low-value addition, in the final analysis, hurt the poorest most. The technological imperatives to lift our people to a new life, and to life, they are entitled to be important. India, aspiring to become a major economic power in terms of trade and increase in GDP, cannot succeed on the strength of turnkey projects designed and built abroad or only through large-scale imports of plant machinery, equipment and know-how. Even while being alive to the short-term realities, medium and long-term strategies to develop core technological strengths within our industry are vital for envisioning a developed India. Q. More productive employment demands

Direction: Read the following passage carefully and answer the question. If India has to develop her internal strengths, the nation has to focus on the technological imperatives, keeping in mind three dynamic dimensions: the people, the overall economy and the strategic interests. These technological imperatives also take into account a ‘fourth’ dimension, time, an offshoot of modern-day dynamism in business, trade, and technology that leads to continually shifting targets. We believe that technological strengths are especially crucial in dealing with this fourth dimension underlying continuous change in the aspirations of the people, the economy in the global context, and the strategic interests. The progress of technology lies at the heart of human history. Technological strengths are the key to creating more productive employment in an increasingly competitive market place and to continually upgrade human skills. Without a pervasive use of technologies, we cannot achieve the overall development of our people in the years to come. The direct linkages of technology to the nation’s strategic strengths are becoming more and more clear, especially since the 1990s. India’s own strength in a number of core areas still puts it in a position of reasonable strength in the geopolitical context. Any nation aspiring to become a developed one needs to have strengths in various strategic technologies and also the ability to continually upgrade them through its own creative strengths. For people-oriented actions as well, whether for the creation of large scale productive employment or for ensuring nutritional and health security for people or for better living conditions, technology is the only vital input. The absence of greater technological impetus could lead to lower productivity and wastage of precious natural resources. Activities with low productivity or low-value addition, in the final analysis, hurt the poorest most. The technological imperatives to lift our people to a new life, and to life, they are entitled to be important. India, aspiring to become a major economic power in terms of trade and increase in GDP, cannot succeed on the strength of turnkey projects designed and built abroad or only through large-scale imports of plant machinery, equipment and know-how. Even while being alive to the short-term realities, medium and long-term strategies to develop core technological strengths within our industry are vital for envisioning a developed India. Envisioning a developed India requires

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The dimensions of a floor are 18 × 24 What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?a)6b)24c)8d)12Correct answer is option 'D'. Can you explain this answer?
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