A wall of dimensions 4 m x 0.6 m x 4 m is constructed by using identical and indistinguishable cubical bricks. The edge of the cubical bricks chosen in such a way that number of bricks used to construct the wall is minimum possible. Some bricks are black and some are red in color. 1.Find the minimum number of bricks required to construct the wall. 2-How many bricks are used to construct the outer layer of the wall?

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A wall of dimensions 4 m x 0.6 m x 4 m is constructed by using identic...

Minimum number of bricks required to construct the wall:

To find the minimum number of bricks required to construct the wall, we need to consider the dimensions of the wall and the dimensions of the bricks.

Given:
Dimensions of the wall: 4 m x 0.6 m x 4 m

Let's assume that each brick has dimensions of a x b x c.

To minimize the number of bricks, we need to find the largest brick dimension that can be used to divide each dimension of the wall evenly. This will ensure that we use the least number of bricks to construct the wall.

Let's consider the length dimension of the wall:
Length of the wall: 4 m
Length of each brick: a

To minimize the number of bricks used, we need to find the largest value of a that divides 4 evenly. The largest value of a that satisfies this condition is 1.

Similarly, for the other dimensions:
Width of the wall: 0.6 m
Width of each brick: b
The largest value of b that divides 0.6 evenly is also 1.

Height of the wall: 4 m
Height of each brick: c
The largest value of c that divides 4 evenly is 1.

Therefore, the dimensions of each brick are 1 m x 1 m x 1 m.

Now, we can calculate the minimum number of bricks required.
Number of bricks required = (Length of the wall / Length of each brick) x (Width of the wall / Width of each brick) x (Height of the wall / Height of each brick)
Number of bricks required = (4 / 1) x (0.6 / 1) x (4 / 1) = 4 x 0.6 x 4 = 9.6

Since we cannot have a fraction of a brick, we need to round up the number to the nearest whole number.
Therefore, the minimum number of bricks required to construct the wall is 10.

Number of bricks used to construct the outer layer of the wall:

To find the number of bricks used to construct the outer layer of the wall, we need to calculate the surface area of the outer layer.

The surface area of the outer layer can be calculated using the formula:
Surface area = 2lw + 2lh + 2wh

Given:
Length of the wall = 4 m
Width of the wall = 0.6 m
Height of the wall = 4 m

Substituting these values into the formula, we get:
Surface area = 2(4)(0.6) + 2(4)(4) + 2(0.6)(4)
Surface area = 4.8 + 32 + 4.8
Surface area = 41.6

Now, we need to calculate the surface area of each brick.
Since each brick has dimensions of 1 m x 1 m x 1 m, the surface area of each brick is:
Surface area of each brick = 2(1)(1) + 2(1)(1) + 2(1)(1)
Surface area of each brick = 2 + 2 + 2
Surface area of each brick = 6

To find the number of bricks used to construct the outer layer, we divide the surface area of the outer layer by the surface

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Read the passages carefully and answer the questions that follow : Time has many dimensions, is a concept often advanced to account for certain inexplicable happenings. The gist of the idea is that time - which seems to unfold in a linear way, with the past coming before the present and the present before the future - might, in another dimension, not be experienced sequentially. The past, present and future could exist simultaneously. The concept that there are unfamiliar dimensions of time is most easily approached by way of those dimensions with which we are already familiar, those of length, height and breadth. These, in turn, are best approached, quite literally, from a starting point, which, geometrically speaking, has a location but no dimensions. It does, however, relate to figures with dimensions in the following way: If a point is moved through space, it marks a line, with the one dimension of length. 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And, in what sort of new direction could a three-dimensional shape be moved to produce one of four dimensions, since a movement other than up and down, backward and forward or side to side would simply produce a larger figure, not one of a different dimension. The answer, of course, is the feature duration. For, as soon as something ceases to endure, it ceases to exit. To the three familiar dimensions, then, we should add duration in time as a fourth dimension. Ordinary, three-dimensional bodies should, therefore, be properly described as having only length, breadth and height but no duration. Is such a thing possible? It is, but only hypothetically. For in fact, the point, line and plane do not truly exist as such. Any line that can be seen has breadth as well as length (and duration), just as any physical plane has a certain thickness as well as length and breadth. What movement, then, must a figure of three dimensions undergo to produce a body of four dimensions? 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Since any perceptible body is, in fact, undergoing all these motions simultaneously, we can say that it is ordinarily imperceptible. Because, motions and the dimensions, they imply, are only perceptible in a framework of time, they can be referred to as dimensions of time.If duration is one aspect of time, what might the others be? Among several possibilities, we can suggest appearance and disappearance, change and recurrence. Of all possibilities, only duration is perceptible. When we say that something is perceptible, we mean that we suddenly note its existence, when something disappears we note its lack of existence. We perceive no intermediate condition of appearing or disappearing. In the same way, we talk of change, but actually only develop the concept, as we perceive aggregates of characteristics that exist or cease to exist. And so we infer, but do not observe, the recurrence of sunset and sunrise, the passage of seasons, the growth of a child. 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If a line is moved through space, it traces the figure of a plane with the two dimensions of length and breadth. And, if a plane is moved in space, it traces a figure with the three dimensions of length, breadth and height.We can also work backward to form a three-dimensional body and find that the cross section of the three-dimensional cube is a two-dimensional plane, the cross section of the two-dimensional plane is a one-dimensional line and that the cross section of the line is a dimensionless point. From this, we can infer that a body of three dimensions is the cross section of a body, when moved in a certain way, of four dimensions. Then comes the question, of what sort of body could a three-dimensional shape be the cross section? And, in what sort of new direction could a three-dimensional shape be moved to produce one of four dimensions, since a movement other than up and down, backward and forward or side to side would simply produce a larger figure, not one of a different dimension. The answer, of course, is the feature duration. For, as soon as something ceases to endure, it ceases to exit. To the three familiar dimensions, then, we should add duration in time as a fourth dimension. Ordinary, three-dimensional bodies should, therefore, be properly described as having only length, breadth and height but no duration. Is such a thing possible? It is, but only hypothetically. For in fact, the point, line and plane do not truly exist as such. Any line that can be seen has breadth as well as length (and duration), just as any physical plane has a certain thickness as well as length and breadth. What movement, then, must a figure of three dimensions undergo to produce a body of four dimensions?We moved a plane in the dimension of height to produce a cube, so the movement of a (hypothetical) cube in the dimension of time should produce a (real) figure of four dimensions. What does movement in the dimension of time mean? As we said, it must mean movement in a new direction, not up, down or sideways. Are there any other kinds of movement? For a start, there is the movement that the Earths rotation imparts to everything upon it and that puts even apparently motionless bodies in motion. Thus, we may say that the cross section of a real body, whose fourth dimension is duration, is inseparable from the motion that the turning world inevitably imparts to everything. Further, inevitable motions are that of the Earth around the Sun, of the Sun around the centre of the galaxy, and, perhaps, of the galaxy itself around some unknown point. Since any perceptible body is, in fact, undergoing all these motions simultaneously, we can say that it is ordinarily imperceptible. Because, motions and the dimensions, they imply, are only perceptible in a framework of time, they can be referred to as dimensions of time.If duration is one aspect of time, what might the others be? Among several possibilities, we can suggest appearance and disappearance, change and recurrence. Of all possibilities, only duration is perceptible. When we say that something is perceptible, we mean that we suddenly note its existence, when something disappears we note its lack of existence. We perceive no intermediate condition of appearing or disappearing. In the same way, we talk of change, but actually only develop the concept, as we perceive aggregates of characteristics that exist or cease to exist. And so we infer, but do not observe, the recurrence of sunset and sunrise, the passage of seasons, the growth of a child. And yet, things really do appear and disappear, change and recur, although not actually perceived to do so. They are, so to speak, hypothetical to us and must have their reality in other dimensions of time, just as the hypothetical three-dimensional body becomes real, that is, perceptible, in the dimension of time we call duration.If access to higher dimensions of time belongs to one body, it is at least theoretically possible that it belongs, though invisibly, to all bodies. We can further assume that such access is by way of unfamiliar modes or levels of consciousness – and that the name we give to one of these is prophecy.Q. In the passage, the author has

View answer

Read the passages carefully and answer the questions that follow :Time has many dimensions, is a concept often advanced to account for certain inexplicable happenings. The gist of the idea is that time - which seems to unfold in a linear way, with the past coming before the present and the present before the future - might, in another dimension, not be experienced sequentially. The past, present and future could exist simultaneously.The concept that there are unfamiliar dimensions of time is most easily approached by way of those dimensions with which we are already familiar, those of length, height and breadth. These, in turn, are best approached, quite literally, from a starting point, which, geometrically speaking, has a location but no dimensions. It does, however, relate to figures with dimensions in the following way: If a point is moved through space, it marks a line, with the one dimension of length. If a line is moved through space, it traces the figure of a plane with the two dimensions of length and breadth. And, if a plane is moved in space, it traces a figure with the three dimensions of length, breadth and height.We can also work backward to form a three-dimensional body and find that the cross section of the three-dimensional cube is a two-dimensional plane, the cross section of the two-dimensional plane is a one-dimensional line and that the cross section of the line is a dimensionless point. From this, we can infer that a body of three dimensions is the cross section of a body, when moved in a certain way, of four dimensions. Then comes the question, of what sort of body could a three-dimensional shape be the cross section? And, in what sort of new direction could a three-dimensional shape be moved to produce one of four dimensions, since a movement other than up and down, backward and forward or side to side would simply produce a larger figure, not one of a different dimension. The answer, of course, is the feature duration. For, as soon as something ceases to endure, it ceases to exit. To the three familiar dimensions, then, we should add duration in time as a fourth dimension. Ordinary, three-dimensional bodies should, therefore, be properly described as having only length, breadth and height but no duration. Is such a thing possible? It is, but only hypothetically. For in fact, the point, line and plane do not truly exist as such. Any line that can be seen has breadth as well as length (and duration), just as any physical plane has a certain thickness as well as length and breadth. What movement, then, must a figure of three dimensions undergo to produce a body of four dimensions?We moved a plane in the dimension of height to produce a cube, so the movement of a (hypothetical) cube in the dimension of time should produce a (real) figure of four dimensions. What does movement in the dimension of time mean? As we said, it must mean movement in a new direction, not up, down or sideways. Are there any other kinds of movement? For a start, there is the movement that the Earths rotation imparts to everything upon it and that puts even apparently motionless bodies in motion. Thus, we may say that the cross section of a real body, whose fourth dimension is duration, is inseparable from the motion that the turning world inevitably imparts to everything. Further, inevitable motions are that of the Earth around the Sun, of the Sun around the centre of the galaxy, and, perhaps, of the galaxy itself around some unknown point. Since any perceptible body is, in fact, undergoing all these motions simultaneously, we can say that it is ordinarily imperceptible. Because, motions and the dimensions, they imply, are only perceptible in a framework of time, they can be referred to as dimensions of time.If duration is one aspect of time, what might the others be? Among several possibilities, we can suggest appearance and disappearance, change and recurrence. Of all possibilities, only duration is perceptible. When we say that something is perceptible, we mean that we suddenly note its existence, when something disappears we note its lack of existence. We perceive no intermediate condition of appearing or disappearing. In the same way, we talk of change, but actually only develop the concept, as we perceive aggregates of characteristics that exist or cease to exist. And so we infer, but do not observe, the recurrence of sunset and sunrise, the passage of seasons, the growth of a child. And yet, things really do appear and disappear, change and recur, although not actually perceived to do so. They are, so to speak, hypothetical to us and must have their reality in other dimensions of time, just as the hypothetical three-dimensional body becomes real, that is, perceptible, in the dimension of time we call duration.If access to higher dimensions of time belongs to one body, it is at least theoretically possible that it belongs, though invisibly, to all bodies. We can further assume that such access is by way of unfamiliar modes or levels of consciousness – and that the name we give to one of these is prophecy.Q. As per the passage, it is not possible to have a true line.

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A wall of dimensions 4 m x 0.6 m x 4 m is constructed by using identical and indistinguishable cubical bricks. The edge of the cubical bricks chosen in such a way that number of bricks used to construct the wall is minimum possible. Some bricks are black and some are red in color. 1.Find the minimum number of bricks required to construct the wall. 2-How many bricks are used to construct the outer layer of the wall? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A wall of dimensions 4 m x 0.6 m x 4 m is constructed by using identical and indistinguishable cubical bricks. The edge of the cubical bricks chosen in such a way that number of bricks used to construct the wall is minimum possible. Some bricks are black and some are red in color. 1.Find the minimum number of bricks required to construct the wall. 2-How many bricks are used to construct the outer layer of the wall? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wall of dimensions 4 m x 0.6 m x 4 m is constructed by using identical and indistinguishable cubical bricks. The edge of the cubical bricks chosen in such a way that number of bricks used to construct the wall is minimum possible. Some bricks are black and some are red in color. 1.Find the minimum number of bricks required to construct the wall. 2-How many bricks are used to construct the outer layer of the wall?.

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