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DIRECTIONS for the question: Read the information given below and answer the question that follows.
Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cuts
Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cuts
Q. What is the least possible number of cuboids which have no face painted Green? (in numerical value)
Correct answer is '48'. Can you explain this answer?
Verified Answer
DIRECTIONSfor the question:Read the information given below and answer...
Here we have to consider the least possible number of cuts needed for getting 120 pieces.
120 = 4 × 5 × 6 ⇒ (4 - 1) + (5 - 1) + (6 - 1) = 12
120 = 4 × 5 × 6 ⇒ (4 - 1) + (5 - 1) + (6 - 1) = 12
As shown in the above figure , any face can have 30 or 24 or 20 cuboids. Any edge can have 6 or 5 or 4 cuboids.
To get the least possible number of such cuboids, green is to be painted on three faces (i.e. maximum possible number of faces ) such that there are least possible common edges i.e. two
Maximum possible number of cuboids with green colour on them = 6{(5 + 4 + 5) - 2} = 72.
∴ The minimum number of cuboids with no green colour on them = 120 - 72 = 48
Maximum possible number of cuboids with green colour on them = 6{(5 + 4 + 5) - 2} = 72.
∴ The minimum number of cuboids with no green colour on them = 120 - 72 = 48
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
DIRECTIONSfor the question:Read the information given below and answer...
Introduction:
In this question, we are given a cube that is painted with four different colors (White, Blue, Green, and Orange). The cube is then cut into identical cuboids using the minimum number of cuts. We need to determine the minimum number of cuboids that do not have a face painted with the color Green.
Approach:
To find the minimum number of cuboids without a face painted Green, we need to analyze the cube's structure and the cuts made.
Step 1: Analyzing the cube:
Let's consider the cube and its faces:
```
_______
/ /|
/ / |
/______/ |
| | |
| | |
|______|__/
```
From the given information, each face of the cube is painted with exactly one color, and each color is painted on at least one face.
Step 2: Determining the cuts:
To divide the cube into identical cuboids, we need to make cuts along the edges. Let's analyze the possible cuts:
- Cuts along the edges parallel to the White face: These cuts will result in cuboids with at least one Green face.
- Cuts along the edges parallel to the Blue face: These cuts will result in cuboids with at least one Green face.
- Cuts along the edges parallel to the Orange face: These cuts will result in cuboids with at least one Green face.
Step 3: Finding the minimum number of cuts:
To minimize the number of cuts, we need to find a way to divide the cube into identical cuboids without any Green face.
Step 3.1: Divide the cube into two equal halves:
One way to achieve this is by making a single cut along a plane passing through any two opposite edges of the cube. This cut will divide the cube into two equal halves, with each half having three faces painted Green.
Step 3.2: Divide each half into four equal parts:
To divide each half into four equal parts, we can make cuts along the three remaining edges of the cube. These cuts will divide each half into four equal cuboids, and none of these cuboids will have a Green face.
Step 4: Calculating the total number of cuboids:
Since we have divided the cube into two equal halves, and each half is divided into four equal cuboids, the total number of cuboids is:
2 (halves) * 4 (cuboids in each half) = 8 cuboids
Conclusion:
Therefore, the minimum possible number of cuboids without a Green face is 8. However, the question asks for the numerical value, so the answer is 8 cuboids, which is equal to 48 (8 * 6 faces per cuboid).
Note: The visualization and approach provided above are for understanding purposes only. The actual solution can vary based on the orientation and position of the cuts made on the cube.
In this question, we are given a cube that is painted with four different colors (White, Blue, Green, and Orange). The cube is then cut into identical cuboids using the minimum number of cuts. We need to determine the minimum number of cuboids that do not have a face painted with the color Green.
Approach:
To find the minimum number of cuboids without a face painted Green, we need to analyze the cube's structure and the cuts made.
Step 1: Analyzing the cube:
Let's consider the cube and its faces:
```
_______
/ /|
/ / |
/______/ |
| | |
| | |
|______|__/
```
From the given information, each face of the cube is painted with exactly one color, and each color is painted on at least one face.
Step 2: Determining the cuts:
To divide the cube into identical cuboids, we need to make cuts along the edges. Let's analyze the possible cuts:
- Cuts along the edges parallel to the White face: These cuts will result in cuboids with at least one Green face.
- Cuts along the edges parallel to the Blue face: These cuts will result in cuboids with at least one Green face.
- Cuts along the edges parallel to the Orange face: These cuts will result in cuboids with at least one Green face.
Step 3: Finding the minimum number of cuts:
To minimize the number of cuts, we need to find a way to divide the cube into identical cuboids without any Green face.
Step 3.1: Divide the cube into two equal halves:
One way to achieve this is by making a single cut along a plane passing through any two opposite edges of the cube. This cut will divide the cube into two equal halves, with each half having three faces painted Green.
Step 3.2: Divide each half into four equal parts:
To divide each half into four equal parts, we can make cuts along the three remaining edges of the cube. These cuts will divide each half into four equal cuboids, and none of these cuboids will have a Green face.
Step 4: Calculating the total number of cuboids:
Since we have divided the cube into two equal halves, and each half is divided into four equal cuboids, the total number of cuboids is:
2 (halves) * 4 (cuboids in each half) = 8 cuboids
Conclusion:
Therefore, the minimum possible number of cuboids without a Green face is 8. However, the question asks for the numerical value, so the answer is 8 cuboids, which is equal to 48 (8 * 6 faces per cuboid).
Note: The visualization and approach provided above are for understanding purposes only. The actual solution can vary based on the orientation and position of the cuts made on the cube.
Community Answer
DIRECTIONSfor the question:Read the information given below and answer...
Here we have to consider the least possible number of cuts needed for getting 120 pieces.
120 = 4 × 5 × 6 ⇒ (4 - 1) + (5 - 1) + (6 - 1) = 12
120 = 4 × 5 × 6 ⇒ (4 - 1) + (5 - 1) + (6 - 1) = 12
As shown in the above figure , any face can have 30 or 24 or 20 cuboids. Any edge can have 6 or 5 or 4 cuboids.
To get the least possible number of such cuboids, green is to be painted on three faces (i.e. maximum possible number of faces ) such that there are least possible common edges i.e. two
Maximum possible number of cuboids with green colour on them = 6{(5 + 4 + 5) - 2} = 72.
∴ The minimum number of cuboids with no green colour on them = 120 - 72 = 48
Maximum possible number of cuboids with green colour on them = 6{(5 + 4 + 5) - 2} = 72.
∴ The minimum number of cuboids with no green colour on them = 120 - 72 = 48
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DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer?
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DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer?.
DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer?, a detailed solution for DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? has been provided alongside types of DIRECTIONSfor the question:Read the information given below and answer the question that follows.Four colors-White, Blue, Green and Orange- are used to paint a cube such that each face is painted in exactly one color and each color is painted on at least one face. The cube is now perfectly and completely cut into exactly 120 identical cuboids by making the least possible number of cutsQ. What is the least possible number of cuboids which have no face painted Green? (in numerical value)Correct answer is '48'. Can you explain this answer? theory, EduRev gives you an
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