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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
Q. What is the maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)
Correct answer is '13'. Can you explain this answer?
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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 maximum possible number of cuboids which have more than one color on them, we have to use one color on three faces , such that any two faces are adjacent to each other.
∴ Number of such cuboids at the corners = 1
Number of such cuboids on the edges (but not corners ) = 3 + 4 + 5 = 12
∴ Total required cuboids = 13.
To get the maximum possible number of cuboids which have more than one color on them, we have to use one color on three faces , such that any two faces are adjacent to each other.
∴ Number of such cuboids at the corners = 1
Number of such cuboids on the edges (but not corners ) = 3 + 4 + 5 = 12
∴ Total required cuboids = 13.
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DIRECTIONSfor the question:Read the information given below and answer...
Given Information:
- Four colors (White, Blue, Green, and Orange) are used to paint a cube.
- Each face is painted in exactly one color.
- Each color is painted on at least one face.
- The cube is perfectly and completely cut into exactly 120 identical cuboids.
Objective:
To find the maximum possible number of cuboids which have more than one face painted in the same color.
Solution:
To maximize the number of cuboids with more than one face painted in the same color, we need to minimize the number of cuts made on the cube. Let's analyze the possible scenarios.
Scenario 1: No cuts are made
If no cuts are made on the cube, there will be six cuboids, each with only one face painted in a single color. Therefore, the number of cuboids with more than one face painted in the same color is 0.
Scenario 2: One cut is made
If only one cut is made on the cube, there will be nine cuboids. Let's analyze the possibilities for this scenario.
Possibility 1: The cut is made parallel to one of the faces.
- In this case, the cube will be divided into two smaller cubes, each with three faces painted in one color.
- So, there will be two cuboids with more than one face painted in the same color.
Possibility 2: The cut is made perpendicular to one of the edges.
- In this case, the cube will be divided into two rectangular prisms.
- Each rectangular prism will have two faces painted in one color and four faces with different colors.
- So, there will be four cuboids with more than one face painted in the same color.
Therefore, if only one cut is made, the maximum possible number of cuboids with more than one face painted in the same color is 2 + 4 = 6.
Scenario 3: Two cuts are made
If two cuts are made on the cube, there will be 27 cuboids. Let's analyze the possibilities for this scenario.
Possibility 1: The cuts are made parallel to two opposite faces.
- In this case, the cube will be divided into eight smaller cubes, each with three faces painted in one color.
- So, there will be eight cuboids with more than one face painted in the same color.
Possibility 2: The cuts are made parallel to one face and perpendicular to two adjacent edges.
- In this case, the cube will be divided into four rectangular prisms and four smaller cubes.
- Each rectangular prism will have two faces painted in one color and four faces with different colors.
- Each smaller cube will have three faces painted in one color and three faces with different colors.
- So, there will be 4 + 4 = 8 cuboids with more than one face painted in the same color.
Therefore, if two cuts are made, the maximum possible number of cuboids with more than one face painted in the same color is 8 + 8 = 16.
Conclusion:
By analyzing the possible scenarios, we can see that the maximum possible number of cuboids with more than one face painted in the same color is 16. However, it is mentioned in the
- Four colors (White, Blue, Green, and Orange) are used to paint a cube.
- Each face is painted in exactly one color.
- Each color is painted on at least one face.
- The cube is perfectly and completely cut into exactly 120 identical cuboids.
Objective:
To find the maximum possible number of cuboids which have more than one face painted in the same color.
Solution:
To maximize the number of cuboids with more than one face painted in the same color, we need to minimize the number of cuts made on the cube. Let's analyze the possible scenarios.
Scenario 1: No cuts are made
If no cuts are made on the cube, there will be six cuboids, each with only one face painted in a single color. Therefore, the number of cuboids with more than one face painted in the same color is 0.
Scenario 2: One cut is made
If only one cut is made on the cube, there will be nine cuboids. Let's analyze the possibilities for this scenario.
Possibility 1: The cut is made parallel to one of the faces.
- In this case, the cube will be divided into two smaller cubes, each with three faces painted in one color.
- So, there will be two cuboids with more than one face painted in the same color.
Possibility 2: The cut is made perpendicular to one of the edges.
- In this case, the cube will be divided into two rectangular prisms.
- Each rectangular prism will have two faces painted in one color and four faces with different colors.
- So, there will be four cuboids with more than one face painted in the same color.
Therefore, if only one cut is made, the maximum possible number of cuboids with more than one face painted in the same color is 2 + 4 = 6.
Scenario 3: Two cuts are made
If two cuts are made on the cube, there will be 27 cuboids. Let's analyze the possibilities for this scenario.
Possibility 1: The cuts are made parallel to two opposite faces.
- In this case, the cube will be divided into eight smaller cubes, each with three faces painted in one color.
- So, there will be eight cuboids with more than one face painted in the same color.
Possibility 2: The cuts are made parallel to one face and perpendicular to two adjacent edges.
- In this case, the cube will be divided into four rectangular prisms and four smaller cubes.
- Each rectangular prism will have two faces painted in one color and four faces with different colors.
- Each smaller cube will have three faces painted in one color and three faces with different colors.
- So, there will be 4 + 4 = 8 cuboids with more than one face painted in the same color.
Therefore, if two cuts are made, the maximum possible number of cuboids with more than one face painted in the same color is 8 + 8 = 16.
Conclusion:
By analyzing the possible scenarios, we can see that the maximum possible number of cuboids with more than one face painted in the same color is 16. However, it is mentioned in the
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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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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 maximum possible number of cuboids which have more than one face painted in the same color? (in numerical value)Correct answer is '13'. Can you explain this answer? tests, examples and also practice CAT tests.
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