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Answer the following questions based on the information given below:
A large cube has a unique whole number, smaller than or equal to 5, written on each of its faces such that the sum of the numbers on opposite faces is equal to 5. Any face that has an odd natural number written on it is painted red, any face that has an even natural number written on it is painted green and any remaining face(s) is/are painted blue. The large cube is then cut into 125 small identical cubes.
Q.How many of the smaller cubes have at least one of their faces painted blue?
- a)0
- b)15
- c)16
- d)25
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Answer the following questions based on the information given below:A ...
The six numbers have to be 0 to 5 such that 0 and 5 are written on opposite faces, 1 and 4 are written on opposite faces and 2 and 3 are written on opposite faces.
The faces with numbers 1, 3 and 5 on them are painted red, the faces with numbers 2 and 4 are painted green and the face with number 0 is painted blue.
Since the original cube is divided into 125 (i.e. 53) identical cubes, each face has 25 (i.e. 52) cubes.
All 25 cubes have exactly one face painted blue. No other cube has any face painted blue.
Hence, option 4.
The faces with numbers 1, 3 and 5 on them are painted red, the faces with numbers 2 and 4 are painted green and the face with number 0 is painted blue.
Since the original cube is divided into 125 (i.e. 53) identical cubes, each face has 25 (i.e. 52) cubes.
All 25 cubes have exactly one face painted blue. No other cube has any face painted blue.
Hence, option 4.
Most Upvoted Answer
Answer the following questions based on the information given below:A ...
Given information:
- A large cube has a unique whole number, smaller than or equal to 5, written on each of its faces.
- The sum of the numbers on opposite faces is equal to 5.
- Any face with an odd natural number is painted red.
- Any face with an even natural number is painted green.
- Any remaining face(s) is/are painted blue.
- The large cube is cut into 125 identical small cubes.
To find:
The number of smaller cubes that have at least one of their faces painted blue.
Solution:
Step 1: Understanding the large cube:
- Let's consider the large cube. It has 6 faces.
- The sum of the numbers on opposite faces is equal to 5.
- So, the possible pairs of numbers on opposite faces are (1, 4), (2, 3), and (3, 2).
- Since the numbers are smaller than or equal to 5, the possible pairs for opposite faces are (1, 4) and (2, 3).
Step 2: Coloring the large cube:
- Any face with an odd natural number is painted red, and any face with an even natural number is painted green.
- Let's consider the pair (1, 4) for opposite faces. In this case, one face will be painted red and the other green.
- Similarly, for the pair (2, 3), one face will be painted red and the other green.
Step 3: Identifying the painted faces:
- From Step 2, we know that 2 faces are painted red and 2 faces are painted green.
- The remaining faces will be painted blue.
Step 4: Cutting the large cube into smaller cubes:
- The large cube is cut into 125 identical small cubes.
- Each small cube will have 6 faces, and some of them will be painted blue.
Step 5: Finding the number of smaller cubes with at least one blue face:
- Since each small cube has 6 faces, we need to find the number of small cubes that have at least one blue face.
- From Step 3, we know that 2 faces of the large cube are painted blue.
- These 2 blue faces will be divided among the 125 small cubes.
- Since each small cube can have at most 1 blue face, the maximum number of small cubes with a blue face is 2.
- However, we need to consider that some small cubes may not have any blue faces.
- Therefore, the number of smaller cubes with at least one blue face is less than or equal to 2.
Conclusion:
The number of smaller cubes that have at least one of their faces painted blue is 2 or less. None of the given options (a) 0, (b) 15, (c) 16, (d) 25 are correct.
- A large cube has a unique whole number, smaller than or equal to 5, written on each of its faces.
- The sum of the numbers on opposite faces is equal to 5.
- Any face with an odd natural number is painted red.
- Any face with an even natural number is painted green.
- Any remaining face(s) is/are painted blue.
- The large cube is cut into 125 identical small cubes.
To find:
The number of smaller cubes that have at least one of their faces painted blue.
Solution:
Step 1: Understanding the large cube:
- Let's consider the large cube. It has 6 faces.
- The sum of the numbers on opposite faces is equal to 5.
- So, the possible pairs of numbers on opposite faces are (1, 4), (2, 3), and (3, 2).
- Since the numbers are smaller than or equal to 5, the possible pairs for opposite faces are (1, 4) and (2, 3).
Step 2: Coloring the large cube:
- Any face with an odd natural number is painted red, and any face with an even natural number is painted green.
- Let's consider the pair (1, 4) for opposite faces. In this case, one face will be painted red and the other green.
- Similarly, for the pair (2, 3), one face will be painted red and the other green.
Step 3: Identifying the painted faces:
- From Step 2, we know that 2 faces are painted red and 2 faces are painted green.
- The remaining faces will be painted blue.
Step 4: Cutting the large cube into smaller cubes:
- The large cube is cut into 125 identical small cubes.
- Each small cube will have 6 faces, and some of them will be painted blue.
Step 5: Finding the number of smaller cubes with at least one blue face:
- Since each small cube has 6 faces, we need to find the number of small cubes that have at least one blue face.
- From Step 3, we know that 2 faces of the large cube are painted blue.
- These 2 blue faces will be divided among the 125 small cubes.
- Since each small cube can have at most 1 blue face, the maximum number of small cubes with a blue face is 2.
- However, we need to consider that some small cubes may not have any blue faces.
- Therefore, the number of smaller cubes with at least one blue face is less than or equal to 2.
Conclusion:
The number of smaller cubes that have at least one of their faces painted blue is 2 or less. None of the given options (a) 0, (b) 15, (c) 16, (d) 25 are correct.
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Answer the following questions based on the information given below:A large cube has a unique whole number, smaller than or equal to 5, written on each of its faces such that the sum of the numbers onopposite faces is equal to 5. Any face that has an odd natural number written on it is painted red, any face that has an even natural number written on it is painted green and any remaining face(s) is/are painted blue. The large cube is then cut into 125 small identical cubes.Q.How many of the smaller cubes have at least one of their faces painted blue?a)0b)15c)16d)25Correct answer is option 'D'. Can you explain this answer?
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