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Directions to Solve
There are 128 cubes with me which are coloured according to two schemes viz.
  1. 64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.
  2. 64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up.
Question -
What is the total number of red faces ?
  • a)
    0
  • b)
    64
  • c)
    320
  • d)
    128
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Directions to Solve ...
No. of red faces among first 64 cubes = 128
No. of red faces among second 64 cubes = 192
Therefore, total number of red faces = 128 + 192 = 320
This question is part of UPSC exam. View all LR courses
Most Upvoted Answer
Directions to Solve ...
To solve this question, we need to analyze the given information and apply logical reasoning to determine the total number of red faces.

Given Information:
- There are 128 cubes in total.
- There are two schemes for coloring the cubes:
- Scheme 1: 64 cubes have two red adjacent faces, one yellow face, and one blue face on their opposite sides. The rest of the faces are green.
- Scheme 2: 64 cubes have two blue adjacent faces, one red face, and one green face on their opposite sides. The rest of the faces are red.

Analysis:
1. Scheme 1:
- There are 64 cubes with two red adjacent faces. Since each cube has 2 red faces, the total number of red faces in these cubes is 64 x 2 = 128.
2. Scheme 2:
- There are 64 cubes with two blue adjacent faces. Since each cube has 2 blue faces, the total number of blue faces in these cubes is 64 x 2 = 128.
- There are 64 cubes with one red and one green face. Since each cube has 1 red face, the total number of red faces in these cubes is 64 x 1 = 64.
- The rest of the faces in these cubes are red, so the total number of red faces in these cubes is 64 x 2 = 128.

Total Number of Red Faces:
To find the total number of red faces, we need to add the red faces from both schemes:
Red faces from Scheme 1: 128
Red faces from Scheme 2: 64 + 128 = 192

Therefore, the total number of red faces is 128 + 192 = 320.

Conclusion:
The correct answer is option 'C', 320. There are a total of 320 red faces in the 128 cubes.
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Directions to Solve There are 128 cubes with me which are coloured according to two schemes viz.64 cubes each having two red adjacent faces and one yellow and other blue on their opposite faces while green on the rest.64 cubes each having two adjacent blue faces and one red and other green on their opposite faces, while red on the rest. They are then mixed up. Question - What is the total number of red faces ?a)0b)64c)320d)128Correct answer is option 'C'. Can you explain this answer?
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