Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV: Consider the following statements: I. > Figures II and III are sufficient to know as to

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Q: 103 (IAS/2006)
Each of the six faces of a cube is numbered by one of the six digits from 1 to 6. This cube is shown in its four different positions in the figures I, II, III and IV: Consider the following statements:
I. Figures II and III are sufficient to know as to which face is opposite to the face numbered 6.
II. Figure II and III are sufficient to know as to which face is opposite to the face numbered 4.
III. Figures I and IV are sufficient to know as to which face is opposite to the face numbered 3.
Which of the statements given are correct?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,1,4,1,0,3,1

keywords: 

{'cube': [0, 0, 2, 0], 'faces': [0, 0, 1, 0], 'different positions': [0, 0, 2, 0], 'figure ii': [0, 0, 1, 0], 'figures ii': [0, 0, 1, 0], 'digits': [0, 0, 3, 2], 'figures': [0, 0, 1, 1], 'face': [0, 0, 7, 2], 'iv': [6, 110, 77, 8]}

The question involves understanding the position of faces on a cube from different figures.

Statement I: Figures II and III depict 5 faces, there is only one face not visible, so we can conclude 6 is the opposite of the face not visible (1 in this case).

Statement II: In figures II and III, we see that face 2 is opposite to face 4 as in figure II, the top face is 2 and in figure III, the bottom face is 4.

Statement III: Figures I and IV allow us to deduce which face is opposite 3. In Figure I, we can see that face 3 is at the top, and in Figure IV, the bottom face is 5. Thus, face 5 is opposite face 3.

Therefore, all three statements are correct in determining the opposite sides of the given numbers. So, the correct answer is the option-4 I, II, and III.