Question

If a cube is to be constructed by folding the given figure along the lines shown, then in the cube so formed, what would the number be opposite to the number 4? 

• A. 1
• B. 2
• C. 3
• D. 5
• E. 6

Hint:

In a cube net, faces that share a common edge are adjacent, not opposite. Opposite faces will not share an edge in the net.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The grid contains numbers where rows follow a specific arithmetic relationship between the outer numbers and the inner numbers.
Step 2: Key Formula or Approach:
The pattern is: the absolute difference between the sum of the first and last columns and the sum of the second and third columns results in a perfect square.
Formula: \( |(C_1 + C_4) - (C_2 + C_3)| = n^2 \)
Step 3: Detailed Explanation:
Let's apply this to each row:
Row 1: \( |(2 + 15) - (10 + 11)| = |17 - 21| = 4 = 2^2 \).
Row 2: \( |(9 + 20) - (8 + 5)| = |29 - 13| = 16 = 4^2 \).
Row 4: \( |(6 + 15) - (9 + 11)| = |21 - 20| = 1 = 1^2 \).
Row 3: Let the missing number be \( x \).
\( |(7 + 10) - (9 + x)| = |17 - 9 - x| = |8 - x| \).
For this to follow the pattern, \( |8 - x| \) must be a perfect square.
Testing Option (E) 17: \( |8 - 17| = |-9| = 9 = 3^2 \).
This satisfies the logic as 9 is a perfect square.
Step 4: Final Answer:
The missing number is 17.