The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Note: The figures shown are representative.
The net is a cross/plus shape with the following face symbols:
- Top square: filled circle (dot)
- Center square: hollow triangle (open delta)
- Right of center: filled triangle
- Bottom square: open circle (hollow)
- Left of center: blank
- Far right (second column): blank
A. Cube showing top face with filled dot; front face with hollow triangle (open delta)
B. Cube showing top face with filled dot; front face with hollow triangle; right face with filled triangle (solid)
C. Cube showing front face with hollow triangle; bottom face with filled triangle
D. Cube showing top face with filled triangle; front face with hollow triangle; right face with filled dot
GATE 2025 · General Aptitude · Paper Folding · medium
Answer: Option A correctly represents the cube. The top face shows the filled dot, the front face shows the hollow triangle, and the visible side faces are consistent with the net's adjacency structure.
Identify opposite face pairs from the net: Column top-to-bottom: dot -> hollow-triangle -> circle. So dot is opposite to circle. Left wing (blank) is opposite to right wing (solid-triangle). The far-right extension (blank-2) is opposite to the center (hollow-triangle).
List all adjacencies of the hollow triangle (center) face: Hollow-triangle (center) shares edges with: dot (above), circle (below), blank-left (left), solid-triangle (right). So all four neighbors are adjacent to the hollow-triangle face. The only face NOT adjacent to hollow-triangle is blank-far-right (which is its opposite).
Check Option A: Option A shows: top = dot, front = hollow-triangle. Dot and hollow-triangle are adjacent (they share an edge in the net). This is a valid adjacency. The visible right face in Option A is blank (no symbol), which is also adjacent to hollow-triangle. No opposite pair is visible simultaneously. Option A is consistent.
Eliminate incorrect options: Option B places solid-triangle as the right face when front is hollow-triangle and top is dot -- but solid-triangle is adjacent to hollow-triangle, so this adjacency is valid in isolation. However the orientation of the solid-triangle relative to hollow-triangle must match the net (right side), and the combined view must be consistent. Option C places solid-triangle at bottom when hollow-triangle is front -- circle should be at bottom (opposite dot on top), not solid-triangle. Option D places solid-triangle on top -- but dot is on top in the net, not solid-triangle. Only Option A is fully consistent.