How many pentagons are there in the 3-dimensional structure shown below? [Figure: see page 5 of source PDF]

A forest lies between two parts of a city. How many unique routes are there to go from the west side to point A in the east side without retracing any portion of the route? [Figure: see page 4 of source PDF]

Some cubes are missing from a 4 x 8 x 8 tightly packed structure made of alternating white and blue solid cubes as shown below. No cubes have been removed from the portion that is not visible. What is the total number of blue cubes in this structure? [Figure: see page 5 of source…

A square with a side of 5 cm was cut along the dotted lines as shown in the figure. This created a square piece of side 3 cm. The centres of the two squares are the same. What is the area (in cm²) of the shaded portion? [Figure: see page 4 of source PDF]

Shown below are two perspective views of a solid object. The pipe section has three identical cuts on its surface along with three identical flanges. How many surfaces are there? [Figure: see page 6 of source PDF]

Four boxes are shown below. The numbers within each box have a specific relationship. What number would replace the question mark? Boxes (top-left, top-right / bottom-left, bottom-right): [3, 6 / 6, 6], [1, 6 / 2, 8], [4, 2 / 7, 6], [3, ? / 9, 4]. [Figure: see page 4 of source PD…

A UNION of three solids (a cylinder of diameter 20 units, a cuboid of side 20 units, and a triangular prism with base of the triangle 20 units and height 20 units) is shown below. Visualise the new solid formed by the INTERSECTION of these three solids in this arrangement. How ma…

If B is an extruded form of A, how many surfaces will the extruded form of C have? [Figure: see page 3 of source PDF]

Shown in the figure are circles of diameter 42 cm. What is the total length (in cm) of the path LRMNOP as indicated by the red arrows? Assume π = 22/7. [Figure: see page 7 of source PDF]