Two tiles are missing in Panel I. Which one of the options in Panel II is the
appropriate choice for the missing tiles?

Step 1: Panel I shows a complete picture divided into a grid of tiles, with two tiles removed. To find the missing pieces, examine how the lines, shapes, and shading in the tiles bordering the empty spaces continue.
Step 2: For each candidate tile pair in Panel II, check whether the edges of the candidate tiles align with the edges of the surrounding tiles already present in Panel I, both in terms of line continuation and shading pattern.
Step 3: Options (ii), (iii) and (iv) each break continuity at some edge, either a line that does not connect properly with the neighbouring tile or a shading pattern that does not match the surrounding tiles.
Step 4: Option (i) is the only pair of tiles whose edges connect seamlessly with all four bordering tiles in Panel I, completing the picture without any visible break in the pattern.
Final Answer: \(\boxed{\text{(i)}}\)
The figure shows two 4-tile patterns.
Either one or both of the patterns can be used any number of times and in any
orientation to construct a new pattern. Which one of the options below cannot be
constructed by using only these two 4-tile patterns assuming there are no overlaps
among them?

A black square PQRS has been cut into two parts. One part of it is shown in
Panel I. Which one of the shapes in Panel II is the other part?

Water : P :: Food : Q
Choose the P and Q combination from the options below to form a meaningful
analogy.
Figures (i) and (ii) represent intercity highway systems. The black dots represent
cities and the line segments between them represent intercity highways.
A salesperson needs to make a trip. She needs to start from a city, visit each of the
remaining cities exactly once, and finally return to the same city from which she
started.
Which one of the following options is then true?
