UDEE - Uniformed Division Entrance Exam Figural Reasoning and Patterns 2

Question 1

A series of four figures shows a triangle that gains one internal line with each step.
The first figure has no internal lines, the second has one diagonal line, the third has two diagonal lines crossing.
How many internal lines does the fourth figure contain?

Accepted Answer

Three lines dividing the triangle into sections

Answer

Two lines forming an X

Answer

Four lines creating a grid inside

Answer

The triangle disappears entirely

Question 2

In a horizontal series of five shapes, the figures alternate between a filled black circle and an unfilled white circle, but each circle is also 25% larger than the previous one. Which of the following best describes the fifth figure?

Accepted Answer

A large filled black circle

Answer

A small unfilled white circle

Answer

A large unfilled white circle

Answer

A medium filled black circle

Question 3

A 3×3 matrix of shapes follows these rules: each row contains a circle, a square, and a triangle (in varying order), and each column contains one small, one medium, and one large version of those shapes. The top-left cell is a small circle, the top-center is a medium square, and the center cell is a large circle. What shape and size belongs in the bottom-right cell?

Accepted Answer

Medium triangle

Answer

Large triangle

Answer

Small square

Answer

Small circle

Question 4

A pentagon rotates 72 degrees clockwise with each step in a series. A small star is fixed to one of its vertices. After four rotations from the starting position, how many total degrees has the shape rotated, and where does the star appear relative to the starting position?

Accepted Answer

288 degrees total; the star is four vertices clockwise from the start

Answer

288 degrees total; the star is one vertex counterclockwise from the start

Answer

360 degrees total; the star returns to its original position

Answer

360 degrees total; the star is at the opposite vertex

Question 5

In a pattern matrix, each figure in a row is the previous figure with one element removed. Row one shows: a rectangle with a circle inside and a triangle on top. Row two begins with the same figure but with the triangle removed. Following this rule, which figure would begin row three?

Accepted Answer

A rectangle with only the circle inside

Answer

A rectangle with a circle inside, a triangle on top, and a new square added

Answer

A plain rectangle with no circle and no triangle

Answer

A rectangle with only the triangle on top

Question 6

Examine the following transformation rule: a shape on the left side of an arrow becomes its mirror image on the right side, AND the shading inverts (filled becomes unfilled, unfilled becomes filled). A filled square with a white dot in its upper-right corner appears on the left. Which figure appears on the right?

Accepted Answer

An unfilled square with a black dot in the upper-left corner

Answer

An unfilled square with a white dot in the upper-right corner

Answer

A filled square with a black dot in the upper-left corner

Answer

An unfilled square with a white dot in the upper-left corner