DAT - Dental Admission Perceptual Ability: Pattern Folding Questions and Answers

Question 1

A 2D pattern for a cube is laid out in a cross shape. The central vertical column contains four squares, and there is one square on each side of the second square from the top. The top square is shaded black. The square below it (the central square) has a white circle. The square below that has a black star. The bottom square is shaded grey. The square to the left of the central square has a white triangle, and the square to the right has a black square. Which of the following 3D cubes can be formed from this pattern?

Accepted Answer

A cube showing the black square face on the right, the white circle face in the front, and the black shaded face on top.

Answer

When the pattern is folded, the white circle is the central face. The black shaded face folds to become the top, the black star becomes the bottom, the white triangle becomes the left, and the black square becomes the right. The grey face is opposite the central white circle face. Therefore, a view showing the black shaded top, white circle front, and black square right is a valid configuration. The other options are incorrect because: the star is on the bottom, not adjacent to the top/front view; the triangle and square are on opposite sides; and the grey face is opposite the circle, so it cannot be on top when the circle is in front.

Question 2

Consider a 2D pattern made of six squares arranged to form a cube. The layout consists of a 2x2 square grid with two additional squares attached: one to the top of the top-left square and one to the right of the top-right square. The faces are marked as follows: Top-left is 'A', top-right is 'B', bottom-left is 'C', bottom-right is 'D'. The square above 'A' is 'E', and the square to the right of 'B' is 'F'. Which of the following views of the folded cube is IMPOSSIBLE?

Accepted Answer

A view showing faces C, D, and E.

Answer

By analyzing the folds, we can determine the opposite faces. If we consider 'C' as the base, 'A' folds up to be the back, and 'D' folds up to be the right side. 'B' then folds over to become the front face. This means 'E' folds over to become the top face, and 'F' becomes the left face. The opposite pairs are: A-D, C-E, and B-F. The impossible view is the one that shows two opposite faces at the same time. Choice B shows faces C and E, which are opposite and thus cannot be seen together.

Question 3

A flat pattern for a cube consists of a horizontal row of four squares, with a fifth square attached above the second square from the left, and a sixth square attached below it. The second square from the left has an arrow pointing to the right (→). The square above it is fully shaded. The square below it has a circle. The square to its left is blank. The two squares to its right are also blank. When folded, which view is correct?

Accepted Answer

A cube with the arrow face on the front, the shaded face on top, and a blank face on the right.

Answer

Let the arrow face be the front. The shaded square folds to become the top face. The circle square folds to become the bottom face. The blank square to the left becomes the left-side face. The adjacent blank square folds to become the right-side face. The final blank square becomes the back face. Therefore, a view with the arrow on the front, the shaded face on top, and a blank face on the right is consistent with the pattern. The other options show incorrect adjacencies or orientations.

Question 4

A promotional die is made from a cardboard cutout in a standard cross shape. The central square of the cross is a company logo. The square above it is marked 'WIN'. The square below the logo is marked 'LOSE'. The square to the left of the logo is 'SPIN AGAIN'. To the right of the logo is 'DRAW CARD'. The final square, attached below 'LOSE', is a 'WILD' card. Which of the following statements is true about the assembled die?

Accepted Answer

The 'SPIN AGAIN' and 'DRAW CARD' faces are on opposite sides.

Answer

In a standard cross-shaped pattern, faces separated by one square in a straight line will be opposite. Therefore, 'WIN' is opposite 'LOSE', and 'LOGO' is opposite 'WILD'. The two arms of the cross, 'SPIN AGAIN' and 'DRAW CARD', will also be opposite each other when folded. Statement B correctly identifies an opposite pair. Statement A is false because 'WIN' and 'LOSE' are opposite. Statement C is false because 'LOGO' is opposite 'WILD'. Statement D is false because 'WILD' is opposite 'LOGO' and cannot be adjacent to 'WIN'.

Question 5

A 2D pattern is formed by six squares in a T-shape: a horizontal row of four squares with two squares stacked vertically below the second square from the left. The markings are: Horizontal row (left to right): Blank, Triangle, Blank, Circle. Vertical stack below Triangle (top to bottom): Square, Plus. Which 3D cube CANNOT be formed from this pattern?

Accepted Answer

A view showing the Triangle, Circle, and Plus face all together.

Answer

Let's determine the opposite faces. If the Triangle is the front face, the Square is the top, and the Plus is the bottom. The left Blank face becomes the left side, and the right Blank face becomes the right side. The Circle wraps around to become the back. The opposite pairs are: Square-Plus, left Blank-right Blank, and Triangle-Circle. The question asks which cube CANNOT be formed. The cube described in C shows the Triangle and Circle faces together. Since they are an opposite pair, they can never be visible at the same time, making this view impossible.

DAT Practice Test

DAT Practice Test

DAT - Dental Admission Perceptual Ability: Pattern Folding Questions and Answers