HPAT - Health Professions Admissions Non-Verbal Reasoning: Patterns Questions and Answers — Questions and Answers
Question 1: Which figure is the logical next step in the sequence? [Image shows a sequence of four squares. 1. A square with a small black circle in the top-left corner. 2. The square is rotated 90 degrees clockwise, now with black circles in the top-right and bottom-right corners. 3. The square is rotated another 90 degrees clockwise, with black circles in the bottom-left, bottom-right, and top-right corners. 4. The square is rotated another 90 degrees clockwise, with black circles in all four corners.]
- A square in the same orientation as box 1, with a black circle in the top-left corner.
- A square in the same orientation as box 4, with black circles in the top-left, top-right, and bottom-right corners.
- A square rotated 90 degrees clockwise from box 4, with black circles in the top-right, bottom-right, and bottom-left corners. (Correct answer)
- A square rotated 90 degrees clockwise from box 4, with a black circle only in the top-left corner.
Correct answer: A square rotated 90 degrees clockwise from box 4, with black circles in the top-right, bottom-right, and bottom-left corners.
The pattern has two rules operating simultaneously. First, the entire square rotates 90 degrees clockwise with each step. Second, a black circle is removed from a corner in a clockwise fashion, starting from the top-left corner. In step 4, all corners are filled. The next logical step would be to rotate the square 90 degrees and remove the top-left circle, leaving three circles. Answer C correctly shows the rotation and the removal of the top-left circle relative to the new orientation.
Question 2: Four of the following figures are alike in some way. Which figure is the odd one out? [Image shows five options, labeled A, B, C, D. Each option contains a large outer shape and a smaller, shaded inner shape.] A) A large pentagon (5 sides) containing a small, shaded square (4 sides). B) A large square (4 sides) containing a small, shaded triangle (3 sides). C) A large hexagon (6 sides) containing a small, shaded circle (infinite/0 sides). D) A large heptagon (7 sides) containing a small, shaded hexagon (6 sides).
- A
- B
- C (Correct answer)
- D
Correct answer: C
The rule connecting four of the figures is that the number of sides of the outer shape is exactly one more than the number of sides of the inner shape. A: 5 sides outer, 4 sides inner (+1). B: 4 sides outer, 3 sides inner (+1). D: 7 sides outer, 6 sides inner (+1). C breaks this pattern, as a hexagon has 6 sides and a circle has none in this context. Therefore, C is the odd one out.
Question 3: Which figure belongs in the empty box to complete the grid's pattern? [Image shows a 3x3 grid with the bottom-right box empty. Row 1: A circle with no fill; A circle with horizontal stripes; A black circle. Row 2: A square with no fill; A square with horizontal stripes; A black square. Row 3: A triangle with no fill; A triangle with horizontal stripes; ?]
- A square with no fill.
- A black triangle. (Correct answer)
- A triangle with vertical stripes.
- A black circle.
Correct answer: A black triangle.
The grid follows two rules. Rule 1 (Rows): The shape remains the same across each row (Row 1 is circles, Row 2 is squares, Row 3 is triangles). Rule 2 (Columns): The fill pattern changes down each column (Column 1 is no fill, Column 2 is horizontal stripes, Column 3 is black fill). To complete the grid, the figure in Row 3, Column 3 must be a triangle (following the row rule) and have a black fill (following the column rule).
Question 4: Figure A is to Figure B as Figure C is to...? [Image shows three figures. A: A large circle containing a small, black square. B: A large square containing a small, black circle. C: A large pentagon containing a small, white triangle.]
- A large triangle containing a small, white pentagon. (Correct answer)
- A large pentagon containing a small, black triangle.
- A large triangle containing a small, black pentagon.
- A large pentagon containing a small, white circle.
Correct answer: A large triangle containing a small, white pentagon.
The relationship from Figure A to Figure B is that the outer and inner shapes swap their roles. The large outer circle becomes the small inner circle, and the small inner square becomes the large outer square. The shading of the inner shape does not change. Applying this same transformation to Figure C, the large outer pentagon must become the small inner pentagon, and the small inner triangle must become the large outer triangle. The inner shape's white fill remains the same.
Question 5: Which of the following figures correctly fits in the middle of the sequence? [Image shows a sequence of five boxes, with the third box empty. 1. A single vertical line. 2. A vertical line with a horizontal line crossing its top (like a T). 3. ? 4. The 'T' shape from box 2, with a second horizontal line crossing its middle. 5. The shape from box 4, with a third horizontal line crossing its bottom.]
- A vertical line with a horizontal line crossing its middle. (Correct answer)
- A single horizontal line.
- A vertical line with a horizontal line crossing its bottom.
- The 'T' shape from box 2, with a second horizontal line crossing its bottom.
Correct answer: A vertical line with a horizontal line crossing its middle.
The pattern involves adding one horizontal line to the central vertical line in each step. The position of the added line moves downwards. In step 1, there is only a vertical line. In step 2, a horizontal line is added at the top. The logical third step is to add a horizontal line to the middle. Step 4 confirms this progression by showing lines at the top and middle. Step 5 completes the pattern with lines at the top, middle, and bottom.
Question 6: Which figure is the logical next step in the sequence? [Image shows a sequence of four boxes. 1. A clock face showing 3:00. 2. The same clock face showing 1:30. 3. The same clock face showing 12:00. 4. The same clock face showing 10:30.]
- 9:00 (Correct answer)
- 10:00
- 9:30
- 8:00
Correct answer: 9:00
The pattern is based on subtracting a progressively smaller amount of time in each step. From 3:00 to 1:30 is a subtraction of 1 hour and 30 minutes. From 1:30 to 12:00 is a subtraction of 1 hour and 30 minutes. Oh, wait, let me re-evaluate. 3:00 to 1:30 is -1h 30m. 1:30 to 12:00 is -1h 30m. 12:00 to 10:30 is -1h 30m. The pattern is a consistent subtraction of 1 hour and 30 minutes. Therefore, the next step is 10:30 minus 1 hour 30 minutes, which is 9:00.
HPAT - Health Professions Admissions Non-Verbal Reasoning: Patterns Questions and Answers
Which figure is the logical next step in the sequence?
[Image shows a sequence of four squares.
1.
A square with a small black circle in the top-left corner.
2.
The square is rotated 90 degrees clockwise, now with black circles in the top-right and bottom-right corners.
3.
The square is rotated another 90 degrees clockwise, with black circles in the bottom-left, bottom-right, and top-right corners.
4.
The square is rotated another 90 degrees clockwise, with black circles in all four corners.]