HPAT - Health Professions Admissions Non-Verbal Reasoning: Sequences Questions and Answers — Questions and Answers
Question 1: A sequence of five figures is presented. Each figure contains a large square divided into four equal quadrants. In Figure 1, a black circle is in the top-left quadrant. In Figure 2, the black circle has moved to the top-right quadrant, and a small white square has appeared in the top-left quadrant. In Figure 3, the black circle is in the bottom-right quadrant, and the white square is in the top-right. In Figure 4, the black circle is in the bottom-left quadrant, and the white square is in the bottom-right. Which of the following is the correct Figure 5 in the sequence?
- A) The black circle is in the top-left quadrant, and the white square is in the bottom-left. (Correct answer)
- B) The black circle is in the top-right quadrant, and the white square is in the bottom-left.
- C) The black circle is in the top-left quadrant, and the white square is in the bottom-right.
- D) The black circle and the white square are both in the top-left quadrant.
Correct answer: A) The black circle is in the top-left quadrant, and the white square is in the bottom-left.
There are two independent patterns. The black circle moves one quadrant clockwise in each step (top-left -> top-right -> bottom-right -> bottom-left). The next step for the circle is to return to the top-left quadrant. The white square is introduced in Figure 2 and follows the position that the black circle occupied in the *previous* figure. In Figure 2, the square is where the circle was in Figure 1 (top-left). In Figure 3, the square is where the circle was in Figure 2 (top-right). In Figure 4, the square is where the circle was in Figure 3 (bottom-right). Therefore, in Figure 5, the white square must move to the position the black circle occupied in Figure 4, which is the bottom-left quadrant. The correct answer combines these two patterns: the black circle in the top-left and the white square in the bottom-left.
Question 2: Consider a sequence of figures. Figure 1 is a regular pentagon (5 sides). Figure 2 is a regular hexagon (6 sides). Figure 3 is a regular heptagon (7 sides). Inside each figure, there is an arrow. In Figure 1, the arrow points to the top vertex. In Figure 2, the arrow points to the vertex immediately to the right of the top vertex (clockwise). In Figure 3, the arrow points to the second vertex, clockwise from the top. Which figure logically continues the sequence?
- A) An octagon where the arrow points to the second vertex clockwise from the top.
- B) An octagon where the arrow points to the fourth vertex clockwise from the top.
- C) A nonagon where the arrow points to the third vertex clockwise from the top.
- D) An octagon where the arrow points to the third vertex clockwise from the top. (Correct answer)
Correct answer: D) An octagon where the arrow points to the third vertex clockwise from the top.
The sequence has two rules. First, the main shape increases its number of sides by one at each step (5 -> 6 -> 7), so the next shape must be an octagon (8 sides). Second, the arrow's position follows a progression. It moves clockwise around the vertices. The number of vertices it moves forward increases by one each time: from Figure 1 to 2, it moves 1 vertex clockwise. From Figure 2 to 3, it moves 2 vertices clockwise. Therefore, from Figure 3 to 4, it must move 3 vertices clockwise. Starting from the second vertex from the top in the heptagon, moving 3 vertices clockwise in an octagon would land it on the third vertex from the top (original position + 3). The correct answer is an octagon with the arrow pointing to the third vertex clockwise from the top.
Question 3: Each figure in a sequence consists of a large triangle. In Figure 1, there is 1 small black dot inside the triangle. In Figure 2, there are 3 small black dots and the entire large triangle is shaded grey. In Figure 3, there are 5 small black dots and the triangle is white (unshaded). In Figure 4, there are 7 small black dots and the triangle is shaded grey. What is the correct next figure in the sequence?
- A) A grey triangle with 8 dots.
- B) A white triangle with 9 dots. (Correct answer)
- C) A grey triangle with 9 dots.
- D) A white triangle with 11 dots.
Correct answer: B) A white triangle with 9 dots.
This sequence follows two patterns. The first pattern is the number of black dots: 1, 3, 5, 7. This is a simple arithmetic progression, increasing by 2 each time. The next number in the sequence is 7 + 2 = 9. The second pattern is the shading of the large triangle, which alternates between white and grey (white -> grey -> white -> grey). The next shading in the sequence must be white. Therefore, the correct figure is a white triangle containing 9 black dots.
Question 4: A sequence shows a 3x3 grid in each figure. In Figure 1, the top row contains three X's. In Figure 2, the middle row contains three O's. In Figure 3, the bottom row contains three X's. In Figure 4, the left column contains three O's. What would Figure 5 be?
- A) The middle column contains three X's. (Correct answer)
- B) The right column contains three O's.
- C) The top row contains three O's.
- D) The middle column contains three O's.
Correct answer: A) The middle column contains three X's.
The sequence involves filling a line of the grid in a specific order and alternating the symbol used. The pattern of filled lines is: top row, middle row, bottom row, left column. This is a logical progression around the grid. The next logical step would be the middle column. The symbols used are also in a pattern: X, O, X, O. Therefore, the next symbol to be used should be X. Combining these two rules, Figure 5 must show the middle column filled with three X's.
Question 5: In a sequence, Figure 1 shows a black square. Figure 2 shows the black square from Figure 1, with a smaller white circle placed on its right side. Figure 3 shows the contents of Figure 2, with an even smaller black triangle placed on the right of the white circle. Figure 4 shows the contents of Figure 3, with a yet smaller white star placed on the right of the black triangle. Which of the following describes Figure 5?
- A) The sequence from Figure 4, with a smaller black pentagon added to the right of the star. (Correct answer)
- B) The sequence from Figure 4, with a smaller white square added to the right of the star.
- C) The sequence from Figure 4, with a smaller black square added to the right of the star.
- D) Only a black pentagon is shown.
Correct answer: A) The sequence from Figure 4, with a smaller black pentagon added to the right of the star.
This is an accumulative sequence with two alternating patterns. First, a new shape is added to the right in each step. Second, the properties of the added shape follow a pattern. The shape pattern is: square (4 sides), circle, triangle (3 sides), star (assuming a 5-pointed star, but the key is the number of sides progression if we treat the circle as an exception or infinite sides). A more consistent pattern is the number of sides of the polygonal shapes: 4, 3, (next polygon should have 5). The color alternates: black, white, black, white. The next added shape should be black. Combining these, the next shape to be added should be a black polygon with 5 sides (a pentagon). This shape is added to the right of the existing sequence of shapes.
Question 6: Each figure in a sequence contains a large circle with a single line inside it, like the hand of a clock. In Figure 1, the line points to the 12 o'clock position. In Figure 2, it points to the 3 o'clock position. In Figure 3, it points to the 7 o'clock position. In Figure 4, it points to the 12 o'clock position. Which figure logically follows in the sequence?
- A) A circle with the line pointing to the 9 o'clock position.
- B) A circle with the line pointing to the 11 o'clock position.
- C) A circle with the line pointing to the 10 o'clock position. (Correct answer)
- D) A circle with the line pointing to the 1 o'clock position.
Correct answer: C) A circle with the line pointing to the 10 o'clock position.
The pattern is the number of hours the line moves forward (clockwise) on a clock face. From Figure 1 (12) to Figure 2 (3), it moves forward 3 hours. From Figure 2 (3) to Figure 3 (5), it moves forward 2 hours. From Figure 3 (5) to Figure 4 (8), it moves forward 3 hours. The pattern of movement is an alternating sequence of adding 3 hours, then adding 2 hours. The last movement was +3, so the next movement must be +2. Starting from the 8 o'clock position in Figure 4, moving forward 2 hours results in the line pointing to the 10 o'clock position.
