11+ Entrance Non-Verbal Reasoning: Matrices Questions and Answers — Questions and Answers
Question 1: A 3x3 grid is presented. The top row contains: [A square with a small black circle in the top-left corner], [A square with a small black circle in the top-right corner], [A square with a small black circle in the bottom-right corner]. The middle row contains: [A triangle with a small black circle in the top-left corner], [A triangle with a small black circle in the top-right corner], [A triangle with a small black circle in the bottom-right corner]. The bottom row contains: [A circle with a small black circle in the top-left corner], [A circle with a small black circle in the top-right corner], [A missing square]. Which of the options below completes the grid?
- A circle with a small black circle in the bottom-left corner
- A square with a small black circle in the bottom-right corner
- A circle with a small black circle in the bottom-right corner (Correct answer)
- A triangle with a small black circle in the bottom-left corner
Correct answer: A circle with a small black circle in the bottom-right corner
The logic of the matrix operates both horizontally and vertically. Each row features the same main shape (square, triangle, circle). Each column features the same position for the small black circle (top-left, top-right, bottom-right). Therefore, the missing square must contain the shape from its row (a circle) and the small circle position from its column (bottom-right).
Question 2: In a 3x3 grid, a sequence of shapes unfolds. The top row shows: [A single horizontal line], [Two horizontal lines], [Three horizontal lines]. The middle row shows: [A single vertical line], [Two vertical lines], [Three vertical lines]. The bottom row shows: [A single diagonal line (bottom-left to top-right)], [Two diagonal lines], [A missing square]. Which of the options below is the correct final square in the sequence?
- Three vertical lines
- Three diagonal lines (bottom-left to top-right) (Correct answer)
- Two diagonal lines (top-left to bottom-right)
- Four horizontal lines
Correct answer: Three diagonal lines (bottom-left to top-right)
The pattern in the matrix is based on the type of line and the quantity. Each row maintains a consistent type of line (horizontal, vertical, or diagonal). The number of lines increases by one in each step from left to right across each row (1, 2, 3). The final square must therefore contain three diagonal lines, matching the pattern of its row.
Question 3: A 3x3 grid contains arrows. The top row: [Arrow points North], [Arrow points North-East], [Arrow points East]. The middle row: [Arrow points South-West], [Arrow points South], [Arrow points South-East]. The bottom row: [Arrow points West], [A missing square], [Arrow points North]. What is the missing arrow?
- Arrow points North-West (Correct answer)
- Arrow points South
- Arrow points East
- Arrow points West
Correct answer: Arrow points North-West
The arrows in the grid are rotating clockwise by 45 degrees. Following the sequence from the top-left (North) across the rows, the pattern is N, NE, E, then it appears to jump. However, if you follow the pattern starting from the bottom-left (West), it goes West, ?, North. To fit the overall clockwise rotation pattern seen in the top row, the missing arrow must be North-West, completing the sequence: West, North-West, North.
Question 4: Consider a 2x2 grid with one square missing. The top-left square contains a large circle with a small triangle inside it. The top-right square contains just a large circle. The bottom-left square contains a large square with a small triangle inside it. Which of the options below correctly fills the missing bottom-right square?
- A large triangle with a small square inside it
- A large circle
- A large square (Correct answer)
- A small triangle
Correct answer: A large square
The rule in this matrix operates from left to right. In the top row, the inner shape (the small triangle) is removed to leave only the outer shape (the large circle). Applying this same 'remove the inner shape' rule to the bottom row, the small triangle is removed from the large square, leaving just the large square.
Question 5: A 3x3 grid contains squares with different shading. In the top row, the squares are: [Shaded top half], [Shaded bottom half], [Fully shaded]. In the middle row, the squares are: [Shaded left half], [Shaded right half], [Fully shaded]. In the bottom row, the squares are: [Shaded top half], [Shaded right half], [A missing square]. What is the missing square?
- A square with the top half and right half shaded (Correct answer)
- A fully shaded square
- A square with the bottom half and left half shaded
- An unshaded square
Correct answer: A square with the top half and right half shaded
The logic in this matrix is that the third square in each row is a superposition, or combination, of the shading in the first two squares. In the top row, shading the top half and the bottom half results in a fully shaded square. The same applies to the middle row (left half + right half = full). Therefore, in the bottom row, combining the shading of the top half and the right half results in a square with both the top and right halves shaded.
Question 6: A 3x3 grid contains cells with a number of black dots. The top row contains cells with 3, 8, and 1 dot respectively. The middle row contains cells with 4, 2, and 6 dots. The bottom row contains cells with 5, 2, and a missing cell. The number of dots in each row adds up to the same total. Which option completes the grid?
- A cell with 4 dots
- A cell with 6 dots
- A cell with 3 dots
- A cell with 5 dots (Correct answer)
Correct answer: A cell with 5 dots
The logic in this matrix is mathematical. First, determine the total number of dots for the completed rows. The top row has 3 + 8 + 1 = 12 dots. The middle row has 4 + 2 + 6 = 12 dots. Since the rule is that each row sums to the same total, the bottom row must also sum to 12. The first two cells of the bottom row have 5 + 2 = 7 dots. Therefore, the missing cell must contain 12 - 7 = 5 dots.
11+ Entrance Non-Verbal Reasoning: Matrices Questions and Answers
A 3x3 grid is presented.
The top row contains: [A square with a small black circle in the top-left corner], [A square with a small black circle in the top-right corner], [A square with a small black circle in the bottom-right corner].
The middle row contains: [A triangle with a small black circle in the top-left corner], [A triangle with a small black circle in the top-right corner], [A triangle with a small black circle in the bottom-right corner].
The bottom row contains: [A circle with a small black circle in the top-left corner], [A circle with a small black circle in the top-right corner], [A missing square].
Which of the options below completes the grid?