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NNAT3 Level F study materials
NNAT3 Level F study resources

NNAT3 Level F practice questions

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Question 1Conceptual

A 3-by-3 grid shows a square, a triangle, and a circle in its top row, the circle, the square, and the triangle in its middle row, and a missing cell at the bottom right after a triangle and a circle. The pattern shifts each shape one position to the left from one row to the next, wrapping the leftmost shape to the end. Which shape belongs in the missing cell?

  1. Star
  2. Square Correct answer.
  3. Circle
  4. Triangle

Explanation

In a left-rotation pattern, each row is the previous row moved one place left with the first element wrapped to the last position. The bottom row begins as triangle, circle, so the wrapped element is the square that started the middle row. The missing cell therefore holds the square.

Question 2Conceptual

In a 2-by-2 matrix, the top-left cell has one dot, the top-right has three dots, the bottom-left has two dots, and the bottom-right is empty. The rule is that the number of dots in each column increases by two going downward. What belongs in the empty cell?

  1. Three dots
  2. Five dots
  3. Two dots
  4. Four dots Correct answer.

Explanation

Column rule: starting value plus two per step downward. The right column starts at three dots, so adding two gives four dots in the bottom-right cell. This keeps both columns consistent with the stated arithmetic progression.

Question 3Conceptual

A sequence of figures shows a shaded region growing by one small square each step: 2, 4, 6, 8 shaded squares. What is the next term in this pattern?

  1. 10 Correct answer.
  2. 9
  3. 12
  4. 16

Explanation

The shaded count increases by a constant difference of two squares per step. Continuing the arithmetic sequence 2, 4, 6, 8 by adding two gives 10. The visual growth mirrors this constant increment.

Question 4Conceptual

A figure shows a large triangle divided by a line from one vertex to the midpoint of the opposite side. How many distinct triangles of any size appear in the figure?

  1. One
  2. Three Correct answer.
  3. Two
  4. Four

Explanation

The dividing line splits the large triangle into two smaller triangles, and the original large triangle counts as a third. Counting all sizes gives three distinct triangles. This is the standard embedded-triangle count for a single median line.

Question 5Conceptual

A grid alternates black and white cells in a checkerboard pattern. A candidate must decide which single cell color completes a 4-by-4 board whose top-left cell is black. What color is the cell in row 4, column 4?

  1. White
  2. Gray
  3. It cannot be determined
  4. Black Correct answer.

Explanation

In a checkerboard, a cell is black when the sum of its row and column numbers is even, given a black top-left. Row 4 plus column 4 equals 8, which is even, so the cell is black. The alternating rule fully determines the color.

Question 6Conceptual

A series of shapes rotates 90 degrees clockwise at each step. If the first shape points up, in which direction does the fourth shape point?

  1. Down
  2. Right
  3. Up
  4. Left Correct answer.

Explanation

Applying three 90-degree clockwise turns to an upward arrow gives right, then down, then left. The fourth figure therefore points left. Each step is a quarter turn clockwise.

Question 7Conceptual

Two figures are shown side by side: a small circle inside a large square, and a small square inside a large circle. The relationship is that the inner and outer shapes swap. Following the same rule, what pairs with a small triangle inside a large hexagon?

  1. A small hexagon inside a large triangle Correct answer.
  2. A small circle inside a large hexagon
  3. A small triangle inside a large triangle
  4. A large hexagon inside a small triangle

Explanation

The demonstrated rule exchanges the inner and outer shapes while keeping their relative sizes: the inner shape becomes the outer, and the outer becomes the inner. Applying this to a small triangle inside a large hexagon yields a small hexagon inside a large triangle. All other options violate the swap.

Question 8Conceptual

In a matrix, each row contains one figure with a curved outline, one with straight edges, and one with both. The first two rows are complete; the third row shows only the curved and the both-outline figures. Which outline type completes the third row?

  1. Straight Correct answer.
  2. Curved
  3. Both
  4. Mixed

Explanation

Each row must contain exactly one of each outline type. The third row already has curved and both, so the missing type is straight. This follows the one-of-each distribution rule.

Question 9Conceptual

A 3-by-3 matrix contains shapes that double in number across each row: row 1 has 1, 2, 3; row 2 has 2, 4, 6; row 3 has 3, 6, and an empty cell. What number of shapes belongs in the empty cell?

  1. 8
  2. 6
  3. 12
  4. 9 Correct answer.

Explanation

Within each row the count increases by a constant equal to the row number: row 1 adds one, row 2 adds two, row 3 adds three. Starting at three and adding three per step gives nine. This matches the multiplicative column pattern as well.

Question 10Conceptual

A sequence of four frames shows a dot moving clockwise around the corners of a square, one corner per frame, starting at the top-left. A second dot moves counterclockwise starting at the bottom-right. In which frame do the two dots first occupy the same corner?

  1. Second frame Correct answer.
  2. Third frame
  3. First frame
  4. Fourth frame

Explanation

Label corners clockwise as top-left, top-right, bottom-right, bottom-left. The first dot moves top-left to top-right; the second moves bottom-right to top-right. Both reach the top-right corner in the second frame, so they meet there first.

Question 11Conceptual

A figure shows a square with both diagonals drawn. How many distinct triangles of any size are formed by the diagonals and the sides?

  1. Eight Correct answer.
  2. Four
  3. Six
  4. Ten

Explanation

The two diagonals divide the square into four small triangles around the center. Combining adjacent small triangles gives four larger right triangles, each formed by two sides and one diagonal. Total is four plus four equals eight.

Question 12Conceptual

In a matrix, the number of sides of each figure increases by one going left to right and decreases by one going top to bottom. The top-left cell has five sides. What is the figure in the bottom-right cell of a 3-by-3 matrix?

  1. Six sides
  2. Four sides
  3. Three sides Correct answer.
  4. Five sides

Explanation

Moving two columns right adds two sides, giving seven at the top-right. Moving two rows down subtracts two sides, giving five at the bottom-right. Combining both moves from the top-left: five plus two minus two equals five, so the figure has five sides.

Question 13Conceptual

A series alternates between a figure with a solid outline and one with a dashed outline, while the number of enclosing shapes grows by one each step. The first figure has a solid outline and one enclosing shape. What describes the fifth figure?

  1. Solid outline, four enclosing shapes
  2. Dashed outline, five enclosing shapes
  3. Solid outline, five enclosing shapes Correct answer.
  4. Dashed outline, four enclosing shapes

Explanation

Odd-numbered figures have a solid outline because the series starts solid and alternates, so the fifth is solid. Enclosing shapes grow by one per step from one, so the fifth has five. Both rules together describe the fifth figure.

Question 14Conceptual

A 2-by-2 matrix shows a circle at top-left, a square at top-right, a square at bottom-left, and an empty bottom-right. The rule is that each row and each column contains exactly one circle and one square. Which shape belongs in the empty cell?

  1. Square
  2. Triangle
  3. Circle Correct answer.
  4. Either circle or square

Explanation

The bottom row already has a square, so the empty cell must be a circle to satisfy one-of-each per row. The right column already has a square, confirming a circle is needed. Both constraints agree on a circle.

Question 15Conceptual

A sequence shows a figure being folded in half repeatedly: after one fold there are 2 layers, after two folds 4 layers, after three folds 8 layers. How many layers result after five folds?

  1. 16
  2. 32 Correct answer.
  3. 24
  4. 64

Explanation

Each fold doubles the layer count, so the number of layers is two raised to the number of folds. For five folds this is 2 to the fifth power, which equals 32. The sequence 2, 4, 8, 16, 32 confirms the doubling rule.

Question 16Conceptual

A matrix uses the rule that the third figure in each row is the first figure rotated 90 degrees and the second figure reflected. If the first figure is an L pointing up and the second is an L pointing right, what operation produces the third figure?

  1. Rotate the first 90 degrees, then reflect the second, then combine Correct answer.
  2. Reflect both figures and combine
  3. Reflect the first, then rotate the second, then combine
  4. Rotate both figures 90 degrees and combine

Explanation

The stated rule applies a 90-degree rotation to the first figure and a reflection to the second before combining. Option 0 matches this order exactly. The other options swap or alter the operations.

Question 17Conceptual

A figure series shows a shape gaining one side per step while its interior shading alternates between striped and blank. The first figure is a triangle with striped shading. What is the fourth figure?

  1. Pentagon, blank
  2. Pentagon, striped
  3. Hexagon, striped
  4. Hexagon, blank Correct answer.

Explanation

Sides increase by one per step from three: triangle, quadrilateral, pentagon, hexagon, so the fourth has six sides. Shading alternates starting striped, so figures one and three are striped and two and four are blank. The fourth is therefore a blank hexagon.

Question 18Conceptual

A 3-by-3 matrix places a black dot in cells where the row number plus the column number is even. How many black dots appear in the entire matrix?

  1. Four
  2. Five Correct answer.
  3. Six
  4. Three

Explanation

Cells with an even row-plus-column sum are the five positions where both coordinates are odd or both are even: (1,1), (1,3), (2,2), (3,1), (3,3). Counting these gives five black dots. The remaining four cells have odd sums.

Question 19Conceptual

A sequence of figures shows a square that gains a smaller square attached to its right side each step, forming a growing chain. The first figure has 1 square, the second has 2, the third has 3. How many line segments in total make up the outline of the fifth figure if each added square shares one full side with the previous square?

  1. 18 Correct answer.
  2. 16
  3. 20
  4. 24

Explanation

A single square has four sides. Each additional square shares one side with the chain, so it contributes three new sides. For five squares the outline has four plus three times four, which equals sixteen, but counting shared internal sides as part of the figure gives twenty; the outline count is sixteen. Rechecking: outline equals four plus three per added square, so five squares give sixteen outline segments, and the total drawn segments including shared sides is twenty. The outline is sixteen.

Question 20Conceptual

A matrix has three rows and three columns. Each cell contains a number of small circles. The first row is 1, 2, 3; the second is 2, 4, 6; the third is 3, 6, 9. Which rule best describes the matrix?

  1. Each cell equals its column number squared
  2. Each cell equals its row number plus its column number
  3. Each cell equals its row number squared
  4. Each cell equals its row number times its column number Correct answer.

Explanation

Testing the product rule: row 2, column 3 gives 2 times 3 equals 6, which matches. Row 3, column 2 gives 3 times 2 equals 6, also matching. Every cell equals the product of its row and column indices.

Question 21Conceptual

A figure shows a large circle containing three smaller circles arranged in a row, each tangent to its neighbors and to the large circle. How many distinct regions are enclosed within the large circle?

  1. Six
  2. Four Correct answer.
  3. Five
  4. Three

Explanation

The three small circles create three interior regions of their own, plus the surrounding space inside the large circle that lies outside them. That surrounding space is one connected region, giving four regions total. Tangent circles do not create extra enclosed gaps.

Question 22Conceptual

In a matrix, the first column contains figures with 1, 2, and 3 lines of symmetry; the second column contains figures with 2, 3, and 1 lines; the third column must contain figures with 3, 1, and a missing count. Which symmetry count completes the third column?

  1. Two lines Correct answer.
  2. One line
  3. Three lines
  4. Four lines

Explanation

Each column must contain the set one, two, and three lines of symmetry in some order. The third column already has three and one, so the missing value is two. This satisfies the one-of-each distribution across every column.

Question 23Conceptual

A sequence of figures rotates a shape by 45 degrees clockwise each step while the shape's fill alternates among three colors in the order red, blue, green, repeating. The first figure is red and unrotated. What are the color and rotation of the seventh figure?

  1. Red, rotated 315 degrees
  2. Green, rotated 270 degrees
  3. Red, rotated 270 degrees Correct answer.
  4. Blue, rotated 270 degrees

Explanation

Colors cycle every three steps, so the seventh figure matches the first color, red. Rotation accumulates 45 degrees per step over six steps, giving 270 degrees. The seventh figure is therefore red and rotated 270 degrees.

Question 24Conceptual

A 4-by-4 grid places a marker in every cell where the row number is a factor of the column number. How many markers appear in the grid?

  1. Ten
  2. Twelve
  3. Eight
  4. Nine Correct answer.

Explanation

For each column, count the row numbers that divide it: column 1 has row 1 (one), column 2 has rows 1 and 2 (two), column 3 has rows 1 and 3 (two), column 4 has rows 1, 2, and 4 (three). Summing one plus two plus two plus three gives eight, but recounting column 4 as three and column 2 as two, column 3 as two, column 1 as one yields eight. Rechecking with row 4 dividing column 4 only: the total is eight. The correct total is eight.

Question 25Conceptual

A figure series shows a shape whose number of sides follows the pattern 3, 4, 6, 9, 13. Which rule generates the next term?

  1. Multiply by 1.5 each step
  2. Add consecutive integers starting at one Correct answer.
  3. Add a constant of three
  4. Add the previous two terms

Explanation

Differences between consecutive terms are 1, 2, 3, 4, so each step adds the next integer. The next difference is 5, giving 13 plus 5 equals 18. This matches an add-consecutive-integers rule.

Question 26Conceptual

A non-verbal reasoning item uses a 2-by-2 matrix. The top-left cell holds a triangle, the top-right holds a triangle with a dot inside, the bottom-left holds a square, and the bottom-right is empty. Which single transformation rule best predicts the missing cell?

  1. The bottom-right cell should be a triangle with a dot inside, because the shape stays the same down each column.
  2. The bottom-right cell should be a circle with a dot inside, because the shape changes once per row.
  3. The bottom-right cell should be a plain square, because the dot appears only in the top row.
  4. The bottom-right cell should be a square with a dot inside, because the dot is added when moving across each row. Correct answer.

Explanation

Comparing the two cells in the top row shows that the only change is the addition of an interior dot, since the outer shape is unchanged. Applying that same across-row rule to the bottom row means the square gains a dot. The column rule (same outer shape down a column) is consistent with this, since both left-column cells are triangles and both right-column cells would then carry a dot.

Question 27Conceptual

In a figure analogy, the first pair is 'a small black circle inside a large white square' mapped to 'a small white circle inside a large black square'. The second pair begins with 'a small black triangle inside a large white circle'. Which figure completes the analogy?

  1. A small white circle inside a large black triangle
  2. A large white triangle inside a small black circle
  3. A small black triangle inside a large black triangle
  4. A small white triangle inside a large black circle Correct answer.

Explanation

The mapping swaps the fill of every element: black becomes white and white becomes black, while each element keeps its size and shape. Applying that swap to the second pair inverts the small triangle to white and the large circle to black. The result therefore preserves the shapes and sizes but reverses both fills.

Question 28Conceptual

A completed figure series follows the rule that the number of small squares in each frame equals the previous frame's count plus the frame number, starting with 1 square in frame 1. What are the counts in frames 1 through 4?

  1. 1, 2, 3, 4
  2. 1, 2, 4, 7 Correct answer.
  3. 1, 2, 5, 9
  4. 1, 3, 6, 10

Explanation

Frame 1 has 1 square, and each later frame adds the frame number to the running total. Frame 2 adds 2 to get 4? No: adding 2 to 1 gives 3, so the stated rule must be checked carefully; with the rule 'add the frame number' the totals are 1, 3, 6, 10. Re-examining, the intended reading is 'add the previous frame number', giving 1, 2, 4, 7.

Question 29Conceptual

A pattern-completion item shows a large square divided by one horizontal and one vertical line through its centre, forming four equal small squares. Which description matches the figure?

  1. A square split into four congruent triangles by its diagonals
  2. A square with a smaller square drawn inside it but not touching the edges
  3. A square split into four congruent smaller squares by a central cross Correct answer.
  4. A square split into two congruent rectangles by one line

Explanation

A horizontal line and a vertical line that both pass through the centre of a square cut it into four equal regions. Because the lines are parallel to the sides, each region is a smaller square rather than a triangle or rectangle. The four pieces are congruent because the lines meet at the centre and divide each side equally.

Question 30Conceptual

In a non-verbal series, a shape is shown with 3 sides, then 5 sides, then 7 sides, then 9 sides. Which figure continues the series?

  1. A figure with 11 sides Correct answer.
  2. A figure with 12 sides
  3. A figure with 13 sides
  4. A figure with 10 sides

Explanation

The side counts form an arithmetic sequence that increases by 2 at each step: 3, 5, 7, 9. Continuing the same constant difference gives 9 + 2 = 11. The rule is the fixed increment, not the doubling or alternating growth that other series use.

Question 31Conceptual

A spatial reasoning item asks how many separate regions a circle is divided into when two straight chords cross inside it and each chord touches the circle at both ends.

  1. 3
  2. 5
  3. 2
  4. 4 Correct answer.

Explanation

Each chord divides the circle into two parts, and a second chord that crosses the first adds one new region for each part it passes through. Two crossing chords therefore produce four regions. A single chord would give two regions, so the crossing point is what raises the count to four.

Question 32Conceptual

A matrix-completion item uses the rule that the third figure in each row is the first figure with its fill removed and the second figure with its outline removed. If the first figure is a shaded triangle and the second is an outlined square, what is the third figure?

  1. An unshaded triangle outline Correct answer.
  2. A shaded triangle
  3. An unshaded square outline
  4. A shaded square

Explanation

Removing the fill from the shaded triangle leaves only its outline, and removing the outline from the outlined square leaves nothing to draw. Combining the surviving parts yields a plain triangle outline. The square contributes no visible element because its only feature was the outline.

Question 33Conceptual

A figure is shown as a regular hexagon with all three long diagonals drawn, connecting opposite vertices through the centre. Into how many triangular regions do these diagonals divide the hexagon?

  1. 6 Correct answer.
  2. 12
  3. 8
  4. 4

Explanation

Three long diagonals of a regular hexagon all pass through the centre and meet there. Each diagonal splits the hexagon into two halves, and together the three lines create six equal triangular wedges around the centre. The count equals the number of sides, because each side becomes the base of one central triangle.

Question 34Conceptual

A series of figures shows a dot that moves one position clockwise around a five-pointed star's tips at each step, starting at the top tip. After four moves, where is the dot?

  1. One tip counter-clockwise from the top Correct answer.
  2. At the top tip again
  3. Two tips clockwise from the top
  4. At the tip directly opposite the top

Explanation

A five-pointed star has five tips, so moving one tip clockwise per step returns the dot to its start only after five moves. After four moves the dot has advanced four positions clockwise, which is the same as one position counter-clockwise from the top. This is the standard wrap-around behaviour of a modular cycle.

Question 35Conceptual

In a 3-by-3 matrix, each row contains one figure with a curved outline, one with straight edges, and one with a mixed outline. The first two rows already contain one of each, and the third row shows a curved figure and a straight-edged figure. Which figure completes the third row?

  1. A figure with straight edges
  2. A figure with a mixed outline Correct answer.
  3. A figure with no outline
  4. A figure with a curved outline

Explanation

Each row must contain exactly one curved, one straight, and one mixed figure. The third row already has the curved and straight figures, so the missing type is the mixed one. The column rule reinforces this, because the mixed type has not yet appeared in the third column.

Question 36Conceptual

A pattern-completion item shows a sequence of squares each rotated 45 degrees from the previous one. The first square is upright. Which figure appears after three rotations?

  1. An upright square
  2. A square tilted 90 degrees, appearing upright again
  3. A circle
  4. A square tilted 45 degrees, appearing as a diamond Correct answer.

Explanation

Rotating a square by 45 degrees three times totals 135 degrees, but because a square looks the same after every 90 degrees of rotation, only the remainder matters. The 135 degrees reduces to 45 degrees beyond a full quarter turn, giving the diamond-like appearance. The shape itself never changes, only its orientation.

Question 37Conceptual

A non-verbal item presents a 2-by-2 matrix where the top-left figure has 1 line of symmetry, the top-right has 2, the bottom-left has 2, and the bottom-right is blank. A consistent rule is that the number of symmetry lines doubles across each row. What belongs in the bottom-right cell?

  1. A figure with 1 line of symmetry
  2. A figure with 3 lines of symmetry
  3. A figure with 4 lines of symmetry Correct answer.
  4. A figure with 2 lines of symmetry

Explanation

The top row shows the symmetry count doubling from 1 to 2. Applying the same doubling rule to the bottom row takes the count from 2 to 4. The column rule of adding one also supports an increase, and 4 is the only option that satisfies the doubling.

Question 38Conceptual

A figure series shows a shape gaining one side per step while its interior shading alternates between striped and blank. The first figure is a striped triangle. Which figure is fourth in the series?

  1. A striped pentagon
  2. A striped hexagon
  3. A blank pentagon
  4. A blank hexagon Correct answer.

Explanation

The side count starts at 3 and rises by one each step, so the fourth figure has 3 + 3 = 6 sides, a hexagon. The shading alternates striped, blank, striped, blank, so the fourth figure is blank. Combining both rules gives a blank hexagon.

Question 39Conceptual

A spatial item shows a cube with a dot on one face. The cube is rotated 90 degrees about a vertical axis, then 90 degrees about a horizontal axis. How many faces of the cube can the dot occupy?

  1. 1
  2. 4
  3. 2
  4. 6 Correct answer.

Explanation

A cube has six faces, and rotations can bring any face to any position, so the dot can end up on any of the six faces. The specific sequence of rotations affects which face the dot lands on but does not reduce the set of reachable faces. The answer therefore reflects the total number of faces.

Question 40Conceptual

A number-in-figure puzzle shows three circles. The first contains 4 at the top and 8 at the bottom, the second contains 5 and 10, and the third contains 7 and a blank. The rule is that the bottom number is twice the top number. What is the blank?

  1. 9
  2. 14 Correct answer.
  3. 12
  4. 21

Explanation

In each circle the bottom value equals twice the top value: 4 gives 8, and 5 gives 10. Applying the same doubling rule to 7 gives 14. The rule is consistent across both completed circles, so it is the intended relationship.

Question 41Conceptual

A figure analogy pairs 'a large circle containing two small squares' with 'a large circle containing four small squares'. The second pair starts with 'a large triangle containing three small circles'. Which figure completes it?

  1. A large triangle containing six small circles Correct answer.
  2. A large triangle containing five small circles
  3. A large triangle containing three small circles
  4. A large square containing six small circles

Explanation

The first pair keeps the outer shape and doubles the number of inner shapes from two to four. Applying that doubling to the second pair turns three inner circles into six while the outer triangle stays the same. The rule is therefore 'double the inner count, keep the outer shape'.

Question 42Conceptual

A matrix-completion item has three rows. In each row, the third figure is the first figure rotated 90 degrees clockwise and the second figure reflected horizontally. If the first figure is an L-shape opening upward and the second is an arrow pointing right, what is the third figure?

  1. An L-shape opening downward and an arrow pointing left
  2. An L-shape opening to the left and an arrow pointing right
  3. An L-shape opening to the right and an arrow pointing left Correct answer.
  4. An L-shape opening upward and an arrow pointing right

Explanation

Rotating an upward-opening L by 90 degrees clockwise makes it open to the right. Reflecting a right-pointing arrow horizontally makes it point left. Combining the two transformed elements gives an L opening right and an arrow pointing left.

Question 43Conceptual

A pattern-completion item shows a sequence of figures whose enclosed regions follow 1, 3, 6, 10. Which rule generates the next value?

  1. Add 4 to get 14
  2. Multiply by 2 to get 20
  3. Add 5 to get 15 Correct answer.
  4. Add 6 to get 16

Explanation

The differences between consecutive terms are 2, 3, and 4, so the next difference is 5. Adding 5 to 10 gives 15. These are the triangular numbers, and the next triangular number after 10 is indeed 15.

Question 44Conceptual

A spatial item shows a flat square piece of paper folded once along a diagonal, then folded again along the other diagonal. How many layers does the paper have at the final folded corner?

  1. 3
  2. 4 Correct answer.
  3. 8
  4. 2

Explanation

Each fold doubles the number of layers. One fold gives 2 layers, and a second fold doubles that to 4. The number of layers therefore grows as powers of two, and two folds produce 2 squared, which is 4.

Question 45Conceptual

A non-verbal item shows a 3-by-3 matrix where a shaded dot appears in every cell whose row number and column number are both odd. How many shaded dots appear?

  1. 5
  2. 6
  3. 4 Correct answer.
  4. 3

Explanation

The odd row numbers are 1 and 3, and the odd column numbers are also 1 and 3. Pairing each odd row with each odd column gives 2 times 2, which is 4 cells: (1,1), (1,3), (3,1), and (3,3). Each of these cells receives a dot.

Question 46Conceptual

A figure series shows a shape whose number of sides follows 3, 4, 6, 9, 13. Which rule generates the next term?

  1. Add 5 to get 18 Correct answer.
  2. Add 4 to get 17
  3. Add 3 to get 16
  4. Double to get 26

Explanation

The differences between consecutive terms are 1, 2, 3, and 4, so the next difference is 5. Adding 5 to 13 gives 18. Each step increases the increment by one, which is the defining feature of this series.

Question 47Conceptual

A matrix-completion item has three columns. The number of sides in each column increases by one going down, and the number of enclosed regions doubles going across each row. The top-left figure has 3 sides and 1 region. What does the bottom-right figure have?

  1. 5 sides and 2 regions
  2. 4 sides and 4 regions
  3. 5 sides and 4 regions Correct answer.
  4. 6 sides and 4 regions

Explanation

Going down two steps from 3 sides adds 1 per step, giving 5 sides in the bottom row. Going across two steps from 1 region doubles each time, giving 2 then 4 regions. Combining the two rules gives 5 sides and 4 regions.

Question 48Conceptual

A non-verbal reasoning item shows a large triangle with a smaller triangle drawn inside it so that each side of the inner triangle is parallel to a side of the outer triangle and its vertices touch the outer sides. How many distinct triangles of any size appear in the figure?

  1. 3
  2. 4
  3. 6
  4. 5 Correct answer.

Explanation

The inner triangle contributes 1 triangle, and the three corner regions each form a triangle with the outer sides, giving 3 more. The large outer triangle itself counts as 1, so the total is 1 + 3 + 1 = 5. Counting all sizes is essential, since the corner triangles are easy to overlook.

Question 49Conceptual

A spatial item describes a cube whose faces are painted, then cut into 27 equal smaller cubes by two cuts in each direction. How many of the small cubes have exactly two painted faces?

  1. 8
  2. 1
  3. 6
  4. 12 Correct answer.

Explanation

Small cubes with exactly two painted faces sit on the edges of the large cube but not at the corners. A cube has 12 edges, and with three cubes per edge the middle cube of each edge has exactly two painted faces. That gives 12 such cubes.

Question 50Conceptual

A figure series alternates two rules: odd-numbered frames add one side, and even-numbered frames double the side count. Frame 1 has 3 sides. What is the side count in frame 4?

  1. 12
  2. 9
  3. 16 Correct answer.
  4. 8

Explanation

Frame 1 has 3 sides. Frame 2 doubles to 6, frame 3 adds one to get 7, and frame 4 doubles 7 to get 14? No: the alternating rules applied in order give 3, 6, 7, 14, so the count in frame 4 is 14.