I85PREP
⌘ K
NNAT3 study materials
NNAT3 study resources

NNAT3 practice questions

One question at a time. Build your NNAT3 understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Pattern Completion

A 3-by-3 grid shows a square with a small black dot in its top-left corner. The same square appears in the next panel with the dot moved to the top-right corner. Which single change best describes the pattern?

  1. The dot is reflected across the horizontal axis.
  2. The dot is shifted one cell downward.
  3. The dot is reflected across the vertical axis. Correct answer.
  4. The dot is rotated 90 degrees clockwise.

Explanation

Moving a corner dot from top-left to top-right keeps it on the same row and swaps its horizontal position, which is exactly a mirror reflection across the vertical midline. A rotation or a downward shift would change the row as well, so only the vertical-axis reflection fits the observed move.

Question 2Pattern Completion

In a sequence of panels, a triangle points up, then right, then down, then left, and the pattern repeats. What does the fifth panel show?

  1. A triangle pointing up Correct answer.
  2. A triangle pointing down
  3. A triangle pointing left
  4. A triangle pointing right

Explanation

The four orientations form a repeating cycle of quarter turns clockwise: up, right, down, left, then back to up. The fifth panel restarts the cycle, so the triangle points up again.

Question 3Pattern Completion

A figure is a circle with a vertical line through its center. In the next panel the same figure appears with a horizontal line through its center. Which transformation maps the first figure onto the second?

  1. A 90-degree rotation Correct answer.
  2. A horizontal reflection
  3. A vertical reflection
  4. A translation to the right

Explanation

Turning a vertical diameter by a quarter turn produces a horizontal diameter, so a 90-degree rotation maps the first figure onto the second. Reflections across either axis leave a vertical line vertical, and a translation does not change orientation at all.

Question 4Pattern Completion

A large square is divided into four equal smaller squares. The top-left small square is shaded. In the next panel the bottom-right small square is shaded. Which transformation of the shaded cell produces this change?

  1. A shift one cell to the right
  2. A reflection across the vertical axis
  3. A 180-degree rotation about the center Correct answer.
  4. A reflection across the horizontal axis

Explanation

A half turn about the grid center sends the top-left cell to the bottom-right cell, swapping both row and column. Reflections change only one coordinate, and a single rightward shift keeps the top row, so none of those reach the bottom-right cell.

Question 5Pattern Completion

A pattern shows a shape growing by one side each step: triangle, square, pentagon, hexagon. What is the next shape?

  1. Heptagon Correct answer.
  2. Square
  3. Pentagon
  4. Octagon

Explanation

Each panel adds exactly one side to the previous polygon, so the sequence of side counts is 3, 4, 5, 6 and continues with 7. A seven-sided polygon is a heptagon, which fits the steady increment rule.

Question 6Pattern Completion

A 3-by-3 grid has a black cell in the center. In the next panel, black cells appear in the top-center and bottom-center positions. Which rule best explains the change?

  1. The single cell is copied into the two corner cells.
  2. The single cell is removed and replaced by a border.
  3. The single cell moves one cell to the left.
  4. The single cell splits into the two cells directly above and below it. Correct answer.

Explanation

The center cell is replaced by the two cells sharing its column, one above and one below, which is a consistent split along the vertical direction. The other options either relocate the cell or place shading in positions unrelated to the center column.

Question 7Pattern Completion

A figure consists of a square with a small circle attached to its right side. In the next panel the circle is attached to the top side. Which transformation was applied?

  1. A 90-degree counterclockwise rotation Correct answer.
  2. A reflection across the horizontal axis
  3. A reflection across the vertical axis
  4. A 90-degree clockwise rotation

Explanation

Moving an attached feature from the right side to the top side is a quarter turn counterclockwise, since right rotates up under that turn. Clockwise rotation would send the circle to the bottom, and reflections would place it on the left or keep it on the right.

Question 8Pattern Completion

A row of panels shows one dot, then two dots, then three dots, then four dots, all arranged in a straight line. What does the sixth panel contain?

  1. Six dots Correct answer.
  2. Seven dots
  3. Five dots
  4. Four dots

Explanation

The number of dots increases by one per panel, so the count in panel n equals n. The sixth panel therefore contains six dots, continuing the simple additive rule.

Question 9Pattern Completion

A 4-by-4 grid has shaded cells along its main diagonal from top-left to bottom-right. In the next panel, shaded cells lie along the other diagonal, from top-right to bottom-left. Which transformation produces this pattern?

  1. A 90-degree clockwise rotation
  2. A reflection across the vertical axis Correct answer.
  3. A reflection across the main diagonal
  4. A translation one cell down

Explanation

Reflecting a top-left-to-bottom-right diagonal across the vertical midline reverses the column order, giving a top-right-to-bottom-left diagonal. The other transformations either leave the diagonal direction unchanged or shift the whole band out of place.

Question 10Pattern Completion

A sequence alternates between a shaded circle and a shaded square: circle, square, circle, square, circle. What comes next, and why?

  1. A circle, because the count of circles is greater.
  2. A square, because the alternation continues. Correct answer.
  3. A triangle, because a new shape is introduced.
  4. A square, because squares are always last.

Explanation

The pattern strictly alternates between two shapes, so each panel is the opposite of the one before it. Since the fifth panel is a circle, the sixth must be a square to preserve the alternation.

Question 11Pattern Completion

A figure shows an arrow pointing up with a small notch on its left edge. In the next panel the arrow points down and the notch is on its right edge. Which single transformation explains both changes?

  1. A 90-degree clockwise rotation
  2. A reflection across the vertical axis
  3. A 180-degree rotation Correct answer.
  4. A reflection across the horizontal axis

Explanation

A half turn reverses both the pointing direction and the left-right position of the notch, which matches the observed panel exactly. Reflections change only one of those features, and a quarter turn would leave the arrow pointing sideways.

Question 12Pattern Completion

A 3-by-3 grid has a shaded L-shape occupying the left column and the bottom row. In the next panel the shaded L-shape occupies the right column and the bottom row. Which transformation maps one onto the other?

  1. A 90-degree counterclockwise rotation
  2. A reflection across the vertical axis Correct answer.
  3. A translation one cell upward
  4. A reflection across the horizontal axis

Explanation

The L keeps its bottom row and swaps the left column for the right column, which is a mirror reflection across the vertical midline. A horizontal reflection or a rotation would move the bottom row to a different row, and a translation would not swap the column.

Question 13Pattern Completion

A sequence of panels shows a dot moving clockwise around the four corners of a square: top-left, top-right, bottom-right, bottom-left. Which corner holds the dot in the seventh panel?

  1. Top-right
  2. Top-left
  3. Bottom-right Correct answer.
  4. Bottom-left

Explanation

The dot visits four corners in a repeating cycle, so positions 5 and 9 return to the start. The seventh panel is the third step of the second cycle, which is the bottom-right corner.

Question 14Pattern Completion

A panel contains a large triangle subdivided into four small triangles, with the central small triangle shaded. In the next panel the three corner small triangles are shaded and the center is blank. Which rule best describes the change?

  1. The shading moves one triangle clockwise.
  2. The shading doubles in area.
  3. The shading is removed entirely.
  4. The shading inverts: shaded becomes blank and blank becomes shaded. Correct answer.

Explanation

Every small triangle that was shaded becomes blank and every blank one becomes shaded, which is an inversion of the fill pattern. The other options describe movement, growth, or removal, none of which matches the swap of filled and empty regions.

Question 15Pattern Completion

A series shows a square, then a square rotated 45 degrees, then a square rotated 90 degrees, then a square rotated 135 degrees. What does the fifth panel show?

  1. A square rotated 45 degrees
  2. A square rotated 180 degrees Correct answer.
  3. A square rotated 90 degrees
  4. A square rotated 225 degrees

Explanation

Each panel adds 45 degrees to the previous rotation, so the fifth panel is rotated 180 degrees. Because a square has fourfold symmetry, a 180-degree rotation looks the same as the original square, but the underlying rule still yields 180 degrees.

Question 16Pattern Completion

A figure shows two overlapping circles with the overlap region shaded. In the next panel the two non-overlapping crescents are shaded and the overlap is blank. Which transformation of the shading occurred?

  1. The shading inverted across the whole figure. Correct answer.
  2. The shading shifted to the right circle.
  3. The shading contracted to a single point.
  4. The shading expanded to cover both circles.

Explanation

The overlap was shaded and the crescents blank, and afterward the crescents are shaded and the overlap is blank, which is a complete inversion of the fill. Shifting, expanding, or contracting would not produce exactly the complementary regions.

Question 17Pattern Completion

A 3-by-3 grid has a shaded cell at the top-left. The next panel shows shading at the top-right, and the panel after shows shading at the bottom-right. What is the rule, and where is the shading in the fourth panel?

  1. Rotate the position 90 degrees clockwise each step; the fourth panel shades the bottom-left. Correct answer.
  2. Reflect across the vertical axis each step; the fourth panel shades the top-left.
  3. Move one cell right each step; the fourth panel shades the bottom-right.
  4. Rotate 90 degrees counterclockwise each step; the fourth panel shades the top-right.

Explanation

Top-left to top-right to bottom-right is a quarter turn clockwise around the grid center at each step. Continuing that rotation places the fourth panel's shading at the bottom-left corner.

Question 18Pattern Completion

A pattern consists of a shape made of unit squares. Panel 1 has 1 square, panel 2 has 4 squares forming a larger square, and panel 3 has 9 squares forming a still larger square. How many unit squares does panel 5 contain?

  1. 25 Correct answer.
  2. 16
  3. 36
  4. 20

Explanation

The counts are perfect squares: 1, 4, 9, which are 1 squared, 2 squared, and 3 squared. Panel 5 therefore contains 5 squared, or 25, unit squares.

Question 19Pattern Completion

In a sequence, a figure alternates between being filled and outlined, while its shape alternates between circle and triangle independently: filled circle, outlined triangle, filled circle, outlined triangle. What is the fifth panel?

  1. An outlined circle
  2. A filled circle Correct answer.
  3. An outlined triangle
  4. A filled triangle

Explanation

Both attributes repeat with a period of two, so the odd-numbered panels are filled circles and the even-numbered panels are outlined triangles. The fifth panel is odd, so it is a filled circle.

Question 20Pattern Completion

A figure shows a small black square in the top-left corner of a large white square. In the next panel the small square is in the bottom-right corner, and in the third panel it is back in the top-left. Which transformation sequence is consistent?

  1. Repeated 90-degree clockwise rotations
  2. Alternating reflections across the vertical axis
  3. Repeated one-cell downward translations
  4. Alternating 180-degree rotations about the center Correct answer.

Explanation

A half turn sends the top-left corner to the bottom-right, and repeating it returns the square to the top-left, matching the three panels. The other rules would place the square at a different corner in the second panel or fail to return it in the third.

Question 21Pattern Completion

A 4-by-4 grid is shaded so that every cell in row 2 and every cell in column 3 is black. In the next panel every cell in row 3 and every cell in column 2 is black. Which transformation maps the first pattern onto the second?

  1. A 180-degree rotation
  2. A reflection across the vertical axis
  3. A translation one cell down and one cell left
  4. A reflection across the main diagonal Correct answer.

Explanation

Reflecting across the main diagonal swaps row and column indices, so a row-2 band becomes a column-2 band and a column-3 band becomes a row-3 band. That yields exactly the row-3 and column-2 pattern described.

Question 22Pattern Completion

A sequence of panels shows a figure rotating 90 degrees clockwise each step while its shading alternates between solid and striped. If panel 1 is solid and upright, what is panel 6?

  1. Striped and upright
  2. Solid and rotated 90 degrees
  3. Striped and rotated 90 degrees Correct answer.
  4. Solid and rotated 180 degrees

Explanation

Shading alternates with period two, so panel 6 is striped because even panels are striped. Rotation accumulates 90 degrees per step, so panel 6 is rotated 450 degrees, which reduces to 90 degrees.

Question 23Pattern Completion

A 3-by-3 grid contains a shaded plus sign centered on the middle cell. Each subsequent panel rotates the plus sign 45 degrees. After how many steps does the shaded pattern first look identical to the starting plus sign?

  1. Two steps
  2. Four steps Correct answer.
  3. Six steps
  4. Eight steps

Explanation

A plus sign has fourfold rotational symmetry, so rotating it by 90 degrees restores its appearance. Since each step is 45 degrees, four steps accumulate 180 degrees, but the plus sign looks the same after every 90 degrees, so the first identical appearance occurs after two steps; among the choices, the pattern repeats at the smallest multiple of 45 that is a multiple of 90, which is two steps.

Question 24Pattern Completion

A figure is built from four small squares arranged in a T shape. In the next panel the same T shape appears rotated so that its stem points left instead of down. Which transformation is consistent with that change?

  1. A reflection across the horizontal axis
  2. A 90-degree clockwise rotation Correct answer.
  3. A 90-degree counterclockwise rotation
  4. A reflection across the vertical axis

Explanation

A downward stem rotated a quarter turn clockwise points left, so that rotation matches the described panel. A counterclockwise quarter turn would point the stem right, and reflections would produce leftward or upward stems only in combination with other changes.

Question 25Pattern Completion

A grid pattern has shading symmetric about both diagonals. A candidate claims the pattern must also be symmetric under a 180-degree rotation. Is that claim correct?

  1. No, because a half turn reverses the colors of every cell.
  2. No, because diagonal symmetry never implies rotational symmetry.
  3. Yes, because two diagonal reflections compose to a half turn. Correct answer.
  4. Yes, because any symmetric grid is rotationally symmetric.

Explanation

Reflecting across one diagonal and then the other composes to a 180-degree rotation, so a pattern invariant under both diagonal reflections is automatically invariant under a half turn. The claim is therefore correct, and the reasoning rests on composing the two reflections.

Question 26Pattern Completion

In a pattern-completion panel, a 3-by-3 grid has a shaded square in the top-left cell. The next panel shows the same shaded square in the top-right cell. The panel after that shows it in the bottom-right cell. Where will the shaded square appear in the fourth panel?

  1. In the center cell
  2. In the bottom-left cell Correct answer.
  3. In the top-left cell
  4. In the top-right cell

Explanation

The shaded square travels clockwise around the four corner cells of the grid: top-left, top-right, bottom-right, so the next corner in that clockwise tour is the bottom-left. The center cell is never part of a corner cycle, and the other corner choices would break the clockwise order.

Question 27Pattern Completion

A panel shows a figure made of three unit squares in a horizontal row. The next panel shows the same three squares in a vertical column. If the figure keeps turning the same way, what does the third panel show?

  1. Three squares arranged in an L-shape
  2. Three separate squares with gaps
  3. Three squares in a vertical column
  4. Three squares in a horizontal row Correct answer.

Explanation

A horizontal bar rotated 90 degrees becomes a vertical bar, and a second 90-degree turn returns it to horizontal. The bar never changes its shape or breaks apart, so the third panel is again a horizontal row of three squares.

Question 28Pattern Completion

A figure is a shaded circle with a small white square centered inside it. In the next panel the square is larger but still centered. In the third panel the square is larger still. What is the most likely fourth panel?

  1. The circle grows while the square stays the same
  2. The inner square shrinks back to its first size
  3. The inner square grows again while the circle stays the same Correct answer.
  4. The square moves to touch the circle's edge

Explanation

Only one element changes across the panels: the inner square increases in size at a steady rate while the outer circle is unchanged. Continuing that single trend gives a fourth panel with an even larger centered square.

Question 29Pattern Completion

Each panel contains a shape with one small dot placed on its outline. The dot sits at the top of the shape, then at the right side, then at the bottom. Where should the dot be in the next panel?

  1. On the left side Correct answer.
  2. Inside the shape
  3. At the top again
  4. At the bottom-right corner

Explanation

The dot moves clockwise around the outline in quarter turns: top, right, bottom, and next left. The dot always stays on the outline, so an interior position would violate the pattern.

Question 30Pattern Completion

A sequence of panels shows a small triangle that alternates between pointing up and pointing down: up, down, up, down. The shape itself never moves or changes size. What does the fifth panel show?

  1. A triangle pointing down
  2. A triangle pointing up Correct answer.
  3. A triangle pointing left
  4. A circle

Explanation

The only change is a flip between up and down, and the fifth step follows an odd number of flips from the first panel. An odd number of alternations returns the triangle to pointing up.

Question 31Pattern Completion

In each panel a shaded region covers exactly half of a square, split by a single straight line. In the first panel the line is vertical, in the second horizontal, in the third vertical again. What is the fourth panel?

  1. A square with no shaded region
  2. A vertical split line
  3. A diagonal split line
  4. A horizontal split line Correct answer.

Explanation

The dividing line alternates between vertical and horizontal, so after a vertical panel the next must be horizontal. The shaded region always remains half the square, so the amount of shading does not change.

Question 32Pattern Completion

A pattern-completion item shows a large square with a small black square tucked into its top-left corner. In the next panel the small square is tucked into the top-right corner, and in the third panel into the bottom-right corner. Which panel comes next?

  1. Small square in the bottom-left corner Correct answer.
  2. Small square in the top-left corner
  3. Small square outside the large square
  4. Small square in the center

Explanation

The small square moves one corner clockwise per panel, so after the bottom-right corner it goes to the bottom-left. It stays tucked inside the large square at every step.

Question 33Pattern Completion

A panel shows two concentric squares, and the region between them is shaded. In the next panel the same two squares appear with the inner square shaded instead. In the third panel the region between them is shaded again. What is shaded in the fourth panel?

  1. The inner square Correct answer.
  2. Neither square
  3. The region between the squares
  4. Both the inner square and the outer square

Explanation

The shading alternates between the ring between the squares and the inner square, so after a ring-shaded panel comes an inner-shaded panel. The two squares themselves never change size or position.

Question 34Pattern Completion

A figure consists of a large circle with a small square attached at its top. In the next panel the square is attached at the right, then at the bottom. Where is the square attached in the fourth panel?

  1. At the top
  2. At the bottom
  3. At the left Correct answer.
  4. At the center of the circle

Explanation

The attached square moves clockwise around the circle in quarter turns: top, right, bottom, left. The square stays on the circle's edge, so a position inside the circle does not fit.

Question 35Pattern Completion

A panel shows a 3-by-3 grid with the entire middle row shaded. The next panel shows the entire middle column shaded. The third panel again shows the middle row shaded. Which cells are shaded in the fourth panel?

  1. The four corner cells
  2. The entire middle row
  3. Only the center cell
  4. The entire middle column Correct answer.

Explanation

The shaded band alternates between the middle row and the middle column, so after a row panel the next is a column panel. The band always spans all three cells of its line.

Question 36Pattern Completion

A sequence shows a shape made of a square with a triangle on top, and the whole figure grows taller by one unit each panel while its width stays fixed. Panel 1 is one unit tall, panel 2 is two units tall, panel 3 is three units tall. What does panel 4 look like?

  1. Four units tall and the same width as before Correct answer.
  2. Three units tall and the same width as before
  3. Two units tall and twice as wide
  4. Four units tall and four units wide

Explanation

Only height changes, increasing by one unit per panel, while width is held constant. The fourth panel therefore has height four with the original width.

Question 37Pattern Completion

In a pattern-completion item, a small arrow starts at the left edge of a square pointing right. In each panel it moves one quarter of the way across the square while keeping the same direction. If it starts at the left edge and reaches the center after two panels, where is it in the fourth panel?

  1. At the center
  2. At the right edge Correct answer.
  3. Outside the square on the right
  4. One quarter of the way across

Explanation

The arrow advances one quarter of the width per panel, so after four panels it has covered the full width and sits at the right edge. Its direction stays pointing right throughout.

Question 38Pattern Completion

A figure shows a square divided into four equal quadrants, with the top-left quadrant shaded. Each panel moves the shading one quadrant counterclockwise. The first panel has top-left shaded. Which quadrant is shaded in the third panel?

  1. Bottom-right
  2. Top-left
  3. Bottom-left Correct answer.
  4. Top-right

Explanation

Counterclockwise from top-left goes to bottom-left, then bottom-right, then top-right. The third panel therefore has the bottom-left quadrant shaded, since two counterclockwise steps land there.

Question 39Pattern Completion

A sequence of panels shows a figure made of five small squares in a cross shape. In each panel one arm of the cross is removed, starting with the top arm, then the right arm, then the bottom arm. What remains in the fourth panel?

  1. The left arm and the right arm
  2. The center square and the left arm Correct answer.
  3. The center square only
  4. The center square and the top arm

Explanation

Arms are removed in clockwise order starting from the top, so the top, right, and bottom arms are gone by the fourth panel. Only the center square and the untouched left arm remain.

Question 40Pattern Completion

A pattern-completion item shows a large triangle with a small circle at each of its three corners. In the next panel the circles move to the midpoints of the three sides. In the third panel the circles return to the corners. Where are the circles in the fourth panel?

  1. At the midpoints of the sides Correct answer.
  2. All at the top vertex
  3. Inside the triangle
  4. At the corners

Explanation

The circles alternate between the triangle's vertices and the midpoints of its sides, so a corner panel is followed by a midpoint panel. All three circles move together as a set.

Question 41Pattern Completion

A 4-by-4 grid has a shaded square in the second row, third column. Each panel moves the shaded square one step to the right, wrapping to the first column of the same row when it passes the last column. Where is the shaded square in the fourth panel?

  1. Second row, fourth column
  2. Third row, second column
  3. First row, second column
  4. Second row, second column Correct answer.

Explanation

Starting at column three, one step right gives column four, the next wraps to column one, and the next returns to column two. The row never changes, so the fourth panel has the square in the second row, second column.

Question 42Pattern Completion

A figure shows a shaded semicircle whose flat edge is at the bottom. In the next panel the flat edge is on the right, then at the top. What does the fourth panel show if the turning continues in the same direction?

  1. Flat edge on the left Correct answer.
  2. Flat edge at the bottom
  3. Flat edge on the right
  4. Flat edge at the top

Explanation

The flat edge rotates a quarter turn in the same direction each panel: bottom, right, top, left. The fourth panel therefore has the flat edge on the left.

Question 43Pattern Completion

In a sequence, a small dot sits at the center of a square. Each panel the dot moves outward along a straight diagonal toward the top-right corner, covering half the remaining distance each time. In which panel does the dot first reach the corner?

  1. In the second panel
  2. In the fourth panel
  3. It never reaches the corner in a finite number of panels Correct answer.
  4. In the third panel

Explanation

Halving the remaining distance each step means the dot keeps getting closer to the corner without ever arriving, so no finite panel places it exactly at the corner. This is a pattern-completion trap where the trend has a limit but no final step.

Question 44Pattern Completion

A panel shows a figure with a small notch cut out of its top edge. In the next panel the notch is on the right edge, then the bottom edge. The figure keeps turning the same way. On which edge is the notch in the fourth panel?

  1. Right edge
  2. Left edge Correct answer.
  3. Top edge
  4. Bottom edge

Explanation

The notch travels clockwise around the figure's edges: top, right, bottom, left. Continuing the same clockwise step from the bottom edge lands on the left edge.

Question 45Pattern Completion

A pattern-completion item shows a 3-by-3 grid where the shaded cells form a diagonal line from bottom-left to top-right. In the next panel the shaded cells form the other diagonal, from top-left to bottom-right. In the third panel the first diagonal returns. Which diagonal is shaded in the fourth panel?

  1. Bottom-left to top-right
  2. Both diagonals at once
  3. No diagonal
  4. Top-left to bottom-right Correct answer.

Explanation

The two diagonals alternate, so after the bottom-left-to-top-right diagonal comes the top-left-to-bottom-right one. Exactly one diagonal is shaded in each panel.

Question 46Pattern Completion

A figure is built from unit squares: panel 1 has a single square, panel 2 adds one square to the right, panel 3 adds one square above the second, and panel 4 adds one square to the right of the third. What shape does panel 4 most closely resemble?

  1. A 2-by-2 block of four squares
  2. A straight horizontal bar of four squares
  3. A staircase of four squares Correct answer.
  4. A vertical column of four squares

Explanation

Each new square is attached to the most recently added square, and the direction of attachment turns, producing a stepped or staircase arrangement. A straight bar or a compact block would require all additions in the same direction or filling a gap.

Question 47Pattern Completion

In a pattern-completion sequence, a figure rotates 90 degrees clockwise each panel while a separate small marker rotates 90 degrees counterclockwise each panel. Both start at the top position. After how many panels do the figure and the marker first point in the same direction again?

  1. After three panels
  2. After eight panels
  3. After four panels Correct answer.
  4. After two panels

Explanation

The figure advances one quarter turn clockwise per panel and the marker one quarter turn counterclockwise, so their relative separation grows by two quarter turns each panel. They realign when the separation reaches a full turn, which takes four quarter-turn pairs, that is, four panels.

Question 48Pattern Completion

A sequence of panels shows a shape whose area doubles each panel while its outline stays a similar shape. Panel 1 has area 1, panel 2 has area 2, panel 3 has area 4. What is the area in panel 5?

  1. 12
  2. 16 Correct answer.
  3. 32
  4. 8

Explanation

The area doubles each panel, so the values run 1, 2, 4, 8, 16. Panel 5 therefore has area 16, which is four doublings from panel 1.

Question 49Pattern Completion

A 4-by-4 grid has shaded cells forming a shape that is symmetric about its vertical axis. The next panel shows the same shape reflected across its horizontal axis instead. The third panel shows the original shape again. If the pattern continues this way, what is true of the fifth panel?

  1. It shows an unshaded grid
  2. It shows a 90-degree rotation
  3. It shows the original shape Correct answer.
  4. It shows the horizontal reflection

Explanation

The panels alternate between the original shape and its horizontal reflection, so odd-numbered panels show the original and even-numbered panels show the reflection. The fifth panel is odd-numbered, so it shows the original shape.

Question 50Pattern Completion

A figure consists of a square ring made of eight unit squares around an empty center. Each panel removes one square from the ring, moving clockwise from the top. After four removals, what is true of the remaining ring?

  1. It has four squares left and is still a closed ring
  2. It has four squares left and is no longer a closed ring Correct answer.
  3. It has three squares left and is no longer a closed ring
  4. It has five squares left and is still a closed ring

Explanation

Eight squares minus four removals leaves four, and removing squares from a closed ring breaks its continuity. The remaining four squares therefore form an open arc rather than a closed loop.