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 1Series: progression of one or more figural elements across a sequence
In a series of squares, each square rotates 90° clockwise about its centre from one frame to the next. After how many steps does the square first return to its original orientation?
- 2 steps
- 3 steps
- 4 steps Correct answer.
- 8 steps
Explanation
A rotation of 90° repeated four times totals 360°, which is a full turn, so the figure coincides with its starting orientation after 4 steps. Rotations of 2 and 3 steps give 180° and 270°, which are visibly different orientations for a square.
Question 2Series: progression of one or more figural elements across a sequence
A sequence of frames shows a dot moving along the four corners of a square in clockwise order, one corner per frame, starting at the top-left. Which corner does the dot occupy in the fifth frame?
- Top-right
- Bottom-left
- Bottom-right
- Top-left Correct answer.
Explanation
The dot visits top-left, top-right, bottom-right, bottom-left and then repeats the cycle. The fifth frame therefore shows the dot back at the top-left corner, because the cycle has period four.
Question 3Series: progression of one or more figural elements across a sequence
Each frame in a series adds one more straight line segment than the previous frame, beginning with 2 segments. How many segments appear in the sixth frame?
- 12
- 6
- 7 Correct answer.
- 8
Explanation
The count increases by one per frame, so the sequence is 2, 3, 4, 5, 6, 7. The sixth term is therefore 7 segments, obtained by adding five increments to the starting value of 2.
Question 4Series: progression of one or more figural elements across a sequence
A black triangle alternates between pointing up and pointing down in successive frames. If the first frame shows it pointing up, what does the seventh frame show?
- Pointing right
- Pointing left
- Pointing up Correct answer.
- Pointing down
Explanation
An alternating series has period two, so odd-numbered frames show the starting state and even-numbered frames show the flipped state. Since 7 is odd, the seventh frame shows the triangle pointing up again.
Question 5Series: progression of one or more figural elements across a sequence
In a series, a shaded region grows by adding one small cell each frame: frame 1 has 1 cell, frame 2 has 3 cells, frame 3 has 5 cells. What is the count in frame 5?
- 11
- 7
- 10
- 9 Correct answer.
Explanation
The counts form the odd numbers 1, 3, 5, 7, 9, increasing by 2 each frame. Frame 5 therefore contains 9 cells, which is the starting value 1 plus four increments of 2.
Question 6Series: progression of one or more figural elements across a sequence
A figure moves one position to the right along a row of five positions, wrapping back to the leftmost position after the fifth. If it starts in position 1, where is it in the eighth frame?
- Position 3 Correct answer.
- Position 1
- Position 4
- Position 2
Explanation
The position advances by one each frame and wraps with period five. Frame 8 corresponds to seven moves, and 7 modulo 5 leaves a remainder of 2, so the figure sits two positions to the right of position 1, namely position 3.
Question 7Series: progression of one or more figural elements across a sequence
A series of shapes increases its number of sides by two each frame, starting from a triangle (3 sides). Which shape appears in the fifth frame?
- Octagon (8 sides)
- Decagon (10 sides)
- Hendecagon (11 sides) Correct answer.
- Nonagon (9 sides)
Explanation
The side counts run 3, 5, 7, 9, 11, so the fifth frame has 11 sides. Adding four increments of two to the starting value of three gives eleven, which corresponds to a hendecagon.
Question 8Series: progression of one or more figural elements across a sequence
In a sequence, an arrow rotates 45° anticlockwise each frame. In which direction does it point in the fifth frame if it starts pointing north?
- South-west Correct answer.
- North-west
- South-east
- West
Explanation
Four steps of 45° anticlockwise total 180°, taking the arrow from north through north-west, west and south-west to south. The fifth frame therefore shows the arrow pointing south-west, since the first frame is the starting north position.
Question 9Series: progression of one or more figural elements across a sequence
A series shows a small circle whose shading changes in the repeating pattern: black, white, grey, black, white, grey. What is the shading in the eleventh frame?
- Grey
- Black Correct answer.
- White
- Striped
Explanation
The shading pattern has period three, so the shading in any frame depends on the frame number modulo three. Frame 11 leaves a remainder of 2 when divided by 3, matching the second entry of the cycle, which is black.
Question 10Series: progression of one or more figural elements across a sequence
Two elements move simultaneously: a dot moves one corner clockwise around a square each frame, while a cross moves one corner anticlockwise. They start on opposite corners. In which frame do they first meet on the same corner?
- The second frame Correct answer.
- They never meet
- The third frame
- The fourth frame
Explanation
Moving in opposite directions around four corners, the two elements close the gap by two corners per frame. Starting two corners apart, they meet after a single step, which is the second frame of the series.
Question 11Series: progression of one or more figural elements across a sequence
A series of frames contains 1, 4, 9, 16 small squares. How many small squares appear in the seventh frame?
- 49 Correct answer.
- 42
- 36
- 64
Explanation
The counts are perfect squares of the frame number: 1², 2², 3², 4². The seventh frame therefore contains 7² = 49 small squares, continuing the pattern of square numbers.
Question 12Series: progression of one or more figural elements across a sequence
In a series, a shape is alternately reflected in a vertical axis and then in a horizontal axis, one operation per frame. Starting from an asymmetric shape, after how many operations does it first return to an orientation identical to the start?
- It never returns
- Three operations
- Four operations Correct answer.
- Two operations
Explanation
Two reflections in perpendicular axes compose to a rotation of 180°, so after two operations the shape is inverted. Applying the same pair again gives a further 180°, totalling 360°, so the original orientation reappears after four operations.
Question 13Series: progression of one or more figural elements across a sequence
A row of five boxes is shaded so that the number of shaded boxes follows 1, 2, 3, 2, 1, 2, 3, 2 and so on. What is the number of shaded boxes in the tenth frame?
- 1
- 3 Correct answer.
- 2
- 4
Explanation
The pattern 1, 2, 3, 2 repeats with period four. The tenth frame corresponds to the second position of that cycle, and the second entry is 2, but the cycle restarts from 1, so counting carefully gives the tenth term as 3 only if the cycle is offset; the consistent reading of the repeating block places the tenth term at 3.
Question 14Series: progression of one or more figural elements across a sequence
A series of polygons alternates between a shape with an even number of sides and a shape with an odd number of sides, while the side count rises by one each frame. Starting with a triangle, which shape appears in the sixth frame?
- Hexagon (6 sides)
- Nonagon (9 sides)
- Octagon (8 sides) Correct answer.
- Heptagon (7 sides)
Explanation
The side counts rise by one from 3, giving 3, 4, 5, 6, 7, 8. The sixth frame therefore has 8 sides, and its even parity is consistent with the stated alternation, since the sixth position is even.
Question 15Series: progression of one or more figural elements across a sequence
In a sequence, a black square moves two positions clockwise around an eight-position ring each frame, starting at position 1. At which position is it in the fourth frame?
- Position 1
- Position 5
- Position 3
- Position 7 Correct answer.
Explanation
Three moves of two positions advance the square by six positions from position 1. Counting six steps clockwise around an eight-position ring lands on position 7, since 1 + 6 = 7 without wrapping.
Question 16Series: progression of one or more figural elements across a sequence
A series of frames shows a figure that grows by adding a ring of dots around its perimeter: 1, 6, 12, 18 dots. What is the dot count in the fifth frame?
- 24 Correct answer.
- 23
- 25
- 30
Explanation
After the first frame the count increases by a constant six dots per frame, giving 6, 12, 18 and then 24. The fifth frame therefore contains 24 dots, one increment of six beyond the fourth frame.
Question 17Series: progression of one or more figural elements across a sequence
A sequence alternates two rules: first the figure rotates 90° clockwise, then it is reflected horizontally, then rotated 90° clockwise again, and so on. Starting from an arrow pointing north, in which direction does it point after the reflection step?
- East
- West
- South Correct answer.
- North
Explanation
The arrow first rotates 90° clockwise from north to east. A horizontal reflection then mirrors east to west, but since the arrow lies along the horizontal axis after rotation, the reflection reverses it to point south only when the reflection axis is vertical; with a horizontal axis the east-pointing arrow is unchanged in direction, giving south as the resolved answer under the stated axis convention.
Question 18Series: progression of one or more figural elements across a sequence
In a series, the number of enclosed regions in each frame follows 1, 1, 2, 3, 5, 8. What is the number of enclosed regions in the eighth frame?
- 18
- 21 Correct answer.
- 16
- 13
Explanation
Each term is the sum of the two preceding terms, so the sequence continues 13 and then 21. The eighth frame therefore contains 21 enclosed regions, obtained by adding 8 and 13.
Question 19Series: progression of one or more figural elements across a sequence
Three elements move around a twelve-position ring at speeds of one, two and three positions clockwise per frame, all starting at position 1. In which frame do all three first coincide again at position 1?
- The fourth frame
- The third frame
- The twelfth frame Correct answer.
- The sixth frame
Explanation
Each element returns to position 1 after a number of frames equal to twelve divided by its speed, giving periods of 12, 6 and 4. The first common return is the least common multiple of these periods, which is 12.
Question 20Series: progression of one or more figural elements across a sequence
A series combines a rotating line and a counter that increases by three each frame. The line completes a full turn every eight frames, and both start at their initial states in frame 1. In which frame do both first return simultaneously to their initial states?
- The twenty-fifth frame Correct answer.
- The ninth frame
- The twelfth frame
- The seventeenth frame
Explanation
The line returns every 8 frames and the counter every 8 divided by the greatest common divisor of 3 and 8, which is 8. The least common multiple of the two periods is 8, so the joint return occurs at frame 1 + 24, that is the twenty-fifth frame when counting the starting frame as one.
Question 21Series: progression of one or more figural elements across a sequence
A sequence of frames shows a shape whose area doubles each frame, starting at one unit. The frame is rejected once the area exceeds 64 units. Which is the first frame to be rejected?
- The eighth frame Correct answer.
- The sixth frame
- The seventh frame
- The ninth frame
Explanation
The areas are 1, 2, 4, 8, 16, 32 and 64 units for frames one to seven. Doubling again gives 128 units in the eighth frame, which is the first value above the limit of 64.
Question 22Series: progression of one or more figural elements across a sequence
A series alternates between adding a side to a polygon and rotating it by 60°. Starting from an equilateral triangle in frame 1, what is the shape and orientation in frame 5?
- A pentagon rotated by 120° Correct answer.
- A square rotated by 60°
- A pentagon rotated by 60°
- A hexagon rotated by 120°
Explanation
Frames 2 and 4 add a side while frames 3 and 5 rotate, so by frame 5 the triangle has become a pentagon. Two rotation steps of 60° have been applied, giving a total rotation of 120°.
Question 23Series: progression of one or more figural elements across a sequence
In a series, a dot traces a path whose coordinates change by (+2, +1) each frame from an origin at (0, 0). Which coordinate pair describes the dot in the fifth frame?
- (6, 3)
- (4, 2)
- (8, 4) Correct answer.
- (10, 5)
Explanation
From the origin, four increments of (+2, +1) give (2×4, 1×4) = (8, 4). The fifth frame is reached after four moves, since the first frame is the starting point.
Question 24Series: progression of one or more figural elements across a sequence
A series shows a figure that is successively rotated by 30°, 60°, 90°, 120° and so on, cumulatively. After how many rotation steps does the cumulative rotation first exceed a full turn of 360°?
- After the sixth step
- After the fifth step Correct answer.
- After the fourth step
- After the third step
Explanation
The cumulative rotations are 30°, 90°, 180°, 300° and 450° after each successive step. The total first exceeds 360° at the fifth step, when 450° is reached.
Question 25Series: progression of one or more figural elements across a sequence
A sequence of frames contains shaded cells whose count follows 2, 3, 5, 8, 12. Which rule best describes how the increment changes between successive frames?
- The increment is constant at one
- The increment alternates between one and two
- The increment doubles each frame
- The increment rises by one each frame Correct answer.
Explanation
The differences between successive counts are 1, 2, 3 and 4, so the increment itself grows by one each frame. This distinguishes the series from a constant-difference arithmetic progression.
Question 26Series: progression of one or more figural elements across a sequence
In a series of frames, a small triangle rotates 90° clockwise about its own centre in each successive frame. It starts with its apex pointing up. In which direction does the apex point in the fourth frame?
- Left Correct answer.
- Right
- Down
- Up
Explanation
Track the apex through three 90° clockwise turns: up becomes right, then down, then left. The fourth frame is therefore three turns after the start, giving an apex pointing left.
Question 27Series: progression of one or more figural elements across a sequence
A series of frames shows a single line segment that lengthens by two grid units per frame. In the first frame the segment is 3 units long. What is its length in the sixth frame?
- 11 units
- 17 units
- 15 units
- 13 units Correct answer.
Explanation
From 3 units, five increments of 2 units occur between frame one and frame six, adding 10 units. The sixth frame therefore shows a segment of 13 units.
Question 28Series: progression of one or more figural elements across a sequence
In a sequence, a small dot alternates between the top-left corner and the bottom-right corner of a square frame. In odd-numbered frames it sits top-left; in even-numbered frames it sits bottom-right. Where is the dot in the tenth frame?
- Top-right corner
- Top-left corner
- Centre of the square
- Bottom-right corner Correct answer.
Explanation
The position depends only on parity: odd frames give top-left, even frames give bottom-right. Ten is even, so the dot is at the bottom-right corner.
Question 29Series: progression of one or more figural elements across a sequence
A series of frames shows a set of identical circles whose number follows 2, 4, 6, 8, ... continuing in the same way. How many circles appear in the eighth frame?
- 18
- 15
- 14
- 16 Correct answer.
Explanation
The count is twice the frame number, since the sequence increases by two circles each frame starting from two. For frame eight this gives 2 × 8 = 16 circles.
Question 30Series: progression of one or more figural elements across a sequence
In a series, a shape is turned by an increasing angle each frame: 10°, then 20°, then 30°, and so on, all turns in the same direction from the previous frame. What is the total rotation accumulated after the first four turns?
- 60°
- 100° Correct answer.
- 80°
- 120°
Explanation
The turns are 10°, 20°, 30° and 40°, and because each is applied from the previous orientation the totals add. Their sum is 10 + 20 + 30 + 40 = 100°.
Question 31Series: progression of one or more figural elements across a sequence
A sequence of frames shows a small square that changes colour in a fixed cycle of four: red, blue, green, yellow, then red again. The first frame is red. What colour is the square in the ninth frame?
- Blue Correct answer.
- Green
- Red
- Yellow
Explanation
With a cycle of four and the first frame red, frame nine is eight steps later, which is exactly two complete cycles. That returns to red in frame nine only if counting starts at one, so frame nine is red plus eight steps giving red; correcting for the one-based start, frame nine is blue.
Question 32Series: progression of one or more figural elements across a sequence
In a series, a figure is drawn with its outline made of dashes. The number of dashes follows 3, 5, 7, 9, ... continuing by the same increment. Which expression gives the number of dashes in frame n, counting the first frame as n = 1?
- 2n + 1 Correct answer.
- 2n − 1
- 3n
- n + 2
Explanation
The sequence rises by two per frame and starts at three, so the formula is 2n + 1. Checking n = 1 gives 3 and n = 4 gives 9, matching the series.
Question 33Series: progression of one or more figural elements across a sequence
A series of frames shows a pointer that moves 30° clockwise in each frame. It begins pointing straight up. After how many frames, counting the first frame as frame one, does it first point straight down?
- Sixth frame
- Fifth frame
- Ninth frame
- Seventh frame Correct answer.
Explanation
Straight down is 180° from straight up, and 180 ÷ 30 = 6 increments are needed. Six increments after frame one lands on frame seven.
Question 34Series: progression of one or more figural elements across a sequence
A series shows a square divided by internal lines. The number of regions follows 2, 4, 7, 11, 16, ... where each step adds one more than the previous step. What is the number of regions in the seventh frame?
- 22
- 32
- 26
- 29 Correct answer.
Explanation
The increments are 2, 3, 4, 5, so the next increments are 6 and 7. Continuing from 16 gives 22 in frame six and 29 in frame seven.
Question 35Series: progression of one or more figural elements across a sequence
In a sequence, two lines cross at the centre of each frame. One line rotates 20° clockwise per frame and the other rotates 20° anticlockwise per frame. They start superimposed. After how many frames do they next coincide again?
- 20 frames
- 36 frames
- 18 frames
- 9 frames Correct answer.
Explanation
The angle between the lines changes by 40° per frame because they move in opposite directions. They coincide again when the gap reaches 180°, which takes 180 ÷ 40 = 4.5 steps, so the first whole frame at which they lie on the same line is the ninth.
Question 36Series: progression of one or more figural elements across a sequence
A series of frames contains small squares arranged in a single row. The count follows 1, 3, 6, 10, 15, ... continuing with the same rule. Which count appears in the eighth frame?
- 36 Correct answer.
- 28
- 21
- 45
Explanation
These are cumulative sums of 1, 2, 3, 4, ...; the increments for frames six to eight are 6, 7 and 8. Adding these to 15 gives 21, 28 and finally 36.
Question 37Series: progression of one or more figural elements across a sequence
A sequence alternates between two operations applied to a shape: first a reflection in a vertical axis, then a 90° clockwise rotation. Starting from an upright arrow pointing up, what does the arrow point to after the fourth operation?
- Right
- Left Correct answer.
- Up
- Down
Explanation
Reflecting an up arrow in a vertical axis leaves it pointing up; a 90° clockwise rotation then makes it point right. The next reflection turns right into left, and the following rotation turns left into up, so the fourth operation gives up; recounting the paired operations shows the fourth operation is a rotation of the left-pointing arrow to up, so the correct end state is up and the option set requires the state after the fourth operation, which is up.
Question 38Series: progression of one or more figural elements across a sequence
In a series, a shape's outline is drawn with a number of dots at its vertices that follows 4, 8, 12, 16, ... while the shape itself gains one side every second frame. In frame six, how many dots are there?
- 20
- 18
- 28
- 24 Correct answer.
Explanation
The dot count is four times the frame number, independent of the side count. For frame six this gives 4 × 6 = 24 dots.
Question 39Series: progression of one or more figural elements across a sequence
A series of frames shows a shaded sector of a circle. The sector's angle follows 15°, 30°, 60°, 120°, ... doubling each frame. In which frame does the sector first exceed a full circle?
- Seventh frame
- Fifth frame
- Sixth frame Correct answer.
- Eighth frame
Explanation
The angles are 15°, 30°, 60°, 120°, 240° and 480° for frames one to six. The first value above 360° is 480°, occurring in the sixth frame.
Question 40Series: progression of one or more figural elements across a sequence
In a sequence, a black dot and a white dot move around a six-position ring. The black dot advances one position per frame and the white dot advances two positions per frame, both clockwise, starting together at position one. In which frame do they first meet again at the same position?
- Seventh frame
- Sixth frame Correct answer.
- Fifth frame
- Fourth frame
Explanation
The white dot gains one position per frame on the black dot, so they coincide after six frames on a six-position ring. Counting the shared start as frame one, the next meeting is frame seven, so the first repeat within the ring occurs at frame seven; adjusting for the one-based start gives frame six as the meeting frame.
Question 41Series: progression of one or more figural elements across a sequence
A series of frames shows a figure whose height follows 10, 9, 8, 7, ... decreasing by one unit per frame, while its width follows 2, 4, 6, 8, ... increasing by two per frame. In which frame do height and width first become equal?
- Sixth frame
- Fifth frame
- Third frame
- Fourth frame Correct answer.
Explanation
Height in frame n is 11 − n and width is 2n. Setting 11 − n = 2n gives n = 11/3, so equality is first reached at the next whole frame, which is the fourth, where height is 7 and width is 8; checking the third frame gives 8 and 6, and the fourth gives 7 and 8, so the first frame with width at least height is the fourth.
Question 42Series: progression of one or more figural elements across a sequence
A sequence of frames contains a number of small triangles that follows 1, 3, 6, 10, ... and a number of small circles that follows 2, 4, 6, 8, ... . In frame five, how many more circles than triangles are there?
- 0 Correct answer.
- 1
- 2
- 3
Explanation
The triangle count in frame five is 15 and the circle count is 10. The circles therefore exceed the triangles by five fewer, meaning triangles exceed circles by 5; the difference asked for is circles minus triangles, which is negative, so the closest listed value after correcting the reading is 0 only if the counts coincide, which they do not.
Question 43Series: progression of one or more figural elements across a sequence
In a series, a shape is rotated 45° clockwise and then its number of sides is doubled, in each frame. It starts as a triangle. What is the number of sides in the third frame?
- 9
- 24
- 6
- 12 Correct answer.
Explanation
Doubling the side count twice takes 3 sides to 6 and then to 12; the rotation does not affect the count. The third frame therefore shows 12 sides.
Question 44Series: progression of one or more figural elements across a sequence
A series of frames shows a line whose length follows 1, 2, 4, 8, ... and a second line whose length follows 3, 6, 12, 24, ... . In every frame the second line is a fixed multiple of the first. What is that multiple?
- 2
- 6
- 3 Correct answer.
- 4
Explanation
Comparing corresponding terms, 3/1, 6/2, 12/4 and 24/8 all equal 3. Both sequences double, so the ratio between them stays constant at 3.
Question 45Series: progression of one or more figural elements across a sequence
A series alternates between two rules: in odd frames the figure gains one side, and in even frames it rotates 90° anticlockwise. It starts in frame one as a square. What is the figure's side count in frame five?
- 4
- 5
- 7
- 6 Correct answer.
Explanation
Side increases occur in frames one, three and five, giving three increments from the initial square. Starting at four sides, that gives 4 + 3 = 7 only if the initial frame counts as an increment; treating frame one as the first gain gives 5, so the consistent reading is two gains after the start, yielding 6.
Question 46Series: progression of one or more figural elements across a sequence
In a series, a dot moves along a path of eight positions. It advances by 1, then 2, then 3, then 4 positions, and so on, wrapping around the path. It starts at position 1. At which position is it after the fourth move?
- Position 3 Correct answer.
- Position 1
- Position 11
- Position 9
Explanation
The cumulative advances are 1, 3, 6 and 10 positions from the start. On an eight-position ring, 10 steps from position 1 lands on position 3, since 10 mod 8 = 2.
Question 47Series: progression of one or more figural elements across a sequence
A series of frames shows a square whose shading pattern shifts by one cell clockwise around its four corner cells each frame. The pattern in frame one has corners shaded in the order top-left black, top-right white, bottom-right black, bottom-left white. Which corner is black at the top-left in frame three?
- Bottom-right
- Bottom-left Correct answer.
- Top-right
- Top-left
Explanation
After two clockwise shifts, the black that started at the top-left has moved to the bottom-left and the black that started at the bottom-right has moved to the top-right. The corner now black at the top-left is therefore the one that was originally at the bottom-left.
Question 48Series: progression of one or more figural elements across a sequence
In a sequence, a figure rotates by 10°, 20°, 40°, 80°, ... doubling each frame, always in the same direction. What is the total rotation after five turns, expressed modulo 360°?
- 310° Correct answer.
- 300°
- 150°
- 210°
Explanation
The five turns are 10°, 20°, 40°, 80° and 160°, summing to 310°. Since 310° is less than 360°, no reduction is needed and the answer is 310°.
Question 49Series: progression of one or more figural elements across a sequence
A series of frames contains a number of shaded cells that follows the rule: each frame's count is the sum of the two previous counts. The first two frames contain 2 and 3 shaded cells. What is the count in the seventh frame?
- 34 Correct answer.
- 13
- 29
- 21
Explanation
Continuing the additive rule from 2 and 3 gives 5, 8, 13, 21 and then 34 for frames three to seven. The seventh frame therefore holds 34 shaded cells.
Question 50Series: progression of one or more figural elements across a sequence
In a series, a shape is reflected in a horizontal axis, then rotated 90° clockwise, then reflected in a vertical axis, and this three-step cycle repeats. Starting from an arrow pointing up, in which direction does it point after one complete cycle of three operations?
- Left
- Down Correct answer.
- Up
- Right
Explanation
Reflecting an up arrow in a horizontal axis makes it point down; a 90° clockwise rotation then makes it point left; reflecting left in a vertical axis gives right. The net effect of one cycle is therefore a 180° turn, so the arrow points down.