Series Completion Questions and Answers

Answer: A

The answer is option (A). Each of the four corner arrows turns by 90 degrees from one square to the next, and each corner has its own direction of turning. The top-left arrow turns clockwise (right, down, left, up) and the top-right arrow also turns clockwise (up, right, down, left). The bottom-left arrow turns anticlockwise (down, right, up, left) and the bottom-right arrow turns anticlockwise (left, down, right, up). One more step gives right at top-left, up at top-right, down at bottom-left and left at bottom-right. That is the arrangement shown in option (A). Options (B), (C) and (D) each have at least one corner arrow pointing the wrong way.

Answer: D

In the three figures of the series the black wedge of the circle moves anticlockwise by one sector each time: it is at the lower right (between 3 and 4:30 on a clock face) in the first figure, then at the upper right (1:30 to 3), then at the top (12 to 1:30). One more step anticlockwise puts it at the upper left, from 10:30 to 12, which is the circle of option (D). Option (A) repeats the wedge position of the second figure, option (B) puts the wedge at the left, nine to ten-thirty, which skips a step, and option (C) puts it at the lower right again, so they do not continue the series. The answer is option (D).

Answer: C

Follow each shape from figure to figure in the 2 by 2 grid. The circle moves clockwise from the top left to the top right, the bottom right and then the bottom left, and it alternates between open and filled. The square moves clockwise too, from the top right to the bottom right, the bottom left and then the top left. The triangle moves clockwise from the bottom left through the top left and top right, alternating between upright and inverted. In the fourth figure the square is therefore at the top left, the filled circle at the bottom left and an inverted triangle at the bottom right, which is option (C). The other options place the shapes in cells they cannot be in.

Answer: C

The missing figure is option 3.

In the three given figures, the filled circle moves one corner at a time, from the bottom right to the top right and then to the top left. The next corner in that direction is the bottom left. The other symbols keep their places in the pattern, so the figure with the filled circle at the bottom left is the one that continues the series, and that is option 3.

Options 1, 2 and 4 put the filled circle at the wrong corner.

The filled circle travels round the corners in a fixed direction: bottom right in the first figure, top right in the second and top left in the third. The fourth position in that direction is the bottom left. Among the answer figures only option 3 has the filled circle at the bottom left.

Answer: B

The missing tile is (B), the tile with five dots (four corners and the centre).

Count the dots in the given tiles: 2, 3, ?, 7, 11. These are consecutive prime numbers, and the prime between 3 and 7 is 5. The fourth tile holds 3 + 1 + 3 = 7 dots and the fifth 4 + 3 + 4 = 11, which confirms the pattern.

Tile (A) has 4 dots, (C) has 6 and (D) has 8, and none of 4, 6 or 8 is prime, so only (B) continues the sequence of primes 2, 3, 5, 7, 11.

Answer: C

The missing tile is (C), the tile with eight dots.

Count the dots in the tiles from left to right: 0, 1, 1, 2, 3, 5. Each count from the third onward is the sum of the two before it (0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5), which is the Fibonacci sequence. The next term is 3 + 5 = 8, so the seventh tile must carry eight dots.

Tile (A) has 4 dots, tile (B) has 6 and tile (D) has 9; none of these continues the sequence. Tile (C) has eight dots arranged round the edge of the tile, which is the only eight-dot choice.

Answer: B

The missing tile is (B), the tile with 5 dots.

Count the dots in the given tiles: 2, 3, ?, 7, 11. These are consecutive prime numbers, and the prime between 3 and 7 is 5. Tile (B) is the only option with five dots.

Tile (A) has 4 dots and tile (C) has 6, neither of which is prime. Tile (D) has 8 dots, which is neither prime nor the term between 3 and 7. A difference pattern does not work either: the gaps 1, ?, ?, 4 are only explained by the primes, so 5 is the term that keeps the sequence consistent.

Answer: C

The missing tile is the tile with 8 dots.

The tiles hold 0, 1, 1, 2, 3 and 5 dots. From the third tile on, each count is the sum of the two before it, which is the Fibonacci sequence:

\[ \begin{aligned} 0 + 1 &= 1, \quad 1 + 1 = 2, \quad 1 + 2 = 3 \\ 2 + 3 &= 5, \quad 3 + 5 = 8 \end{aligned} \]

So the next tile must carry 8 dots. The tiles with 4 and 6 dots fall short, and the 3 by 3 tile with 9 dots is one too many; a simple 'add one more dot' or 'square number' rule does not fit the counts already shown.

Answer: A

The next figure is option (A), with the circle in row 2 of the first column and the triangle in the bottom row of the third column.

Track each shape separately. The triangle stays in the third column and moves down one row each step: row 1, row 2, row 3, so next it is in row 4. The circle stays in the first column and also moves down one row each step, wrapping round from the bottom to the top: row 3, row 4, row 1, so next it is in row 2.

Option (B) swaps the shapes' columns, option (C) moves the circle into the middle column and puts the triangle back in row 1, and option (D) leaves the circle in row 4 and the triangle in row 1. Only (A) continues both movements.

Answer: B

The next figure is (B).

Two things change from figure to figure. The shaded sector grows by 45° each time: 90° in I, 135° in II and 180° in III, so IV must shade 225°. And the sector's starting edge turns 90° clockwise each time: I starts at 9 o'clock, II at 12 o'clock and III at 3 o'clock, so IV must start at 6 o'clock.

A 225° sector running clockwise from 6 o'clock covers the left side and the top and ends at about half past one, leaving 135° unshaded on the right. That is option (B).

(A) shades only a half, like III. (C) shades a sector of about 135°, and (D) shades the right side, the mirror image of the required figure.