Series Completion Questions and Answers

Answer: C

The entries are I, J, 10, and 8.

In each 2 by 2 block the numbers are the alphabet positions of the two letters above, written in the opposite order. N is 14 and U is 21, and the block shows 21, 14.

• Top right: F is 6 and the bottom row reads 9, 6, so (i) is the 9th letter, I.
• Bottom left: H is 8 and L is 12; the bottom row reads 12, (iv), so (iv) = 8.
• Bottom right: the bottom row reads 15, (iii); 15 is the value of O, the second letter, so (iii) is the value of the first letter (ii). J and 10 fit.

Only option C gives (ii) = J and (iii) = 10, consistent with J being the 10th letter, together with (i) = I and (iv) = 8. The other options break the rule: K and L are not the 9th letter, and Q with 12 do not match.

Answer: C

The missing tile is (C), the tile with 8 dots.

Count the dots in the tiles in order: 0, 1, 1, 2, 3, 5. From the third tile on, each count is the sum of the two before it (1 = 0 + 1, 2 = 1 + 1, 3 = 1 + 2, 5 = 2 + 3), which is the Fibonacci sequence.

The next count is therefore 3 + 5 = 8. Tile (C) has 8 dots, while (A) has 4, (B) 6 and (D) 9, none of which continues the sequence.

Answer: C

The entries are I, J, 10, and 8.

Read each 2 × 2 block as two letters above two numbers, with letters standing for their alphabet positions (A = 1, ..., Z = 26). In every block the left number is the left letter's position plus a fixed step, and the right number is the right letter's position minus the same step:

• Top left: N = 14 and 14 + 7 = 21; U = 21 and 21 - 7 = 14.
• Top right: F = 6 and 6 + 3 = 9; so (i) must be the letter whose position minus 3 is 6, which is 9 = I.
• Bottom left: H = 8 and 8 + 4 = 12; L = 12, so (iv) = 12 - 4 = 8.
• Bottom right: (ii) + 5 = 15 gives 10 = J; O = 15, so (iii) = 15 - 5 = 10.

Only I (9) satisfies the top-right block, since 9 - 3 = 6; Q (17), K (11) and L (12) all fail it, which rules out the other three options at the first entry.

Answer: C

The missing tile holds 8 dots, which is the tile in option (C).

Count the dots in the six tiles: 0, 1, 1, 2, 3, 5. From the third tile on, each count is the sum of the two before it (1 = 0 + 1, 2 = 1 + 1, 3 = 1 + 2, 5 = 2 + 3), the Fibonacci rule. The next count is therefore 3 + 5 = 8.

Option (C) shows 8 dots (three in the top row, one at each side of the middle row, three in the bottom row). Option (A) has 4, option (B) has 6 and option (D) has 9, none of which continues the sequence; 9 is the trap for anyone who simply fills the grid.

Answer: B

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

The tiles hold 2, 3, ?, 7 and 11 dots. These are consecutive prime numbers, and the prime between 3 and 7 is 5, so the missing tile must carry 5 dots. Tile (B) has four dots at the corners and one in the centre, five in all.

Tile (A) has 4 dots, (C) has 6 and (D) has 8, and none of these is prime. The prime sequence also accounts for the uneven growth of the tiles: the gaps 1, 2, 2, 4 between 2, 3, 5, 7 and 11 are exactly the gaps between consecutive primes, which no simple arithmetic rule would give.

Answer: B

Correct answer: 36

Each term is a perfect square of the counting numbers: \[ 1^2=1,\; 2^2=4,\; 3^2=9,\; 4^2=16,\; 5^2=25 \] so the next is \( 6^2 = \mathbf{36} \).

Answer: B

Correct answer: 13

The terms are the prime numbers in order - 2, 3, 5, 7, 11 - and the one that follows 11 is 13, with 17 coming after it as the series shows.

Answer: A

Correct answer: 14

The gaps between the terms increase by one each time: \[ 5-2=3,\quad 9-5=4,\quad \_-9=5,\quad 20-\_=6,\quad 27-20=7 \] so the missing term is \( 9 + 5 = \mathbf{14} \).

Answer: D

Correct answer: 14

The series falls by one more each time: \( -1, -2, -3, -4, -5 \). From 17 the next step subtracts 3, giving \[ 17 - 3 = \mathbf{14} \] and then \( 14 - 4 = 10 \) and \( 10 - 5 = 5 \), as shown.

Answer: D

Each number in the series is the product of the digits of the preceding number
Thus, \(7 \times 7 =49, 4\times9=36,..\)
\(\therefore\) The missing number \(= 1\times8=8\)