Odd Man Out & Series Questions and Answers

Answer: A

Two series are interleaved. The even positions are all 16, while the odd positions count up by one.

\[ \text{odd positions: } 5,\; 6,\; 7,\; \mathbf{8} \]

\[ \text{even positions: } 16,\; 16,\; 16 \]

The seventh term should be 8, not 9.

So 9 is the wrong number. The repeated 16 is the clue that two separate sequences are woven together.

Answer: D

The differences should be the prime numbers in order.

\[ 125 \xrightarrow{+2} 127 \xrightarrow{+3} 130 \xrightarrow{+5} 135 \xrightarrow{+7} 142 \xrightarrow{+11} 153 \xrightarrow{+13} 166 \]

The last term should be \( 153 + 13 = 166 \), not 165.

So 165 is wrong. The actual last gap is 12, which is not prime.

Answer: C

Each term is the previous one divided by a falling even number.

\[ 46080 \xrightarrow{\div 12} 3840 \xrightarrow{\div 10} 384 \xrightarrow{\div 8} 48 \xrightarrow{\div 6} 8 \xrightarrow{\div 4} 2 \xrightarrow{\div 2} 1 \]

The fifth term should be \( 48 \div 6 = 8 \), not 24.

So 24 is the wrong number. Checking forwards from 8 confirms it: \( 8 \div 4 = 2 \) and \( 2 \div 2 = 1 \).

Answer: D

The differences alternate between \( +7 \) and \( +5 \).

\[ 6 \xrightarrow{+7} 13 \xrightarrow{+5} 18 \xrightarrow{+7} 25 \xrightarrow{+5} 30 \xrightarrow{+7} 37 \xrightarrow{+5} 42 \]

The last term should be \( 37 + 5 = 42 \), not 40.

So 40 is the wrong number.

Answer: B

The series alternates between multiplying by 1.5 and dividing by 3.

\[ 36 \xrightarrow{\times 1.5} 54 \xrightarrow{\div 3} 18 \xrightarrow{\times 1.5} 27 \xrightarrow{\div 3} 9 \xrightarrow{\times 1.5} 13.5 \xrightarrow{\div 3} 4.5 \]

The sixth term should be \( 9 \times 1.5 = 13.5 \), not 18.5.

So 18.5 is wrong. The final 4.5 confirms it, since \( 13.5 \div 3 = 4.5 \) while \( 18.5 \div 3 \) is not a clean value.

Answer: D

Each term is a product of two consecutive integers.

\[ 7 \times 8 = 56,\quad 8 \times 9 = 72,\quad 9 \times 10 = 90,\quad 10 \times 11 = 110,\quad 11 \times 12 = 132 \]

The next should be \( 12 \times 13 = 156 \), not 150.

So 150 is the wrong number. Equivalently the differences run 16, 18, 20, 22, 24 - and 132 to 150 is a gap of only 18.

Answer: A

The series is the squares of the odd numbers.

\[ 5^{2},\; 7^{2},\; 9^{2},\; 11^{2},\; 13^{2},\; 15^{2} = 25,\; 49,\; 81,\; 121,\; 169,\; 225 \]

\[ 36 = 6^{2}, \text{ the square of an even number} \]

So 36 is the wrong number. Being a perfect square, it fits the looser pattern - which is exactly the trap.

Answer: A

Each term is roughly double the previous, with the correction alternating between \( +1 \) and \( -1 \).

\[ 16 \times 2 + 1 = 33 \]

\[ 33 \times 2 - 1 = 65 \]

\[ 65 \times 2 + 1 = 131 \]

\[ 131 \times 2 - 1 = 261 \]

\[ 261 \times 2 + 1 = \mathbf{523} \]

Doubling alone would give 522, so the alternating sign is what separates 523 from the 521 on offer.

Answer: B

Two series are interleaved.

\[ \text{positions 1, 3, 5, 7: } 10,\; 13,\; 16,\; 19 \quad (+3) \]

\[ \text{positions 2, 4, 6, 8: } 5,\; 10,\; 20,\; \mathbf{40} \quad (\times 2) \]

The missing eighth term belongs to the doubling series:

\[ 20 \times 2 = 40 \]

Reading the list as a single sequence gets nowhere; the alternation is the whole structure.

Answer: C

The series is the perfect squares in order.

\[ 1^{2},\; 2^{2},\; 3^{2},\; 4^{2},\; 5^{2},\; 6^{2},\; 7^{2} \]

\[ \text{next} = 8^{2} = \mathbf{64} \]

The differences are the odd numbers 3, 5, 7, 9, 11, 13, so the next gap is 15 and \( 49 + 15 = 64 \) - the same answer from the other direction.