Odd Man Out & Series Questions and Answers

Answer: C

Two series are interleaved and run in opposite directions.

\[ \text{positions 1, 3, 5, 7, 9: } 3,\; 6,\; 9,\; 12,\; 15 \quad (+3) \]

\[ \text{positions 2, 4, 6, 8, 10: } 7,\; 5,\; 3,\; 1,\; \mathbf{-1} \quad (-2) \]

The tenth term belongs to the falling series:

\[ 1 - 2 = -1 \]

Nothing in the rule stops the second series going negative, which is what makes \( -1 \) the answer rather than 3.

Answer: D

Each step multiplies by an increasing integer and adds the same integer.

\[ 7 \times 1 + 1 = 8 \quad\checkmark \]

\[ 8 \times 2 + 2 = 18 \quad\checkmark \]

\[ 18 \times 3 + 3 = 57 \quad\checkmark \]

\[ 57 \times 4 + 4 = 232 \quad\text{but the series shows } 228 \]

So 228 is wrong. The rest confirm 232: \( 232 \times 5 + 5 = 1165 \) and \( 1165 \times 6 + 6 = 6996 \).

Answer: B

The series is the factorials.

\[ 0! = 1,\; 1! = 1,\; 2! = 2,\; 3! = 6,\; 4! = 24,\; 5! = 120,\; 6! = 720 \]

The sixth term should be \( 5! = 120 \), not 96.

So 96 is wrong. Equivalently each term is the previous multiplied by its position: \( 24 \times 5 = 120 \), and \( 120 \times 6 = 720 \) closes the series correctly.

Answer: D

The series is the squares counting down from 14.

\[ 14^{2},\; 13^{2},\; 12^{2},\; 11^{2},\; 10^{2},\; 9^{2},\; 8^{2} = 196,\; 169,\; 144,\; 121,\; 100,\; 81,\; 64 \]

The sixth term should be \( 9^{2} = 81 \), not 80.

So 80 is the wrong number - off by one from a perfect square.

Answer: C

Each term is obtained by subtracting 3 and halving.

\[ \frac{445 - 3}{2} = 221 \quad\checkmark \qquad \frac{221 - 3}{2} = 109 \quad\checkmark \]

\[ \frac{109 - 3}{2} = 53 \quad\text{but the series shows } 46 \]

So 46 is wrong. The rest confirm 53: \( \tfrac{53-3}{2} = 25 \), \( \tfrac{25-3}{2} = 11 \), \( \tfrac{11-3}{2} = 4 \).

Answer: D

Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number.

190 - 24 = 166
166 - 21 = 145
145 - 18 = 127 [Here, 128 is placed instead of 127]
127 - 15 = 112
112 - 12 = 100 ... and so on.

Therefore, 128 is wrong.

Answer: B

The gaps should be the odd numbers, rising by 2 each time.

\[ 19 \xrightarrow{+7} 26 \xrightarrow{+9} 35 \xrightarrow{+11} 46 \xrightarrow{+13} 59 \xrightarrow{+15} 74 \xrightarrow{+17} 91 \]

The third term should be \( 26 + 9 = 35 \), not 33.

So 33 is the wrong number - every term after it fits the corrected value.

Answer: D

The multiplier alternates between 2 and 3, with 1 added each time.

\[ 1 \times 2 + 1 = 3 \quad\checkmark \qquad 3 \times 3 + 1 = 10 \quad\checkmark \]

\[ 10 \times 2 + 1 = 21 \quad\checkmark \qquad 21 \times 3 + 1 = 64 \quad\checkmark \]

\[ 64 \times 2 + 1 = 129 \quad\checkmark \qquad 129 \times 3 + 1 = 388 \quad\text{not } 356 \]

So 356 is wrong. The final term settles it: \( 388 \times 2 + 1 = 777 \).

Answer: C

Each even term of the series is obtained by multiplying the previous term by 2.

2nd term = (1st term) x 2 = 6 x 2 = 12

4th term = (3rd term) x 2 = 48 x 2 = 96.

6th term = (5th term) x 2 = 384 x 2 =768.

 4th term should be 96 instead of 100.

Answer: C

Each term is the previous one divided by 4.

\[ 40960 \to 10240 \to 2560 \to 640 \to 160 \to 40 \to 10 \]

The fifth term should be \( 640 \div 4 = 160 \), not 200.

So 200 is the wrong number - and \( 200 \div 4 = 50 \), which would not give the 40 that follows.