Odd Man Out & Series Questions and Answers

Q: Find out the wrong number in the series 445, 221, 109, 46, 25, 11, 4

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: \( \tfrac{53-3}{2} = 25 \), \( \tfrac{25-3}{2} = 11 \), \( \tfrac{11-3}{2} = 4 \).

Q: Find the one which does not belong to that group ?

Boxing, chess and wrestling are all contested one against one - a single competitor faces a single opponent.Baseball is a team game, played nine a side.So Baseball does not belong. That some are physical and chess is not would split the group differently, leaving two on each side - so it cannot be the intended rule.

Q: Find the one which does not belong to that group ?

The Ganga, Yamuna and Sutlej are rivers.Hirakud is a dam, built across the Mahanadi in Odisha.So Hirakud does not belong - it is a structure on a river, not a river itself.

Q: Insert the missing number 15, 31, 63, 127, 255, (....)

Each term is double the previous plus one.\[ 15 \times 2 + 1 = 31,\quad 31 \times 2 + 1 = 63,\quad 63 \times 2 + 1 = 127 \]\[ 127 \times 2 + 1 = 255,\quad 255 \times 2 + 1 = \mathbf{511} \]Equivalently every term is \( 2^{n} - 1 \): 15, 31, 63, 127, 255, 511. The 513 on offer is \( 2^{9} + 1 \), one on the wrong side.

Q: Find the odd man out. 10, 14, 16, 18, 21, 24, 26

Every number in the list is even except one.\[ 10,\; 14,\; 16,\; 18,\; 24,\; 26 \;\text{are even} \]\[ 21 \;\text{is odd} \]So 21 is the odd man out.

Q: Find the one which does not belong to that group ?

Skin, eyes and nose are sense organs - they carry the senses of touch, sight and smell respectively.The leg is a limb used for movement and carries no sense of its own.So Leg does not belong.

Q: Find out the wrong number in the given sequence of numbers 1, 2, 6, 15, 31, 56, 91

The differences should be the perfect squares in order.\[ 1 \xrightarrow{+1} 2 \xrightarrow{+4} 6 \xrightarrow{+9} 15 \xrightarrow{+16} 31 \xrightarrow{+25} 56 \xrightarrow{+36} 92 \]The last term should be \( 56 + 36 = 92 \), not 91.So 91 is the wrong number.

Q: Find the odd man out. 8, 27, 64, 100, 125, 216, 343

Each number is a perfect cube.\[ 8 = 2^{3},\; 27 = 3^{3},\; 64 = 4^{3},\; 125 = 5^{3},\; 216 = 6^{3},\; 343 = 7^{3} \]\[ 100 = 10^{2} \text{, a square but not a cube} \]So 100 breaks the pattern. It sits between \( 4^{3} = 64 \) and \( 5^{3} = 125 \), which is exactly why it looks plausible.

Important Instructions

91.

Find out the wrong number in the series 445, 221, 109, 46, 25, 11, 4

A.221
B.109
C.46
D.25

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: \( \tfrac{53-3}{2} = 25 \), \( \tfrac{25-3}{2} = 11 \), \( \tfrac{11-3}{2} = 4 \).

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92.

Find the one which does not belong to that group ?

A.Baseball
B.Boxing
C.Chess
D.Wrestling

Answer: A

Boxing, chess and wrestling are all contested one against one - a single competitor faces a single opponent.

Baseball is a team game, played nine a side.

So Baseball does not belong. That some are physical and chess is not would split the group differently, leaving two on each side - so it cannot be the intended rule.

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93.

Find out the wrong number in the series 7, 8, 18, 57, 228, 1165, 6996

A.8
B.18
C.57
D.228

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 \( 1165 \times 6 + 6 = 6996 \).

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94.

Find the one which does not belong to that group ?

A.36
B.49
C.64
D.81

Answer: B

All four are perfect squares, so look at what is being squared.

\[ 36 = 6^{2}, \quad 49 = 7^{2}, \quad 64 = 8^{2}, \quad 81 = 9^{2} \]

The roots 6, 8 and 9 are composite; 7 is prime.

So 49 does not belong - the square of the only prime root.

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95.

Find the one which does not belong to that group ?

A.Ganga
B.Hirakud
C.Yamuna
D.Sutlej

Answer: B

The Ganga, Yamuna and Sutlej are rivers.

Hirakud is a dam, built across the Mahanadi in Odisha.

So Hirakud does not belong - it is a structure on a river, not a river itself.

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96.

Insert the missing number 15, 31, 63, 127, 255, (....)

A.513
B.511
C.517
D.523

Answer: B

Each term is double the previous plus one.

\[ 15 \times 2 + 1 = 31,\quad 31 \times 2 + 1 = 63,\quad 63 \times 2 + 1 = 127 \]

\[ 127 \times 2 + 1 = 255,\quad 255 \times 2 + 1 = \mathbf{511} \]

Equivalently every term is \( 2^{n} - 1 \): 15, 31, 63, 127, 255, 511. The 513 on offer is \( 2^{9} + 1 \), one on the wrong side.

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97.

Find the odd man out. 10, 14, 16, 18, 21, 24, 26

A.26
B.24
C.21
D.18

Answer: C

Every number in the list is even except one.

\[ 10,\; 14,\; 16,\; 18,\; 24,\; 26 \;\text{are even} \]

\[ 21 \;\text{is odd} \]

So 21 is the odd man out.

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98.

Find the one which does not belong to that group ?

A.Skin
B.Eye
C.Leg
D.Nose

Answer: C

Skin, eyes and nose are sense organs - they carry the senses of touch, sight and smell respectively.

The leg is a limb used for movement and carries no sense of its own.

So Leg does not belong.

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99.

Find out the wrong number in the given sequence of numbers 1, 2, 6, 15, 31, 56, 91

A.31
B.91
C.56
D.15

Answer: B

The differences should be the perfect squares in order.

\[ 1 \xrightarrow{+1} 2 \xrightarrow{+4} 6 \xrightarrow{+9} 15 \xrightarrow{+16} 31 \xrightarrow{+25} 56 \xrightarrow{+36} 92 \]

The last term should be \( 56 + 36 = 92 \), not 91.

So 91 is the wrong number.

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100.

Find the odd man out. 8, 27, 64, 100, 125, 216, 343

A.27
B.100
C.125
D.343

Answer: B

Each number is a perfect cube.

\[ 8 = 2^{3},\; 27 = 3^{3},\; 64 = 4^{3},\; 125 = 5^{3},\; 216 = 6^{3},\; 343 = 7^{3} \]

\[ 100 = 10^{2} \text{, a square but not a cube} \]

So 100 breaks the pattern. It sits between \( 4^{3} = 64 \) and \( 5^{3} = 125 \), which is exactly why it looks plausible.

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