Find the odd man out. 41, 43, 47, 53, 61, 71, 73, 81
Answer: D
Every number here is prime except one.
\[ 41,\; 43,\; 47,\; 53,\; 61,\; 71,\; 73 \;\text{are prime} \]
\[ 81 = 3^{4} = 3 \times 27 \]
So 81 is the odd man out. Its digit sum is 9, so it is divisible by 3 - the fastest way to spot it.
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Find the odd man out. 3, 5, 7, 12, 17, 19
Answer: D
Every number here is prime except one.
\[ 3,\; 5,\; 7,\; 17,\; 19 \;\text{are prime} \]
\[ 12 = 2^{2} \times 3 \]
So 12 is the odd man out - and the only even number in the list besides, which gives it away at a glance.
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Find out the wrong number in the given sequence of numbers. 582, 605, 588, 611, 634, 617, 600
Answer: A
The series alternates between adding 23 and subtracting 17.
\[ 582 + 23 = 605 \quad\checkmark \]
\[ 605 - 17 = 588 \quad\checkmark \]
\[ 588 + 23 = 611 \quad\checkmark \]
\[ 611 - 17 = 594 \quad\text{but the series shows } 634 \]
So 634 is wrong; it should be 594. The rest then follow: \( 594 + 23 = 617 \) and \( 617 - 17 = 600 \).
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Find out the wrong number in the given sequence of numbers. 22, 33, 66, 99, 121, 279, 594
Answer: C
Every term should be a multiple of 11.
\[ 22,\; 33,\; 66,\; 99,\; 121,\; 594 \;\text{are all divisible by 11} \]
\[ 279 \div 11 = 25.36 \ldots \]
So 279 is the wrong number. The alternating-sum test confirms it: \( 2 - 7 + 9 = 4 \), which is not a multiple of 11.
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Find out the wrong number in the given sequence of numbers. 8, 13, 21, 32, 47, 63, 83
Answer: A
The differences should grow by 3 each time.
\[ 8 \xrightarrow{+5} 13 \xrightarrow{+8} 21 \xrightarrow{+11} 32 \xrightarrow{+14} 46 \xrightarrow{+17} 63 \xrightarrow{+20} 83 \]
The fifth term should therefore be \( 32 + 14 = 46 \), not 47.
So 47 is the wrong number. Every later term is consistent with 46, which is what confirms the error sits at that single position.
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Find out the wrong number in the given sequence of numbers 1, 8, 27, 64, 124, 216, 343
Answer: D
The series is the cubes of the natural numbers.
\[ 1^{3},\; 2^{3},\; 3^{3},\; 4^{3},\; 5^{3},\; 6^{3},\; 7^{3} = 1,\; 8,\; 27,\; 64,\; 125,\; 216,\; 343 \]
The fifth term should be \( 5^{3} = 125 \), not 124.
So 124 is wrong - off by exactly one, which is what makes it hard to spot.
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Find out the wrong number in the given sequence of numbers 1, 2, 6, 15, 31, 56, 91
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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Find out the wrong number in the given sequence of numbers 52, 51, 48, 43, 34, 27, 16
Answer: B
The numbers should fall by successive odd amounts.
\[ 52 \xrightarrow{-1} 51 \xrightarrow{-3} 48 \xrightarrow{-5} 43 \xrightarrow{-7} 36 \xrightarrow{-9} 27 \xrightarrow{-11} 16 \]
The fifth term should be \( 43 - 7 = 36 \), not 34.
So 34 is wrong. Equivalently the terms are \( 52 - n^{2} \) for \( n = 0,1,2,\ldots \): 52, 51, 48, 43, 36, 27, 16.
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Find out the wrong number in the given sequence of numbers 4, 6, 8, 9, 10, 11, 12
Answer: B
The series lists the composite numbers in order.
\[ 4,\; 6,\; 8,\; 9,\; 10,\; 12,\; 14 \ldots \]
\[ 11 \text{ is prime} \]
So 11 is the wrong number - every other entry has a divisor other than 1 and itself.
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Find out the wrong number in the given sequence of numbers 105, 85, 60, 30, 0, -45, -90
Answer: D
The gaps should widen by 5 each time.
\[ 105 \xrightarrow{-20} 85 \xrightarrow{-25} 60 \xrightarrow{-30} 30 \xrightarrow{-35} -5 \xrightarrow{-40} -45 \xrightarrow{-45} -90 \]
The fifth term should be \( 30 - 35 = -5 \), not 0.
So 0 is the wrong number. Every term after it fits the corrected value, which confirms the single break.
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