Find the odd man out. 10, 25, 45, 54, 60, 75, 80
Answer: C
Every number here is a multiple of 5 except one.
\[ 10,\; 25,\; 45,\; 60,\; 75,\; 80 \;\text{end in 0 or 5} \]
\[ 54 \;\text{does not} \]
So 54 is the odd man out. A quick test for divisibility by 5 is the last digit alone.
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Find the odd man out. 396, 462, 572, 427, 671, 264
Answer: B
In each three-digit number, the middle digit is the sum of the outer two.
So 427 is the odd one out.
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Find the odd man out. 6, 9, 15, 21, 24, 28, 30
Answer: A
Every number here is a multiple of 3 except one.
\[ 6,\; 9,\; 15,\; 21,\; 24,\; 30 \;\text{are all divisible by 3} \]
\[ 28 = 3 \times 9 + 1 \]
So 28 is the odd man out. Its digit sum is 10, which is not divisible by 3 - the quickest test.
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Find the odd man out. 1, 4, 9, 16, 23, 25, 36
Answer: B
Each number is a perfect square.
\[ 1 = 1^{2},\; 4 = 2^{2},\; 9 = 3^{2},\; 16 = 4^{2},\; 25 = 5^{2},\; 36 = 6^{2} \]
\[ 23 \text{ lies between } 16 \text{ and } 25 \text{ and is not a square} \]
So 23 is the odd man out.
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Find the odd man out. 1, 4, 9, 16, 20, 36, 49
Answer: C
Each number is a perfect square.
\[ 1,\; 4,\; 9,\; 16,\; 36,\; 49 = 1^{2},\, 2^{2},\, 3^{2},\, 4^{2},\, 6^{2},\, 7^{2} \]
\[ 20 \text{ is not a square} \]
So 20 breaks the run. Note that \( 5^{2} = 25 \) is missing from the list, and 20 has been slipped in where it would have stood.
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Find the odd man out. 2, 5, 10, 17, 26, 37, 50, 64
Answer: D
Each term is one more than a perfect square.
\[ n^{2} + 1: \quad 2,\; 5,\; 10,\; 17,\; 26,\; 37,\; 50,\; 65 \]
The eighth term should be \( 8^{2} + 1 = 65 \), not 64.
So 64 is the odd man out - a perfect square itself, which is what makes it convincing.
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Find the odd man out. 10, 14, 16, 18, 21, 24, 26
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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Find the odd man out. 16, 25, 36, 72, 144, 196, 225
Answer: B
Each number is a perfect square.
\[ 16 = 4^{2},\; 25 = 5^{2},\; 36 = 6^{2},\; 144 = 12^{2},\; 196 = 14^{2},\; 225 = 15^{2} \]
\[ 72 \text{ lies between } 64 \text{ and } 81 \text{ and is not a square} \]
So 72 is the odd man out.
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Find the odd man out. 331, 482, 551, 263, 383, 362, 284
Answer: B
In each number, the middle digit is the product of the outer two.
So 383 is the odd one out. Trying sums first is the natural instinct, and it fails on the very first number - the signal to try products instead.
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Find the odd man out. 835, 734, 642, 751, 853, 981, 532
Answer: A
In each number, the middle digit is the difference of the outer two.
So 751 is the odd one out.
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