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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Insert the missing number 2, 4, 12, 48, 240, (....)
Answer: B
The multiplier grows by one at each step.
\[ 2 \times 2 = 4,\quad 4 \times 3 = 12,\quad 12 \times 4 = 48,\quad 48 \times 5 = 240 \]
\[ 240 \times 6 = \mathbf{1440} \]
Assuming a constant multiplier of 5 would give 1200, and of 4 would give 960 - the first option.
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Find the one which does not belong to that group ?
Answer: B
Three of the four are perfect cubes.
\[ 343 = 7^{3}, \quad 1331 = 11^{3}, \quad 2197 = 13^{3} \]
\[ 121 = 11^{2} \text{, a square rather than a cube} \]
So 121 does not belong. It is deliberately paired with 1331, the cube of the same number 11.
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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 one which does not belong to that group ?
Answer: B
In each group the two digits, read together, give the letter's position in the alphabet.
So 2Y4 does not belong.
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Find the one which does not belong to that group ?
Answer: B
Three of the four numbers are odd.
\[ 3,\; 5,\; 9 \;\text{are odd}; \qquad 4 \;\text{is even} \]
So 4 does not belong. The list avoids making them all prime - 9 is \( 3^{2} \) - so oddness, not primality, is the shared property.
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Find the one which does not belong to that group ?
Answer: B
Three of the four words end in the same three letters.
\[ \text{P-art}, \quad \text{C-art}, \quad \text{D-art} \]
Each is a single letter followed by -art.
Trap does not fit that shape - it is an anagram of "part" rather than a member of the -art family.
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Find the one which does not belong to that group ?
Answer: D
Walk, talk and drink are verbs - each names an action.
Plank is a noun, a flat length of timber.
So Plank does not belong. The rhyme with "walk" and "talk" is the distraction; the grammatical class is the real grouping.
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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 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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