Find the one which does not belong to that group ?
Answer: A
A mother, a sister and a daughter are related by blood.
A daughter-in-law is related by marriage - she joins the family through a son.
So Daughter-in-law does not belong.
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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, 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 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 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 the one which does not belong to that group ?
Answer: D
A blacksmith, a carpenter and a sculptor all work the material with their hands - iron, wood and stone respectively.
An architect designs buildings and leaves the making to others.
So Architect does not belong.
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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 the one which does not belong to that group ?
Answer: C
Three of the four numbers read the same forwards and backwards.
\[ 42624 \to 42624 \quad\checkmark \qquad 37573 \to 37573 \quad\checkmark \]
\[ 93339 \to 93339 \quad\checkmark \qquad 84284 \to 48248 \quad\times \]
So 84284 is not a palindrome and does not belong. Checking only the outer digits is not enough - 84284 starts and ends with different digits, which settles it at a glance.
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Find out the wrong number in the series. 10, 26, 74, 218, 654, 1946, 5834
Answer: D
2nd term = (1st term) x 3 - 4 = 10 x 3 - 4 = 26.
3rd term = (2nd term) x 3 - 4 = 26 x 3 - 4 = 74.
4th term = (3th term) x 3 - 4 = 74 x 3 - 4 = 218.
5th term = (4th term) x 3 - 4 = 218 x 3 - 4 = 650.
5th term must be 650 instead of 654.
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Find out the wrong number in the given sequence of numbers 56, 72, 90, 110, 132, 150
Answer: D
Each term is a product of two consecutive integers.
\[ 7 \times 8 = 56,\quad 8 \times 9 = 72,\quad 9 \times 10 = 90,\quad 10 \times 11 = 110,\quad 11 \times 12 = 132 \]
The next should be \( 12 \times 13 = 156 \), not 150.
So 150 is the wrong number. Equivalently the differences run 16, 18, 20, 22, 24 - and 132 to 150 is a gap of only 18.
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