Find out the wrong number in the series 3, 7, 15, 39, 63, 127, 255, 511
Answer: C
Each term is double the previous plus one.
\[ 3 \to 7 \to 15 \to 31 \to 63 \to 127 \to 255 \to 511 \]
The fourth term should be \( 15 \times 2 + 1 = 31 \), not 39.
So 39 is wrong. Every term is \( 2^{n} - 1 \), and 39 is not one less than a power of two.
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Find out the wrong number in the series 64, 71, 80, 91, 104, 119, 135, 155
Answer: D
The gaps should be the successive odd numbers.
\[ 64 \xrightarrow{+7} 71 \xrightarrow{+9} 80 \xrightarrow{+11} 91 \xrightarrow{+13} 104 \xrightarrow{+15} 119 \xrightarrow{+17} 136 \xrightarrow{+19} 155 \]
The seventh term should be \( 119 + 17 = 136 \), not 135.
So 135 is wrong - the final 155 confirms it, since \( 136 + 19 = 155 \).
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Find out the wrong number in the series. 15, 16, 34, 105, 424, 2124, 12756
Answer: D
2nd term = (1st term) x 1 + 1 = 15 x 1 + 1 = 16.
3rd term = (2nd term) x 2 + 2 = 16 x 2 + 2 = 34.
4th term = (3th term) x 3 + 3 = 34 x 3 + 3 = 105.
5th term = (4th term) x 4 + 4 = 105 x 4 + 4 = 424
6th term = (5th term) x 5 + 5 = 424 x 5 + 5 = 2125
6th term should 2125 instead of 2124.
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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 series. 2880, 480, 92, 24, 8, 4, 4
Answer: B
The divisor falls by one at each step.
\[ 2880 \div 6 = 480 \quad\checkmark \qquad 480 \div 5 = 96 \quad\text{not } 92 \]
\[ 96 \div 4 = 24 \quad\checkmark \qquad 24 \div 3 = 8 \quad\checkmark \]
\[ 8 \div 2 = 4 \quad\checkmark \qquad 4 \div 1 = 4 \quad\checkmark \]
So 92 is the wrong number; it should be 96.
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Find out the wrong number in the series. 3, 7, 15, 27, 63, 127, 255
Answer: C
Each term is double the previous plus one.
\[ 3 \to 7 \to 15 \to 31 \to 63 \to 127 \to 255 \]
The fourth term should be \( 15 \times 2 + 1 = 31 \), not 27.
So 27 is wrong. Every correct term is \( 2^{n} - 1 \), and 27 is not.
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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: A
Three of the four numbers are prime.
\[ 37,\; 47,\; 67 \;\text{have no divisors other than 1 and themselves} \]
\[ 27 = 3^{3} = 3 \times 9 \]
So 27 does not belong. Its digit sum is 9, so it is divisible by 3 - the quickest test.
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Find the one which does not belong to that group ?
Answer: B
Three of the four numbers are perfect squares.
\[ 16 = 4^{2}, \qquad 36 = 6^{2}, \qquad 64 = 8^{2} \]
\[ 28 = 2^{2} \times 7 \text{, which lies between } 25 \text{ and } 36 \]
So 28 does not belong.
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Find the one which does not belong to that group ?
Answer: D
Three of the four numbers are prime.
\[ 41,\; 43,\; 53 \;\text{are prime} \]
\[ 57 = 3 \times 19 \]
So 57 does not belong. Its digit sum is 12, a multiple of 3 - 57 is a classic "looks prime but isn't" number.
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