Odd Man Out & Series Questions and Answers

Answer: A

In each number, the middle digit is the difference of the outer two.

• 835: \( 8 - 5 = 3 \) ✓
• 734: \( 7 - 4 = 3 \) ✓
• 642: \( 6 - 2 = 4 \) ✓
• 853: \( 8 - 3 = 5 \) ✓
• 981: \( 9 - 1 = 8 \) ✓
• 532: \( 5 - 2 = 3 \) ✓
• 751: \( 7 - 1 = 6 \neq 5 \) ✗

So 751 is the odd one out.

Answer: B

The series is the factorials.

\[ 0! = 1,\; 1! = 1,\; 2! = 2,\; 3! = 6,\; 4! = 24,\; 5! = 120,\; 6! = 720 \]

The sixth term should be \( 5! = 120 \), not 96.

So 96 is wrong. Equivalently each term is the previous multiplied by its position: \( 24 \times 5 = 120 \), and \( 120 \times 6 = 720 \) closes the series correctly.

Answer: D

Go on subtracting 24, 21, 18, 15, 12, 9 from the numbers to get the next number.

190 - 24 = 166
166 - 21 = 145
145 - 18 = 127 [Here, 128 is placed instead of 127]
127 - 15 = 112
112 - 12 = 100 ... and so on.

Therefore, 128 is wrong.

Answer: D

The multiplier alternates between 2 and 3, with 1 added each time.

\[ 1 \times 2 + 1 = 3 \quad\checkmark \qquad 3 \times 3 + 1 = 10 \quad\checkmark \]

\[ 10 \times 2 + 1 = 21 \quad\checkmark \qquad 21 \times 3 + 1 = 64 \quad\checkmark \]

\[ 64 \times 2 + 1 = 129 \quad\checkmark \qquad 129 \times 3 + 1 = 388 \quad\text{not } 356 \]

So 356 is wrong. The final term settles it: \( 388 \times 2 + 1 = 777 \).

Answer: B

In each of the groups ABB, CCCDDDD, BBCCC and DDDDEEEEE, only two letters of the alphabet are used and each letter is written as many times as its place value in the alphabet.

This pattern is not followed in the group BCC.

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 \( 136 + 19 = 155 \).

Answer: D

Convert the letters to their positions and look at the steps between them:

• P(16) → M(13) → S(19): \( -3,\; +6 \)
• R(18) → O(15) → U(21): \( -3,\; +6 \)
• G(7) → D(4) → J(10): \( -3,\; +6 \)
• K(11) → I(9) → M(13): \( -2,\; +4 \)

Three groups step back three and then forward six; KIM steps back two and forward four, so it is the odd one. To fit the rule it would have to be KHN.

Answer: B

A museum, an exhibition and a botanical park are places where things are put on display for people to look at.

An auction is an event at which things are sold to the highest bidder; the display is incidental to the sale.

So Auction does not belong.

Answer: C

Each group of five should alternate forward four and back two:

• Y(25), C(3), A(1), E(5), C(3): \( +4,\; -2,\; +4,\; -2 \)
• K(11), O(15), M(13), Q(17), O(15): \( +4,\; -2,\; +4,\; -2 \)
• G(7), K(11), I(9), M(13), K(11): \( +4,\; -2,\; +4,\; -2 \)
• P(16), T(20), R(18), U(21), T(20): \( +4,\; -2,\; +3,\; -1 \)

PTRUT breaks the rhythm at the third step, taking three instead of four. PTRVT would fit. As with YCAEC, the alphabet is taken to wrap round from Z to A.

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.