Odd Man Out & Series Questions and Answers

Answer: B

The missing number is 28.

Look at the differences between consecutive terms:

\[ \begin{aligned} 6 - 1 &= 5,\quad 15 - 6 = 9 \\ 28 - 15 &= 13,\quad 45 - 28 = 17 \\ 66 - 45 &= 21,\quad 91 - 66 = 25 \end{aligned} \]

The differences increase by 4 each time (5, 9, 13, 17, 21, 25), so the missing term is 15 + 13 = 28, and the next difference, 45 - 28 = 17, confirms it. (These are the hexagonal numbers, n(2n - 1).) 36, 32 and 25 break the pattern of differences.

Answer: B

The missing numbers are 13, 4.

Look at the differences between successive terms:

12 → 14 → 17 → 13 → 8 → 14 → 21: +2, +3, −4, −5, +6, +7.

The size of the step rises by one each time, and the sign follows the pattern two additions, two subtractions. So the next two steps are −8 and −9:

\[ 21 - 8 = 13, \qquad 13 - 9 = 4 \]

Adding instead of subtracting, or using a constant step, gives the other pairs.

Answer: A

The sum is 68.

The pattern is the sequence of consecutive prime numbers: 13, 17, 19, 23, 29. The next two primes are 31 and 37, since 30, 32, 33, 34, 35 and 36 all have factors other than 1 and themselves.

\[ 31 + 37 = 68 \]

A common slip is to look for a constant difference. The gaps here are 4, 2, 4, 6, which follow no fixed rule, a clue that the numbers are primes. Taking 31 and then 41, or 37 and 41, gives sums such as 72 or 78, none of which are among the options.

Answer: C

The sum of the next two numbers is 1209.

Each term is three times the previous term plus a number that goes up by 1 each time:

\[ \begin{aligned} 3 \times 3 + 1 &= 10 \\ 10 \times 3 + 2 &= 32 \\ 32 \times 3 + 3 &= 99 \\ 99 \times 3 + 4 &= 301 \\ 301 \times 3 + 5 &= 908 \end{aligned} \]

So the next two numbers are 301 and 908, and \(301 + 908 = 1209\).

Spotting only the 'multiply by 3' part and missing the growing addition is the usual trap; the next terms must keep the rule, so 302 or 300 in place of 301 would break it.

Answer: C

The missing number is 94.

Look at the differences between consecutive terms:

\[ \begin{aligned} 325 - 259 &= 66, \quad 259 - 204 = 55 \\ 204 - 160 &= 44, \quad 160 - 127 = 33 \\ 127 - 105 &= 22 \end{aligned} \]

The differences fall by 11 each time, so the next difference is 11 and the next term is \(105 - 11 = 94\).

96, 98 and 90 would need differences of 9, 7 and 15, which break the pattern.

Answer: D

The next two terms are 216 and 343.

The pattern is the cubes of the natural numbers:

\[ 1^{3}, 2^{3}, 3^{3}, 4^{3}, 5^{3} = 1, 8, 27, 64, 125 \]

\[ 6^{3} = 216, \quad 7^{3} = 343 \]

256 is \(4^{4}\) or \(16^{2}\) and 289 is \(17^{2}\), so the options containing them do not continue the pattern of cubes.

Answer: A

The missing number is 61.

The sequence lists the consecutive prime numbers: 43, 47, 53, 59, 61, 67, 71, 73. The prime between 59 and 67 is 61.

60 and 65 are not prime (60 is even, 65 = 5 × 13), and 63 = 7 × 9 is not prime either.

Answer: D

Three of the four are anagrams of cereals.

• Hewat → Wheat
• Ceri → Rice
• Rowaj → Jowar

Cereals is the name of the whole class, not a scrambled member of it, so it does not belong.

Answer: A

Each term is roughly double the previous, with the correction alternating between \( +1 \) and \( -1 \).

\[ 16 \times 2 + 1 = 33 \]

\[ 33 \times 2 - 1 = 65 \]

\[ 65 \times 2 + 1 = 131 \]

\[ 131 \times 2 - 1 = 261 \]

\[ 261 \times 2 + 1 = \mathbf{523} \]

Doubling alone would give 522, so the alternating sign is what separates 523 from the 521 on offer.

Answer: B

Three of the four letters are vowels.

\[ A,\; E,\; I \;\text{are vowels}; \qquad R \;\text{is a consonant} \]

So R does not belong.