Odd Man Out & Series Questions and Answers

Answer: B

Each number is a perfect square.

\[ 16 = 4^{2},\; 25 = 5^{2},\; 36 = 6^{2},\; 144 = 12^{2},\; 196 = 14^{2},\; 225 = 15^{2} \]

\[ 72 \text{ lies between } 64 \text{ and } 81 \text{ and is not a square} \]

So 72 is the odd man out.

Answer: C

Written as position numbers, three of the groups move the same way:

• K(11), M(13), N(14), L(12): \( +2,\; +1,\; -2 \)
• P(16), R(18), S(19), Q(17): \( +2,\; +1,\; -2 \)
• J(10), L(12), M(13), K(11): \( +2,\; +1,\; -2 \)
• V(22), W(23), Y(25), Z(26): \( +1,\; +2,\; +1 \)

VWYZ is the exception. The other three also share a neat property: the fourth letter sits immediately after the first, which VWYZ does not.

Answer: D

The series is the squares counting down from 14.

\[ 14^{2},\; 13^{2},\; 12^{2},\; 11^{2},\; 10^{2},\; 9^{2},\; 8^{2} = 196,\; 169,\; 144,\; 121,\; 100,\; 81,\; 64 \]

The sixth term should be \( 9^{2} = 81 \), not 80.

So 80 is the wrong number - off by one from a perfect square.

Answer: C

Three of the four are state capitals.

• Thiruvananthapuram - capital of Kerala
• Hyderabad - capital of Telangana
• Bangalore - capital of Karnataka
• Calicut (Kozhikode) - a city in Kerala, but not a capital

So Calicut does not belong. Note that Kerala appears twice in the list, which is the hint that being a capital, not the state, is the shared property.

Answer: A

Three of the four are multiples of 9.

\[ 27 = 9 \times 3, \quad 36 = 9 \times 4, \quad 45 = 9 \times 5 \]

\[ 30 = 9 \times 3 + 3 \]

So 30 does not belong. Digit sums make it immediate: 9, 9 and 9 against 3.

Answer: D

Asteroids, stars and planets are natural bodies found in space.

A rocket is man-made - a vehicle built to travel through space, not an object that occurs there.

So Rocket does not belong.

Answer: D

In each group the number should be the square of the letter's position.

• B4: \( 2^{2} = 4 \) ✓
• D16: \( 4^{2} = 16 \) ✓
• E25: \( 5^{2} = 25 \) ✓
• F35: \( 6^{2} = 36 \neq 35 \) ✗

So F35 does not belong - it is one short of the square it should be.

Answer: B

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

• 331: \( 3 \times 1 = 3 \) ✓
• 482: \( 4 \times 2 = 8 \) ✓
• 551: \( 5 \times 1 = 5 \) ✓
• 263: \( 2 \times 3 = 6 \) ✓
• 362: \( 3 \times 2 = 6 \) ✓
• 284: \( 2 \times 4 = 8 \) ✓
• 383: \( 3 \times 3 = 9 \neq 8 \) ✗

So 383 is the odd one out. Trying sums first is the natural instinct, and it fails on the very first number - the signal to try products instead.

Answer: C

Each term is a product of two consecutive integers.

\[ 1 \times 2 = 2,\quad 2 \times 3 = 6,\quad 3 \times 4 = 12,\quad 4 \times 5 = 20,\quad 5 \times 6 = 30 \]

\[ 6 \times 7 = 42,\quad 7 \times 8 = 56,\quad 8 \times 9 = \mathbf{72} \]

Equivalently the differences are the even numbers 4, 6, 8, 10, 12, 14, so the next gap is 16 and \( 56 + 16 = 72 \).

Answer: B

Two series are interleaved.

\[ \text{positions 1, 3, 5, 7, 9: } 8,\; 11,\; 14,\; 17,\; \mathbf{20} \quad (+3) \]

\[ \text{positions 2, 4, 6, 8: } 7,\; 12,\; 17,\; 22 \quad (+5) \]

The ninth term belongs to the first series:

\[ 17 + 3 = 20 \]

Continuing the second series instead would give 27, which is offered as the first option.