In the following question, four options are given, out of which three are alike in a particular way while one is different. Choose the odd one.

185

The correct answer is Option (2) → 185

Logical Analysis:

To find the "odd one out," we look for a mathematical property that three of the numbers share, which the fourth does not. In this case, the relationship is based on divisibility by 23.

• 161: $23 \times 7 = 161$ (Divisible by 23)
• 253: $23 \times 11 = 253$ (Divisible by 23)
• 299: $23 \times 13 = 299$ (Divisible by 23)
• 185: $23 \times 8 = 184$. Therefore, 185 is not divisible by 23.

Alternative Logic:

Another way to view this is through the factors of the numbers:

• $161 = 7 \times 23$
• $253 = 11 \times 23$
• $299 = 13 \times 23$
• $185 = 5 \times 37$

The numbers 161, 253, and 299 are all multiples of the prime number 23, whereas 185 is a multiple of 5 and 37.