Question

Which one of the following numbers is odd one out?
31541 42651 53791 64871 75981

• A. 31541
• B. 42651
• C. 53791
• D. 75981

Hint:

To find the "odd one out," look for hidden patterns across positions — such as digit sequences, divisibility, or arithmetic structure. Consistency across all but one often reveals the answer.

Answer 1

The Correct Option is C

Step 1: Examine the units digit of each number.

Let’s write down the numbers and observe:
\[ \begin{aligned} 31541 &\Rightarrow \text{Sum of digits: } 3+1+5+4+1 = 14 \\ 42651 &\Rightarrow \text{Sum of digits: } 4+2+6+5+1 = 18 \\ 53791 &\Rightarrow \text{Sum of digits: } 5+3+7+9+1 = 25 \\ 64871 &\Rightarrow \text{Sum of digits: } 6+4+8+7+1 = 26 \\ 75981 &\Rightarrow \text{Sum of digits: } 7+5+9+8+1 = 30 \\ \end{aligned} \]

Step 2: Check divisibility by 9.

A number is divisible by 9 if the sum of its digits is divisible by 9.
\[ \begin{aligned} 14 &\Rightarrow \text{Not divisible by 9} \\ 18 &\Rightarrow \textbf{Divisible by 9} \\ 25 &\Rightarrow \text{Not divisible by 9} \\ 26 &\Rightarrow \text{Not divisible by 9} \\ 30 &\Rightarrow \textbf{Divisible by 3 and 9} \\ \end{aligned} \]

Step 3: Check the structure of the numbers.

Looking closely:
All numbers except 53791 follow the pattern where the digits increase in an arithmetic sequence:
\[ \begin{aligned} 31541 &\Rightarrow 3,1,5,4,1 \\ 42651 &\Rightarrow 4,2,6,5,1 \\ 53791 &\Rightarrow 5,3,7,9,1 \quad \textbf{(Notice irregular jump from 7 to 9)} \\ 64871 &\Rightarrow 6,4,8,7,1 \\ 75981 &\Rightarrow 7,5,9,8,1 \\ \end{aligned} \]

Step 4: Observe positional symmetry.

Every number except 53791 has the structure:
First digit increasing from 3 to 7.
Second digit: decreases by 1.
Third digit: 5,6,7,8,9 (in sequence).
Fourth digit: always one less than third digit.
Fifth digit: always 1.

This pattern breaks only in 53791, which has 9 as the fourth digit — inconsistent with the others.