Question

Find the Odd one among: \[23,13,34,25,56,51\]
A.\[23\]
B.\[13\]
C.\[34\]
D.\[51\]

Answer 1

Hint: One by one check for the series. What is common in the series and which pattern is being followed. Add the squares of the digits of the numbers which is resulting in the second number for the first two patterns. Where this pattern breaks, there we get the answer.

Complete step-by-step answer:
We are given the series \[23,13,34,25,56,51\].
There is no commonality in the series like prime no.s or multiples of any numbers till now.
Let’s check for which pattern it is following.
Add the digits of the numbers, do we get the pattern or not:
 \[
  23 = 2 + 3 = 5 \\
  13 = 1 + 3 = 4 \\
  34 = 3 + 4 = 7 \\
  25 = 2 + 5 = 7 \\
  56 = 5 + 6 = 11 \\
  51 = 5 + 1 = 6 \;
 \]
We can see that no pattern is being followed.
Let’s check for some other results like Adding of the squares of the digits of the numbers and what pattern is being followed here:
\[
  23 = {2^2} + {3^2} = 4 + 9 = 13 \\
  13 = {1^2} + {3^2} = 1 + 9 = 10 \\
  34 = {3^2} + {4^2} = 9 + 16 = 25 \\
  25 = {2^2} + {5^2} = 4 + 25 = 29 \\
  56 = {5^2} + {6^2} = 25 + 36 = 61 \\
  51 = {5^2} + {1^2} = 25 + 1 = 26 \;
 \]
 From this pattern we can clearly see that the sum of squares of the digits of first number is the second number of the series and the pattern we obtained is:
\[
  23 = {2^2} + {3^2} = 4 + 9 = 13 \\
  13 \\
  34 = {3^2} + {4^2} = 9 + 16 = 25 \\
  25 \\
  56 = {5^2} + {6^2} = 25 + 36 = 61 \\
  51 \;
 \]
So, according to this \[51\]should be the odd one out of the series because by following the pattern we obtained \[61\] as the next value after \[56\].
Therefore, \[51\] is the odd one out of the series \[23,13,34,25,56,51\].
Hence, Option D that is \[51\] is correct for the series given.
So, the correct answer is “Option D”.

Note: Always recheck the patterns before coming to a conclusion.
There can be an error in recognising the pattern of the series like most of the terms of the series are looking like prime numbers so don’t get confused.