Question

In a certain code 123 is coded as 14, 234 as 29 then what is the code for 531?
(a) 32
(b) 34
(c) 35
(d) 37

Answer 1

Hint: Firstly, we should know the pattern which the question is following to get a particular output. The question is following the pattern of the sum of squares of the individual digits of the given number. To get the final answer for each number, the calculated squared terms are added.

Complete step by step solution:
In this question, we are supposed to find the sum of the individual squares of the digits of the number to get the particular code of the number.
Suppose we have number as 12 and we need to find the code for the same by above mentioned pattern:
$\begin{align}
  & {{1}^{2}}+{{2}^{2}} \\
 & \Rightarrow 1+4 \\
 & \Rightarrow 5 \\
\end{align}$
So, to find the code for the number 123, we proceed in the following way and find the appropriate sum of squares of the digits of the number:
$\begin{align}
  & {{1}^{2}}+{{2}^{2}}+{{3}^{2}} \\
 & \Rightarrow 1+4+9 \\
 & \Rightarrow 14 \\
\end{align}$
So, the code found by using the above mentioned pattern for the number 123 is 14.
Again finding the code for the number 234, we proceed in the same way as done above:
$\begin{align}
  & {{2}^{2}}+{{3}^{2}}+{{4}^{2}} \\
 & \Rightarrow 4+9+16 \\
 & \Rightarrow 29 \\
\end{align}$
So, the code found by using the above mentioned pattern for the number 234 is 29.
It is evident from the two codes answer matching the given pattern that the above explained pattern is used in this question.
Now finding the code for the number 531, we proceed in the same way as done above:
$\begin{align}
  & {{5}^{2}}+{{3}^{2}}+{{1}^{2}} \\
 & \Rightarrow 25+9+1 \\
 & \Rightarrow 35 \\
\end{align}$
So, the code found by using the above mentioned pattern for the number 531 is 35.
Hence, option c is correct.

Note: The mistake while calculating the square of the number is that if we are finding the square of 3 as ${{3}^{2}}$ which is actually equal to 9 but while solving, you may consider ${{3}^{2}}$ as 6 which is the multiplication of the 3 and 2. So, keep the check on these mistakes and avoid these kind of errors as power denotes the multiplication of the number to itself the number of times power is i.e. ${{3}^{2}}=3\times 3$ which is 9. If we take 6 instead of 9, we might get 25+6+1=32 and mark option (a) as the correct answer.