Question

If $$398 = 964$$, $$118 = 164$$, $$356 = 936$$, $$423 = ?$$

Answer 1

Hint: Here the given question is generally asked in the aptitude test of the public service exam. We need to find the missing number in the given pattern of numbers. For this, first we need to observe and analyze the number of given questions and compare the same observation in all the numbers then apply that observation in the last pattern to get the required solution.

Complete step by step solution:
Consider the given question:
$$398 = 964$$, $$118 = 164$$, $$356 = 936$$, $$423 = ?$$.
We need to find the number of the last pattern.
Now observe each pattern in the given question.
Let’s observe the first term of the pattern i.e., $$398 = 964$$.
Square the first digit of LHS that is $${3^2} = 9$$ and then square the third digit of LHS $${8^2} = 64$$, so on combining the both numbers we get a RHS 964.
Observe the second term of the pattern $$118 = 164$$.
Square the first digit of LHS that is $${1^2} = 1$$ and then square the third digit of LHS $${8^2} = 64$$, so on combining the both numbers we get a RHS 164.
Similarly, Observe the second term of the pattern $$356 = 936$$.
Square the first digit of LHS that is $${3^2} = 9$$ and then square the third digit of LHS $${6^2} = 36$$, so on combining the both numbers we get a RHS 936.
Now, consider the number $$423$$.
Square the first digit of LHS that is $${4^2} = 16$$ and then square the third digit of LHS $${3^2} = 9$$, so on combining the both numbers we will get a RHS 169.
Therefore, The complete pattern is:
$$398 = 964$$, $$118 = 164$$, $$356 = 936$$, $$423 = 169$$.
So, the correct answer is “169”.

Note: On Solving a aptitude type of questions, student must observe carefully the each and every number of whole pattern and analyze it may be square number, cube number, successor or predecessor etc.. and compare the same observation on whole pattern and apply it for the required number.