Question

Suppose \[2,1 = 9\,\,4,2 = 18\,\,5,3 = 18\,\,6,3 = 27\]then \[9,4 = \]?

Answer 1

Hint: The question is based on a particular pattern. We can solve the question by analysing the pattern and finding out some common relationship between the terms. Math Patterns are repeating sequences based on rules, and a rule is a predetermined method of calculating or solving an issue.

Complete step-by-step answer:
Mathematics patterns are extremely common and can be found in routine life. For e.g, such patterns can be based on types of shape, different colours, odd-even numbers etc.
There are different tricks to solve patterns. Addition, subtraction, multiplication, division, percentage, factoring and other methods can be used to solve the problem. The key to finding out the answer is applying logic and critical thinking. Common types of mathematics patterns are Arithmetic, Geometric, Fibonacci, Repeating, Growing, Shrinking etc.
Let us proceed to solve the pattern now:
Consider the first two terms:
\[2,1 = 9\] and \[4,2 = 18\]
We have to think about what can lead to a continuing pattern by using different operators. In the given case we can deduct the inverse of given numbers from the number itself to get the solution.
Applying subtraction logic, we can find out that pattern is in the form of-
\[X,Y = XY - YX\]
So, we can conclude that:
\[2,1 = 21 - 12 = 9\]
\[4,2 = 42 - 24 = 18\]
\[5,3 = 53 - 35 = 18\]
\[6,3 = 63 - 36 = 27\]
Therefore,
\[9,4 = 94 - 49 = 45\]
Hence, we can conclude that \[2,1 = 9\,\,4,2 = 18\,\,5,3 = 18\,\,6,3 = 27\]then \[9,4 = 45\]
So, the correct answer is “\[9,4 = 45\]”.

Note: There can be more than one solution to a given pattern as there is no one fixed method or formula to solve the patterns. By trial-and-error method we have to solve the sum. For e.g. considering the first two terms of the sum we can see the pattern can be formed by multiplying the first term with \[4\]and adding the seconding term i.e.
\[X,Y = (X \times 4) + Y\]
\[2,1 = (2 \times 4) + 1 = 9\]
\[4,2 = (4 \times 4) + 2 = 18\]
However, the third term doesn’t fit the pattern formed
\[5,3 = (5 \times 4) + 3 \ne 18\]
So, we cannot use this method. This can only be found out after considering all the information and constructing the pattern by using different methods and tricks.