Evaluate: $6:35::11:x$?
A) 120
B) 121
C) 115
D) 122

Hint:
Here, the question is based on the number analogy and we have to find the fourth term. Number Analogy is the identification and pointing out relationships, similarities or differences, and dissimilarities in a series or between groups of numbers. First, we will find the relation between the first two terms. Then by using the same relation we will find the fourth term.

Complete step by step solution:
We will find the relation by which the first term is related with the second term. Also, the relation is the same between the third term and the fourth term.
Now, first we will consider 6 and 35.
We know that the square of 6 is 36 and 35 is 1 less than 36. So we can say that the second term is the difference of 1 from the square of the first term.
So, we get \[{6^2} - 1 = 35\].
We have found out the relation between the first and second term. Thus, we will find the fourth term using the same relation. We find the square of 11 and subtract 1 from it to get the fourth number.
\[{11^2} - 1 = 121 - 1 = 120\]
So, the fourth number is 120 and the analogy will be \[6:35::11:120\].

Hence, option A is the correct answer.

Note:
Understanding Number Analogy is a crucial step in solving questions on reasoning ability. We shall see how to identify and use this concept to solve some questions. We can say that the number analogy based questions may be of two types, which includes:
1) Find a missing number from a given analogy.
2) Finding a set of numbers that are related to the same rule as the one given.
In this type, we shall be provided with one pair of numbers and the second pair will be incomplete. We are supposed to find a relation between the first pair of numbers and then choose the correct alternative to complete the second pair.