Solution:
In this context, the appropriate preposition to use is "by".
The sentence "You can obtain the answer by adding the date of birth to this figure." suggests that the answer can be obtained through the action of adding the date of birth to the given figure.
The preposition "by" is commonly used to indicate the method or means by which an action is performed. In this case, the action of obtaining the answer is performed by adding the date of birth to the given figure.
436. Two cars collided . . . . . . . . each other near the school.
Solution:
We use 'inside' when we refer to the inner part of something. Here, we refer to the inner part of the 'nest'. Hence 'inside' makes the sentence meaningful.
439. They have been studying . . . . . . . . three hours todays.
Solution:
Preposition of reason indicates some relationship of a noun or pronoun with regard to some reason, cause or purpose. These prepositions include to, for, with the view to, in order to, so as to, because of, due to, for the purpose of, etc.
441. Hamza was standing . . . . . . . . the front of the queue.