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  1. The data either the statement I alone or statement II alone are sufficient to answer the question
  2. The data even in the both statements I and II together are not sufficient to answer the question.
  3. The data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question.
  4. The data I the both the statement I and II together are necessary to answer the question
  5. The data in statement I alone are sufficient to answer question while the data in statement II alone are not sufficient to answer the question.
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Option 4 : The data I the both the statement I and II together are necessary to answer the question

We use propositional logic to solve this.

Statement I: If Ram studies hard for exam, his father will gift him a laptop.

Let s: Ram studies hard for exam.

g: Ram gets a laptop.

Given that s ⇒ g.

Thus, from statement I we cannot conclude whether Ram gets a laptop or not. Thus nothing can be said whether Ram had worked hard or not.

Statement II: Ram did not get a laptop.

Nothing is said about the hard work.

Combining both statements we get,

Therefore, we can conclude that Ram did not study hard. So, both statements together are necessary to determine the given conclusion.

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