Each question is followed by two statements I and II 1 If the question can be answered by any one of...........

Math and Mental Ability Data Sufficiency

Each question is followed by two statements, I and II.

1.If the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.

2.If the question can be answered by using either statement alone.

3.If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

4.If the question cannot be answered even by using both statements together.

How many people are watching TV programme?

I. Number of people watching TV programme Q is 1,000 and number of people watching both the programmes p and q, is 100.

II.Number of people watching either p and q or both is 1,500.

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Explanation:

- Statement I: We know 1,000 people watch program Q, and 100 people watch both P and Q. However, this doesn't tell us how many watch only P or only Q.

- Statement II: We know 1,500 people watch either P or Q or both. This by itself isn't enough to determine the total watching any specific program without overlap information.

- Combining Statements I and II: Together, they provide enough information, since we can use the principle of inclusion-exclusion to find how many people watch any program:

- Let A be the number of people watching P.

- Given: \(A + 1000 - 100 = 1500\).

- Solving gives A = 600.

- Total people watching any program = \(A + 1000 - 100 = 1500\).

Thus, the correct option is:

- Option 3: 3. Both statements together are needed to answer the question.