In a test consisting of 143 questions, any question can be classified as Difficult/Easy or Precise/Long or Quants/Reasoning based. It was found that 20 of the questions are Easy, Precise and Reasoning based and 20 of the questions are Difficult, Precise and Reasoning based, 50 of the difficult questions are either Long or Quant based. 20 questions are Easy, Long and Quants based. In total, 64 questions are Quants based of which one fourth are Precise and Difficult. 10 of the questions are Difficult, Long and Quants based. How many of the questions are Difficult, Long and Reasoning based?Choices:- 20 24 28 36

The problem can be solved by using the principle of inclusion and exclusion.

First, let's find out how many questions are Difficult, Precise and Reasoning based. According to the problem, there are 20 such questions.

Next, we know that 50 of the difficult questions are either Long or Quant based. This means that there are 50 - 20 = 30 questions that are Difficult, Long and not Quant based.

We also know that 20 questions are Easy, Long and Quants based. This means that there are 64 - 20 = 44 questions that are not Easy, Long and are Quants based.

Out of these 44 questions, one fourth are Precise and Difficult. This means that there are 44/4 = 11 questions that are Precise, Difficult and Quants based.

We also know that 10 of the questions are Difficult, Long and Quants based. This means that there are 11 - 10 = 1 question that is Precise, Difficult and not Long based.

Therefore, the number of questions that are Difficult, Long and Reasoning based is 30 - 1 = 29.

However, this is not one of the choices given in the problem. It seems like there might be a mistake in the problem or in the choices given.

The problem can be solved by using the principle of inclusion and exclusion.

First, let's find out the total number of Difficult, Precise, and Reasoning based questions. We know that there are 20 such questions.

Next, we know that there are 20 questions that are Easy, Precise, and Reasoning based.

We also know that there are 50 difficult questions that are either Long or Quant based.

Then, we know that there are 20 questions that are Easy, Long, and Quants based.

We also know that there are 64 questions that are Quants based, of which one fourth are Precise and Difficult. This means that there are 64/4 = 16 questions that are Precise, Difficult, and Quants based.

Finally, we know that there are 10 questions that are Difficult, Long, and Quants based.

Now, we need to find out how many of the questions are Difficult, Long, and Reasoning based.

We can do this by subtracting the number of questions that are Difficult, Precise, and Reasoning based, the number of questions that are Easy, Precise, and Reasoning based, the number of questions that are Easy, Long, and Quants based, and the number of questions that are Precise, Difficult, and Quants based from the total number of questions.

This gives us:

143 - 20 - 20 - 20 - 16 = 67

However, we also need to add back the number of questions that are Difficult, Long, and Quants based, since we have subtracted these twice.

So, the final answer is:

67 + 10 = 77

However, this number is not in the choices given. There seems to be a mistake in the problem or the choices given.