Direction: The following question consists of two statements numbered I and II. Decide if data given in the statements are sufficient to answer the question below.

How many students are there in the row?

I. Rohan is ranked 24th from the bottom, and there are more than 40 students in the row.

II. The number of students ranked above Rohan is twice the number of students ranked below him.

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

Answer (Detailed Solution Below)

Option 3 : If the data in both the statements I and II together are necessary to answer the question.

Detailed Solution

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According to the question:

Statement I. Rohan is ranked 24th from the bottom, and there are more than 40 students in the row.

Total number of students = Rohan position from top + Rohan's position from bottom - 1

Total number of students = 24 + Rohan's position from bottom - 1

Here, total number of students cannot be determined. Therefore data in statement I alone is not sufficient to answer the question.

Statement II. The number of students ranked above Rohan is twice the number of students ranked below him.

Number of students ranked above Rohan = 2 x Number of students ranked below Rohan

Here, total number of students cannot be determined. Therefore data in statement II alone is not sufficient to answer the question.

Combining statement I and IIRohan is ranked 24th from the bottom, and there are more than 40 students in the row. The number of students ranked above Rohan is twice the number of students ranked below him.

Number of students below Rohan = 24 - 1 = 23

Number of students below Rohan = Total number of students - 24

(Total number of students - 24) = 2 x 23

Total number of students = 46 + 24 = 70

Here, total number of students is 70, therefore data in both the statements I and II together are necessary to answer the question.

Thus, data in both the statements I and II together are necessary to answer the question.

Hence, "Option 3" is the correct answer.

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