Multiple choice

Directions: The following problem consists of a question followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. 11 people appeared for examinations A and B each. The total marks scored by the people who appeared for examination A were 366. What is the total of the marks obtained by the people who appeared for examination B? (I) Average marks scored by the top five performers who appeared for examination B were 4 more than the average marks scored by the top five performers who appeared for examination A. (II) Total marks of the bottom six performers who appeared for examination B were 7 less than the total marks of the bottom six performers who appeared for examination A.

  1. The question can be answered by using statement I alone but cannot be answered using the other statement alone.

  2. The question can be answered by using statement II alone but cannot be answered using the other statement alone.

  3. The question can be answered by using either of the statements alone.

  4. The question can be answered using both of the statements together, but cannot be answered using either of the statements alone.

  5. The question cannot be answered even by using both the statements together.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the average of the top 5, and Statement II gives the total of the bottom 6. Neither alone provides the total for all 11 people in exam B, as we do not know the marks of the middle person or the specific distribution. Together, we can relate the total marks of B to A, but the problem is missing the total marks for exam B's top 5 or bottom 6 specifically relative to A's total. However, standard logic for these types of problems usually requires both to establish a relationship.

AI explanation

Statement I provides a relationship between the top five performers of both exams, but lacks enough data to find the total marks for exam B. Statement II provides the total marks of the bottom six performers for exam B relative to exam A, which alone is also insufficient. However, using both statements together allows you to calculate the top five and bottom six marks for exam B, which covers all 11 people since 5 plus 6 equals 11. Therefore, both statements together are necessary and sufficient to answer the question.

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