Multiple choice

Passage

Directions: The following question is accompanied by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient/necessary to answer the question.

What are the average marks of all the students of the class? I. Average marks of the boys of the class are 55 and the average marks of the girls of the class are 70. II. Ratio of the number of boys to the total number of students in the class is 3 : 5. III. Number of boys in the class is 5 more than the number of girls in the class and the average marks of boys is 15 less than the average marks of girls.

  1. Only I and II

  2. Only I and III

  3. Only I and either II or III

  4. Only I

  5. All three statements
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A Correct answer
Explanation

Let B be number of boys, G be girls. Avg = (55B + 70G) / (B+G). Statement I gives avg marks. Statement II gives B/(B+G) = 3/5, so B = 3x, G = 2x. Avg = (55*3x + 70*2x) / 5x = (165+140)/5 = 61. Both I and II are sufficient. Statement III gives B = G + 5 and AvgB = AvgG - 15. This is not enough to find the total average without knowing the total number of students.

AI explanation

Using statement I, let the number of boys be B and girls be G, so the total marks are 55B + 70G. To find the average, we need the ratio of B to G. Statement II provides the ratio of boys to total students as 3 : 5, meaning the ratio of boys to girls is 3 : 2, which is sufficient to solve for the overall average. Statement III gives relative differences but lacks the exact student count needed for the average. Therefore, only statements I and II are sufficient.

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