Multiple choice

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Quantity I: The average mark of the class when in a class of 60 students, 23 are girls, the average mark of boys is 45, and the average mark of girls is 52 Quantity II: The average mark of the class when in a class of 40 students, 15 are boys, the average mark of boys is 60, and the average mark of girls is 40

  1. Quantity I < Quantity II

  2. Quantity I > Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or the relationship cannot be established from the information given.
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B Correct answer
Explanation

Quantity I: (23*52 + 37*45)/60 = (1196 + 1665)/60 = 2861/60 = 47.68. Quantity II: (25*40 + 15*60)/40 = (1000 + 900)/40 = 1900/40 = 47.5. Since 47.68 > 47.5, Quantity I > Quantity II.

AI explanation

Using the weighted average formula, Quantity I is calculated as 23 times 52 plus 37 times 45, all divided by 60, which equals 47.68. Quantity II is calculated as 15 times 60 plus 25 times 40, all divided by 40, which equals 47.5. Comparing the two results, 47.68 is greater than 47.5, so Quantity I > Quantity II.

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