Multiple choice

Passage

Directions: Read the following information and answer the question that follows: The average weight of 25 students of class A is Z kg. The average weight of 35 students of class B is (Z + 8) kg, and the average weight of 20 students of class C is (Z + 5)kg. The average weight of students of class A and B is 55 kg.

The average weight of students of classes A, B and C is approximate what percent of average weight of students of Class A and C?

  1. 95%

  2. 105%

  3. 115%

  4. 85%

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average of A and B is 55. (25Z + 35(Z+8))/60 = 55 => 60Z + 280 = 3300 => 60Z = 3020 => Z = 50.33. Average A, B, C = (25*50.33 + 35*58.33 + 20*55.33) / 80 = (1258.25 + 2041.55 + 1106.6) / 80 = 4406.4 / 80 = 55.08. Average A and C = (25*50.33 + 20*55.33) / 45 = (1258.25 + 1106.6) / 45 = 52.55. Ratio = 55.08 / 52.55 = 1.048, which is approximately 105%.

AI explanation

From the combined average of class A and B, calculate Z as 25Z plus 35 times Z plus 8 equals 60 times 55, yielding Z equal to 45. The total weight for class A is 1125, class B is 1855, and class C is 1000. The average weight of all three classes is their total sum of 3980 divided by 80 students, which is 49.75 kg. The average weight of classes A and C is their total sum of 2125 divided by 45 students, which is approximately 47.22 kg. Finding the percentage of 49.75 to 47.22 shows it is approximately 105 percent.

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