Multiple choice

Directions : Answer the question independently. In a class there were 10 students and the average weight of the students in the class was 54.5 kg. Five students weighing 89 kg, 46 kg, 82 kg, 93 kg and 60 kg joined the class one by one (not necessarily in that order). After the addition of every student, the average weight (in kg) of the class was an integer. If the weight of the first student that joined in was 82 kg, then what was the average weight of the class after the 4th student joined in?

  1. 60 kg

  2. 59 kg

  3. 61 kg

  4. 63 kg

  5. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 10 students, avg 54.5, total 545. 1st added (82): 11 students, total 627, avg 57. 2nd added (93): 12 students, total 720, avg 60. 3rd added (89): 13 students, total 809, avg 62.23 (not integer). The sequence must be ordered to keep averages as integers. Testing the sequence leads to the 4th student resulting in an average of 59.

AI explanation

Using the properties of modular arithmetic to keep the running total's remainder manageable, start with the initial sum of 545 kg for 10 students. Adding the first student weighing 82 kg makes the sum 627 kg; the average is 627 / 11, which leaves a remainder of 0, so the integer average is 57 kg. Adding the second student requires the new sum to be divisible by 12; testing the remaining weights (89, 46, 93, 60), only 93 works, making the new sum 720 kg and the average 60 kg. Adding the third student requires divisibility by 13, and only 46 works, making the sum 766 kg and the average 59 kg. Adding the fourth student requires divisibility by 14, and only 60 works, making the sum 826 kg and the new average exactly 59 kg.

Keep practicing — related questions