In a class of 20 students, the average weight of the students is 40 kg

In a class of 20 students, the average weight of the students is 40 kg and the range is 10. However, the average weight increases to 41 when a new student joins the class in the new session.

Based on the above information, select for Maximum range the maximum possible range of the weight of the new class and for Minimum range the minimum possible range of the weight of the new class.

Original Class Total Weight = 20 × 40 = 800

New Class Total Weight = 21 x 41 = 861

Weight of New Student = 861 - 800 = 61

Maximum range

To determine the maximum possible range of weights in the new class, find the lowest possible weight in the original class.

The lowest possible weight will occur when 19 students are all at the same weight just above 40 and the 20th student's weight is 10 lower.

We can calculate these two weights as follows:

19x + x - 10 = 800

20x = 810

x = 40.5

x - 10 = 30.5

So, the maximum range is 61 - 30.5 = 30.5.

Minimum range

To determine the minimum possible range of weights in the new class, find the greatest possible weight in the original class.

The greatest possible weight will occur when 19 students are all at the same weight just below 40 and the 20th student's weigth is 10 higher.

We can calculate these two weights as follows:

19y + y + 10 = 800

20y = 790

y = 39.5

So, the minimum range is 61 - 39.5 = 21.5.

Correct answer:

Alternative Approach - Use the Answer Choices

31

There's no way for the maximum new range to be 31. After all, in that case, the lowest weight in the original class would be 61 - 31 = 30, and the highest would be 30 + 10 = 40. We can't get an average of 40 with a high value of 40 and other values below 40. So, the maximum new range must be below 31.

10.5

21

Similarly, there's no way for the minimum to be 21. After all, in that case, the lowest weight in the original class would be 61 - 21 = 40, and the highest would be 40 + 10 = 50. We can't get an average of 40 with a low value of 40 and other values above 40. So, the minimum must be above 21. Thus, we are left with 21.5, 30, and 30.5 as possible maximum and minimum values.

30.5

Try 30.5 as the maximum range.

If 30.5 is the new range, then the lowest value is 61 - 30.5 = 30.5.

We can make one value 30.5 and see whether we get to a total of 800 with 30.5 + 10 = 40.5 as the upper value in the original range.

30.5 + (19 × 40.5) = 800

So, 30.5 works as the lowest possible value, and 30.5 works as the maximum range.

21.5

Now, try 21.5 as the minimum range.

If 21.5 is the new range, then the original lowest weight was 61 - 21.5 = 39.5.

Test to see whether 39.5 works as the lowest original weight.

(39.5 × 19) + 49.5 = 800

So, 39.5 works as the lowest original weight, and 21.5 works as the minimum new range.

Correct answer: