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

Question

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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.

Bunuel · Accepted Answer

Official Solution: • The average weight of 20 students being 40 kg implies their total weight is 20 * 40 = 800 kg. • After adding a new student, the average weight increasing to 41 kg implies the total weight became 21 * 41 = 861 kg. • Thus, the weight of the new student is 861 - 800 = 61 kg. We also know that the range of weights for the 20 students was 10 kg. To maximize the new range, we need to minimize the weight of the lightest student in the class. This can be achieved by assuming one student weighs x kg, and the remaining 19 students each weigh x + 10 kg. We get x + 19(x + 10) = 800 , which gives x = 30.5 . Therefore, the maximum possible range is 61 - 30.5 = 30.5. To minimize the new range, we need to maximize the weight of the lightest student in the class. This can be achieved by assuming 19 students each weigh x kg, and the remaining student weighs x + 10 kg. We get 19x + (x + 10) = 800 , which gives to x = 39.5 . Therefore, the minimum possible range is 61 - 39.5 = 21.5. Correct answer: Maximum range "30.5" Minimum range "21.5" GMAT-Club-Forum-btw2gbyu.png

Kinshook · Answer

Given:  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.

Asked:  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.

Total weight of 20 students = 20*40 = 800
Let the weight of 21st student = x 
800 + x = 21*41 = 861
x = 61 kg

For 20 students: - 
Range = 10
Average = 40
2 extreme situations exist.
1 student weighs 30.5 kgs and other 19 weigh 40.5 kgs.
1 student weights 49.5 kgs and other 19 weigh 39.5 kgs

After adding student with weight 61 kgs in these extreme situations.
1 student weighs 30.5 kgs and other 19 weigh 40.5 kgs and added student weighs 61 kgs. : Range = 61-30.5 = 30.5 kgs
1 student weights 49.5 kgs and other 19 weigh 39.5 kgs and added student weights 61 kgs. : Range = 61 - 39.5 = 21.5 kgs

Minimum range = 21.5 kgs
Maximum range = 30.5 kgs

Schinchan_bh · Answer

Sum of weight of 20 kids =800kg
Sum of weight of 21 kids =861kg
1 kid=61kg
Let's maximize the range how can we do so:
assume the lowest number is x and the other 19 numbers are x+10 as given for the first 20 kids:
This will give us 
20x+190=800
x=30.5
So the max range is 61-30.5=30.5
Let's minimize the ranges now:
Assume the highest range as x+10 and lowest 19 numbers as x:
20x+10=800
x=39.5
so the gap is 61-39.5=21.5 
Max is 30.5
Min is 21.5

brp616 · Answer

Timed out of the error log for this unfortunately (doing it at work

) but I think the answers are minimum: 21.5 and maximum: 31.5 First, wanted to find the weight of the new student. If we had average of 40 for 20 students, we have 800 total kg. adding 1 student and getting average to 41kg, we need to do 41 * 21 = 861... so our new student is 61 kg! So from here we need to get min and max possible values when average is 40 and the range is 10. The scenarios are as follows: min: 19 students are as close to possible to the mean on the low end then we have 1 student on the high end of the range where we still average 40 -> 800 (total weight) - 20 x (min average) - 10 = 790 - 20x -> 790/20 = 39.5... and indeed, if we have 19 students at 39.5 then one at 49.5 we can distribute 19 .5s to each student from the top weight so they equal 40 each and that heaviest student still has 40 leftover. So our high end is 49.5 and 61 - 49.1 = 21.5 max: flip it, 19 students are close to the mean on the high end then we have a low outlier -> 800 - 20x + 10 = 810 - 20x -> x = 40.5 - so we know 19 students are 40.5, then we have 1 student at 30.5... similarly, 19 * 40 .5 gets us 769.5, and we add the last student to get to 800! 61 - 30.5 = 30.5, so that is our max range

MartyMurray · Answer

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:  30.5, 21.5

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:  30.5, 21.5

Gemmie · Answer

N = 20 : Avg = 40 => Total = 40 * 20 = 800

N = 21 : Avg = 41 => Total = 41 * 21 = 861

==> The new one weighs 61kg (=861 - 800)

1. Min range

Avg = 40 & Range  
eq{0}  => There must be one weighing less than 40

==> The min range must be more than 61 - 40 = 21

==> Min range = 21.5

2. Max range:  
Avg = 40 & Range  
eq{0}  => There must be one weighing more than 40
The range is 10
==> The lightest one must weigh more than 30

==> The max range must be less than 61 - 30 = 31

==> Max range = 30.5

samarpan.g28 · Answer

Total number of students=20, their avg weight=40. Therefore, the total weight 20*40=800.
When the weight=41, the total number of students=21. Therefore, the total weight 21*41=861.

We can conclude that the new student who joined weights 861-800=61.

The range is maximum when the maximum number of students has the maximum weight. Let the minimum weight be x. Given, that the range is 10. So max weight is x+10.
x+19(x+10)=800 or, x=30.5. So, the max range is 61-30.5=30.5

The range is minimum when the minimum number of students has the minimum weight. Similarly from above, 19x+(x+10)=800 or, x=39.5
So, the min range is 61-39.5=21.5

KarishmaB · Answer

Avg of 20 students is 40 kg.
1 new person joins and avg increases to 41. So the new person came in with 40 + extra 21 so that the avg for all goes up by 1. 
So the new student came in at 61.

Range of initial group is 10 and average is 40. So no one in the initial group was at or above 61. Hence the greatest value in the new group is fixed at 61. We need to focus on the lowest value in the new group to evaluate the range of the new group.

To get the   maximum range  , the weight of one student should be as low as possible.

So let's assume that 19 students were at a weight just above 40 and 1 student was as below 40 as possible. Say the 1 student is at weight x. Then the 19 students are at weight x+10.

\frac{1}{19} = \frac{(x+10) - 40}{40 - x} 
 x = 30.5

Range = 61 - 30.5 = 30.5

To get the   minimum range  , the lowest weight in the group should be as high as possible.

So let's assume that 19 students were at a weight just below 40 and 1 student was as above 40 as possible. Say the 19 students are at weight x. Then the 1 student would be at weight (x+10).

\frac{19}{1} = \frac{(x+10) - 40}{40 - x} 
 x = 39.5

Range = 61 - 39.5 = 21.5

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

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