The list of scores obtained by 3 students in a test is as follows: 21,

Question

GMATBusters’ Quant Quiz Question -5

For past quiz questions, click  here

The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score was less by ‘x’ points due to a calculation error. If the average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction, which of the following could be the range of list of corrected scores?

A 2
B 5
C 7
D 11
E 20

A 2
B 5
C 7
D 11
E 20

cchen679 · Answer

The answer is E because the average increased by 3, and because there are three numbers, that means one of the scores increased by 9 points. Since we keep 25, it must be the 21 or 32 that gets the +9. This gives us the sets of either 21,25,41 (range of 20) or 30, 25, 32 (range of 7). But because we know that the median stays the same, it must be 21, 25, 41, so answer is E, 20.

Raxit85 · Answer

Scores obtained by three students are 21, 25, 32. Sum of the scores = 78 and average of these three scores = 78/3=26
Median of scores = 25
After correcting the error
• Sum of scores = 78 + x
• Average of new scores = 78+x3=29
• x = 87-78 = 9
We do not know which student’s mark got corrected.
But it is given to us that median of scores before and after correction is same means median of list of corrected scores = 25
Let’s look at the following cases:
1st case; If student who got scored 21 improves by 9 points then his new score will be 30
List of corrected scores = {30, 25, 32}
In this case median = 30
So, this case is not possible, as we need a set which has a median score of 25.
2nd case: If student who got scored 32 improves by 9 points then his new score will be 41
List of corrected scores = {21, 25, 41}
In this case median = 25
So, this case is possible, as we needed a set which has a median score of 25.
So, the range of corrected score = 41-21 = 20
Imo. E

ashwini2k6jha · Answer

Answer:E
3=Average after correct list - Average before correct list of scores
3= (78+x)/3-78/3
x=9
New list of scores satisfying median remain same
21,25,32+x
21,25,41
Range=41-21=20

uc26 · Answer

Since the average score increases by 3 points after correcting the error, the impact on the set would be= 3*3= 9
Since the student found that his score was less by 'x', we need to add 9 to one of the values without changing the median.
The only value to which 9 can be added without altering the median is 32. So 32+9= 41.
And the range would be 41-21=20
Answer: E

gurmukh · Answer

If the average of 3 scores increases by 3 points then total score of a student increase by 9 points. As the median remains same so student having 32 points will increase by 9 points and his new score will become 41 points. 
So range =41-21=20
Option E is the answer.

Posted from my mobile device

R1taja · Answer

Option E,

The difference between the old and new total is 3*(29-26) = 9, thus one score increased by 9. Now if 21 were to increase, 25 will no longer be the median thus 32 increased to 41. Range then will be 41-21 I.e 20

Posted from my mobile device

Archit3110 · Answer

for given three scores 21,25,32 the median is 25 and avg is 78/3 ; 26
later when score error is know the avg score increase by 3 points or say to 29 so total sum = 29*3 ; 87
net change in points of one of scores ; 87-78 ; 9
given that median remains same so the +9 gets added to 32 ; new score ; 41
21,25,41 ; range = 41-21 ; 20
OPTION E

The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score was less by ‘x’ points due to a calculation error. If the average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction, which of the following could be the range of list of corrected scores?

A 2
B 5
C 7
D 11
E 20

A 2
B 5
C 7
D 11
E 20

yashikaaggarwal · Answer

Average of 3 students = 21+25+32/3 = 78/3 = 26
If the student's score is increased by X no. The average increase by 3 point.
Therefore 78+x/3 = 26+3
78+x/3 = 29
78+x = 87
X = 9
The student's marks has to be increase by 9 marks such that median = 25 remain same.

If we add 9 to 21 marks of student 1, median will shift to 30(21,25,32 --> 21+9,25,32 ->>> 25,30,32)

If we add 9 to 25 marks of student 2, median will shift to 32(21,25,32 --> 21,25+9,32 ->>> 21,32,34)

If we add 9 to 32 marks of student 3, median will remain same 25(21,25,32 --> 21,25,32+9 ->>> 21,25,41)

The range of marks is (highest-lowest) => 41-21 =20
Answer is supposedly E

Posted from my mobile device

Gamerboyttt · Answer

E.
No which will be increased is 32 by 9 points(avg change).
Range will be 41-21=20

Posted from my mobile device

SohGMAT2020 · Answer

The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. One of the students found that his score was less by ‘x’ points due to a calculation error. If the average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction, which of the following could be the range of list of corrected scores?

A 2
B 5
C 7
D 11
E 20

A 2
B 5
C 7
D 11
E 20

Since the average of the scores increases by 3, the total score will increase by 9.

If the median does not change, 21 and 25 cannot increase by 9, So 32 will increase by 9 to 41.

The range of the new score is 41-21 = 20.

Answer E is correct

Kinshook · Answer

Given: 
1. The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. 
2, One of the students found that his score was less by ‘x’ points due to a calculation error.
3. The average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction,

Asked: Which of the following could be the range of list of corrected scores?

1. The list of scores obtained by 3 students in a test is as follows: 21, 25, 32. 
Scores = {21,25,32}

2, One of the students found that his score was less by ‘x’ points due to a calculation error.
3. The average of three score increases by 3 points after correcting this error and the median score remains the same before and after correction,
Median = 25 before and after correction 
Sum increased by 3*3 = 9 points after correcting the error
x = 9

21 + 9 = 30; Not feasible since median will change
25 + 9 = 34; Not feasible since median will change
32+9 = 41; Feasible since median will remain 25 before and after correction

Corrected Scores = {21,25,41}; Range = 41 - 21 = 20

IMO E

HoneyLemon · Answer

E ,  IMO

median = 25 . 
score increased by 3*3 = 9 points . 
so earlier 32 will become now 32+9=41
so range = 41-21= 20 .

coreyander · Answer

Let C be the corrected score & I be the incorrect score. 
The student found his score is less by x points. So his Correct score would be greater.
 	herefore C = I +x

Sum of Scores = 21+25+32 = 78
 Average = \frac{78}{3} = 26

Since after correction, the average increased by 3,
 Average+3 = \frac{SumOfCorrectedScores}{3} 
 26+ 3= \frac{(78+x)}{3} 
 	herefore x=9

Adding 9 to 21 results in the scores: 25,30,32 --->  Median Changed 
Adding 9 to 25 results in the scores: 21,32, 34--->  Median Changed 
Adding 9 to 32 results in the scores: 21,25,41 ---->  Median remains the same as stated in question stem. 
 
Range = 41-21 = 20. Answer (E) 20

Babineaux · Answer

Three scores 21, 25, 32
Now some incorrect calculation happened.
Total score 21+25+32 = 78
Average is 26.
After correction avg score increased by 3;
Therefore 26+3=29
Total score is 87.

But median remains same i.e., 25. 
So 87-25=62 remains for two person

Additional amount 62-(21+32)=9 will add to only one person.

Let, 21+9= 30 so 30, 25, 32 this cannot happen here median changes.
If 32+9= 41 so 21, 25, 41 here median is same as required.

Thus the new score list will be 21, 25, 41
Therefore the range is 20.

IMO ans is E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

The list of scores obtained by 3 students in a test is as follows: 21,

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

The list of scores obtained by 3 students in a test is as follows: 21,

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards