Problem Solving

Jake - 51
Keri - 63
Luke - 15
Mia - 38
Nora -22

The table above shows the number of points held by 5 players of a certain game. If an integer number of Keri's points were taken from her and given to Luke, and the median score of the 5 players increased, how many points were transferred from Keri to Luke?

A. 23
B. 24
C. 25
D. 26
E. 27

The OA is B.

The original Median is 38 for this set of scores.
I did quick summations to reach at option B wherein the Median increases to 39 - for all others, it remains at 38.
Is there another way to do it via a formula or something? Thanks!

Scores in ascending order are 15, 22, 38, 51, 63
So the median is 38,
Now, to increase the median, we have to assure that first 2 terms will be 22, 38 and next three terms will be greater than that
So, let x points are transferred from 63 to 15, in that case, it will become 15+x>38 and 63-x>38, it gives: x>23 and x<25
So, x can only be 24

Jake = 51
Keri = 63
Luke = 15
Mia = 38
Nora = 22
In ascending order = 15, 22, 38, 51, 63
Median here = 38
Keri lost point to Luke
Keri's point reduced,
Luke's point increased
Median also increased
How many point did Keri lose.

If Keri lost 27 points
Therefore, [15 + 27], 22 38, 51, [63-27]
=42, 22, 38, 51, 36
Ascending order = 22, 36, 38, 42, 51
Median is still the same, option E is wrong.

If Keri lost 26 points
Therefore, [15 + 26] 22, 38,51, [63-26]
=41, 22, 38, 51,37
Ascending order = 22, 37, 38, 41, 51
Median is still 38 option D is wrong
If Keri lost 25 points = [15 + 25], 22, 38, 51, [63-25]
=40, 22, 38, 51, 38
Ascending order = 22, 38, 38, 40, 51
Median is not increased option C is wrong.

If Keri lost 23 points = [15 + 23], 22, 38, 51, [63-23]
=38, 22, 38, 51, 40
Ascending order= 22, 38, 38, 40, 51
Median is not increased, Option A is wrong.

Therefore, if Keri lost 24 points = [15 + 24], 22, 38, 51, [63-24]
= 39, 22, 38, 51, 39.
Ascending order = 22, 38, 39, 39, 51
Median has increased from 38 to 39,
Option B is the answer.

swerve wrote:Jake - 51
Keri - 63
Luke - 15
Mia - 38
Nora -22

The table above shows the number of points held by 5 players of a certain game. If an integer number of Keri's points were taken from her and given to Luke, and the median score of the 5 players increased, how many points were transferred from Keri to Luke?

A. 23
B. 24
C. 25
D. 26
E. 27

The OA is B.

The original Median is 38 for this set of scores.
I did quick summations to reach at option B wherein the Median increases to 39 - for all others, it remains at 38.
Is there another way to do it via a formula or something? Thanks!

Put the points in ascending order:
15, 22, 38, 51, 63

The median is 38.
Keri has 63 points and Luke has 15 (one figure more than 38 and the other less than 38).
For median to change, both figures need to be either more than 38 or less than 38 since all other points remain the same. Let's find what we get when both have equal points (63 + 15)/2 = 39.
So when 24 points (63 - 39 = 24) are shifted from Keri to Luke, each gets 39 points. We don't need to worry whether this is the unique answer since it is a Problem Solving question. The answer must be unique.

Answer (B)