IMO: Answer Choice B

Align the numbers: 15, 22, 38, 51, 63. A certain integer will be subtracted from 63 and added to 15 so that the median increases. Plug in the values from the AC's. B fits with new median of 39.

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

CONCEPT: Median is the middle terms (for odd no. of terms in set) or Average of two middle terms (for Even no. of terms in set) in the set after arranging the terms in Ascending/Descending order.

Here the Set (in Ascending order) is {15, 22, 38, 51, 63} i.e. Median = 38

Now, an integer number of Keri's points were taken from her and given to Luke, and the median score of the 5 players increased

Let's say x was the number of points transferred from Keri's points to Luke's points.

Now the Set becomes {15+x, 22, 38, 51, 63-x} But now the median becomes a bigger number

i.e. The New median could be either 51 or 63-x where both these numbers must be greater than 38

But, For Median = 51, 63-x and 15+x both should be greater than 51 Which is NOT POSSIBLE

Hence, Median Must be 63-x, and 15+x should be greater than 38
i.e. 38 < 63-x < 51 AND 15+x > 38

i.e. 12 < x < 25 AND x > 23

i.e. x can only be 24

Answer: Option
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When you have a set of odd numbers, the median will always be the middle number. Originally the median was 38 (Mia). We need to take out enough from Keri to give to Luke so that Luke surpasses 38 (Mia). Therefore, (38-15)+1 = 24. Answer choice B. The 1 was the smallest integer increment needed for Luke to surpass Mia.

ALTERNATE

Arrangement of terms in ascending order becomes {15, 22, 38, 51, 63} and median = 38

Just Check the options

Option A: 23

The new arrangement of values becomes {15+23, 22, 38, 51, 63-23} i.e. {22, 38, 38, 40, 55} New median = 38

New Median is not a bigger value than previous median hence, INCORRECT

Option B: 24

The new arrangement of values becomes {15+24, 22, 38, 51, 63-24} i.e. {22, 38, 39, 39, 55} New median = 39

New Median is a bigger value than previous median hence, CORRECT

Answer: option
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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

Solution:

Initial median of the list {15, 22, 38, 51, 63} is 38.

After transferring x points from Keri to Luke, the median score must increase from 38.

15+x>38 -> 15+x = 63-x -> x=24. This value satisfy the inequality, hence the answer B.

Thanks,

Please give me Kudos.

Solution.
Lets arrange point in ascending order.
L(15), N(22), M (38), J (51) , K (63)

Now we have to reduce K's point and add it to L's point such that current median score (38) is increased.
Assume that, new median is 39. Since only option is to add the number to K (which is short of 24 to 39), we will add 24 to L and subtract 24 from N

So new set will be
N(22), M(38), L(39), K (39), J (51)

Anything more than 24 will actually make K less than 39 and hence medianwont change median.
Anything less than 24 will make L less than 39 and hence median wont change

Option B is correct.

Using the given options,
If K gives L 24 points
then the five people will have
J=51
K=39
L=39
M=38
N=22
Median=39 which has increased from the earlier median 38
Answer B

only B fits in for the answer... the median changes from 38 to 39...
any value above 24 will get the median back to 38 due to the corresponding change in Keri's points
ans B
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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?

Cribbing for the formula where it's not needed is the first sign of going on wrong path of learning.

So beware!

Statistics doesn't require any formula. It just requires basic understanding of Median, Standard Deviation, Mode (rarely) and Range.

basic conceptual method is right here

CONCEPT: Median is the middle terms (for odd no. of terms in set) or Average of two middle terms (for Even no. of terms in set) in the set after arranging the terms in Ascending/Descending order.

Here the Set (in Ascending order) is {15, 22, 38, 51, 63} i.e. Median = 38

Now, an integer number of Keri's points were taken from her and given to Luke, and the median score of the 5 players increased

Let's say x was the number of points transferred from Keri's points to Luke's points.

Now the Set becomes {15+x, 22, 38, 51, 63-x} But now the median becomes a bigger number

i.e. The New median could be either 51 or 63-x where both these numbers must be greater than 38

But, For Median = 51, 63-x and 15+x both should be greater than 51 Which is NOT POSSIBLE

Hence, Median Must be 63-x, and 15+x should be greater than 38
i.e. 38 < 63-x < 51 AND 15+x > 38

i.e. 12 < x < 25 AND x > 23

i.e. x can only be 24
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Hello GMATinsight

I am one of those who keep trying to solve without a formula and lose on time.. so trying to strike a balance

Thank you for the explanation

MANHATTAN GMAT OFFICIAL SOLUTION:

The key to this problem is that by taking enough points from Keri and giving them to Luke, the median of the set can change.

We can understand this best by thinking about it visually. Order the scores from low to high on a number line, and represent the change in Luke's score with x:


The current median is Mia's 38, circled in the diagram. In order for the median to change, Luke's score must leap-frog those of Nora and Mia, pushing Mia into the bottom two scores and making Luke's score the median. But be careful! We don't want to decrease Keri's score so much that Luke and Mia surpass her, leaving Mia once again in the median score position.

If 15 + x = 38, Luke would match the current median score. That is x = 23, and Keri's new score would be 63 – 23 = 40. However, the median score would remain 38, with both Luke and Mia having that score. Therefore, x must be greater than 23.

If 63 – x = 38, Keri would match the current median score. That is x = 25, and Luke's new score would be 15 + 25 = 40. The median score would again remain 38, because Keri (and Mia) would now represent the median. Therefore, x must be less than 25. Because x must be an integer, x = 24. The scores after the point transfer will be:


Keri and Luke would now both have the median score of 39.

The correct answer is B.


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Currently, the median is 38.

Let’s analyze the answer choices:

A) 23

If Keri gives 23 points to Luke, then Keri has 40 points and Luke 38, and the numbers are: 22, 38, 38, 40, 51. The new median is 38, but it has not increased.

B) 24

If Keri gives 24 points to Luke, then Keri has 39 points and Luke 39, and the numbers are: 22, 38, 39, 39, 51. The new median is 38, and it HAS increased.

Answer: B
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