Set A consists of scores obtained by each of the students in Class X

Question

Set A consists of scores obtained by each of the students in Class X and Set B consists of scores obtained by each of the students in Class Y. Is the median of scores in Set A equal to the median of scores in Set B?

(1) All the scores in Set A are also there in Set B

(2) Class X and Class Y have an equal number of students.

BlahBlah99988 · Answer

The wording seems misleading. It tells us that the sets consist of scoreS by each of the studentS. The plurality in the question makes it seem that each student can have any number of scores in the set.

If this is true, then knowing the number of students and that the scores in A are in B does not necessarily mean that the medians are the same.

For example: Set A has John{3, 5, 6} and Mark{2, 3, 7}. Set be has Paul{3, 5, 6} and Daniel{2, 7, 8}. Set B has all of the scores from Set A with an additional "8". This means that the median for A is 4   and the median for B is 5.5  .

Therefore, not sufficient.

nick1816 · Answer

Statement 1- 
Case 1
Set A- {2,3,5} and Set B {2,3,5} median are equal

Case 2
Set A- {2,3,5} and Set B {2,3,5,7} median are not equal

Insufficient

Statement 2- 
Case 1
Set A- {2,3,5} and Set B {2,3,5} median are equal

Case 2
Set A- {2,3,5} and Set B {5,6,7} median are not equal

Insufficient

Combining both equation

Case 1
Set A- {2,3,3,5} and Set B {2,3,3,5} median are equal

Case 2
Set A- {2,3,3,5} and Set B {2,2,3,5} median are not equal

Insufficient!!

CrackverbalGMAT · Answer

This is a good question on median with a very subtle trap laid for someone who’s not careful. It’s very easy to assume certain things and fall for this trap.

The median of a set of scores, is the value that divides the given data into 2 equal parts when the values are arranged in ascending or descending order.

From statement I alone, we can only say that Set A is a subset of set B. But, there may be elements in set B that are not there in set A. In this case, the medians of the two sets will be different.

There may be a case where the elements in set A are exactly identical to the ones in set B. In this case, the medians of the two sets will be the same. Since this data is giving us a YES and a NO, this statement is insufficient.

Answer options A and D can be eliminated. Possible answer options are B, C or E.

Statement II alone tells us that the number of values in both the sets is the same. This is hardly sufficient to ascertain anything about the median. 
Option B can be eliminated. Possible answers at this stage are C or E.

When we combine statements I and II, we know that there are same number of values in both the sets; we also know that all the values in A are in B. 
However, we do not know whether the frequency of each value in A is the same as that of each value in B. The frequency is what decides the median. Therefore, the combined data is also insufficient. 
The correct answer option is E.

So, the trap that is laid here is ‘ Set A and Set B have the same number of values, all values of set A are there in set B – therefore, set A and set B have same elements’. If you make this assumption when you combine the statements, this is when you will mark C, which is quite naturally the trap answer.

Hope this helped!

iamjatinagrawal · Answer

Hi  Bunuel ,

From statement 1, is it implied that when we talk "all" in statement 1, it means all distinct elements of A are in B? Or this statement should have been properly worded?

Bunuel · Answer

The wording is poor overall. Ignore the question.

Set A consists of scores obtained by each of the students in Class X

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 Data Sufficiency (DS) Questions

Set A consists of scores obtained by each of the students in Class X

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