Data Sufficiency

Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?

(1) The mean of Set A is greater than the median of Set B.

(2) The median of Set A is greater than the median of Set C.


OA - E Any idea of the level of difficulty of this problem? It took me some time to solve this problem. Wondering if there is a quicker way to work this out. Pls explain.

crackgmat007 wrote:Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?

(1) The mean of Set A is greater than the median of Set B.

(2) The median of Set A is greater than the median of Set C.


OA - E Any idea of the level of difficulty of this problem? It took me some time to solve this problem. Wondering if there is a quicker way to work this out. Pls explain.

i am no expert but i think that this could be a upper 600 level problem..
Here, acc. to the problem what i assumed that members of A are the sum of the corresponding members from set B and set C.i am not sure whether we need this assumption or not..
now take statement 1: we don't know the relationship between median of A and median of B.. hence insuff.

By 2nd statement, median of A > median of C. we don't know anything about median of B. hence insuff.

by both the statements together, still we don't know the relationship between the 2 medians. Hence insuff.
experts please lemme know if i missed something.

Can someone throw some light on fastest approach to solve this one..??

sumanr84 wrote:Can someone throw some light on fastest approach to solve this one..??

gud question...experts please help

nikhilkatira wrote:

sumanr84 wrote:Can someone throw some light on fastest approach to solve this one..??

gud question...experts please help

Actually plugging in numbers works here very well. Still u can do this mentally.

One MGMAT explanation for a complicated problem stated that when two sets are combined, the MEDIAN of the combined set must be between the medians of the individual sets, or equal to the median of ONE or BOTH of the individual sets. If that is the case. How can the median of Set A (combined) be greater than the median of Set C?

Also, if you were picking numbers, can I just see a few combinatoins you might use to prove this? Its becoming hard for me to come up with some (quickly) on my own. Looking for some sort of strategy.

Hey guys,

I don't know if plugging in would be the best method here since we don't know anything about the numbers that are in each sets other than they are positive integers. The numbers could be super low numbers or super high numbers - which would BOTH GREATLY impact the mean and the median.

So the problem:

Set A = Set B + Set C

Question: Median of B > A?

(1) The mean of Set A is greater than the median of Set B.

Avg of A > Median of B

This is clearly insufficient. The only time you can compare Avg/Median is when you have consecutive integers or consecutive multiples. Other than that, the avg/median will be different for different sets!

(2) The median of Set A is greater than the median of Set C.

This is also insufficient! Median of Set A > C. We want to know about B > A?

Together:

Avg of A > Median of B
Median of A > Median of C

This is again insufficient. We don't know about the relationship of of A-B or C-B.


An effective technique to solving this question:

When ever on DS questions the two statements are giving you identical information, the answer can only be (D) or (E).

Knowing you can't use Avg/Median comparison in statement 1 since the sets are not consecutive means (1) is not sufficient. Therefore (D) cannot be sufficient. Then the only answer choice I am left with is (E).

I hope this helps!

great explanation. putting it in "inequality" terms definitely help grasp why its E as you can't make an "continuous" inequality to connect the medians of both sets. i guess knowing inequalities has its benefits throughout all areas of quant!!
Would you mind opining on this other sets, median thread: wud love to get ur "simple easy to understand" analysis!

https://www.beatthegmat.com/sets-std-dev ... tml#291293

missrochelle wrote:great explanation. putting it in "inequality" terms definitely help grasp why its E as you can't make an "continuous" inequality to connect the medians of both sets. i guess knowing inequalities has its benefits throughout all areas of quant!!
Would you mind opining on this other sets, median thread: wud love to get ur "simple easy to understand" analysis!

https://www.beatthegmat.com/sets-std-dev ... tml#291293

Glad I could help

Let me have a look.....

taking a second look at this - im curious how u deduced that they were both giving "similar" informaiton.... just because they both relate different aspects of what we're looking for...wihtout "actually" giving us the info we're looking for?


also, i find it hard to belive that you can only compare mean and median for consecutive sets (in general) but i assume you mean that in terms of GMAT , whats important to note is that there is only a relationship when they are consecutive sets, otherwise it could be anything.

missrochelle wrote:taking a second look at this - im curious how u deduced that they were both giving "similar" informaiton.... just because they both relate different aspects of what we're looking for...wihtout "actually" giving us the info we're looking for?


also, i find it hard to belive that you can only compare mean and median for consecutive sets (in general) but i assume you mean that in terms of GMAT , whats important to note is that there is only a relationship when they are consecutive sets, otherwise it could be anything.

(1) Stmt 1. gives you Avg of A > Median of B So we are missing C
(2) Median of Set A > C. And now we are missing B

So they are giving similar information in that each statement hides 1 variable.


Your second question, by compare i meant mean=media ONLY when you have consecutive sets. therefore, knowing mean or median is kind of only useful when you have consecutive sets. otherwise the two will be different.

what's a good way to solve such questions? Is there a methodical approach to tackle such questions?

Though I understand the answer explanation now but it took me a lot of time to totally assimilate the information in the question.

Are there any rules of thumb/special properties/special cases of mean/median/mode/SD that one should remember?