S is a set containing 9 different numbers. T is a set contai

So this is a property of sets?

Sure. The range of a subset cannot be greater than the range of the whole set.

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@Bunuel:

I agree with you that the range of subsequent set is less than the whole set, but it can also be the same ? For exmaple:

100 14 13 2 whole set.
100 14 2 subsequent set.

All mebers of the subsequent set are also members of the whole set. But the range are in both cases the same. So it must be as follows: The range of the subsequent set can be equal or less than that of the whole set ?

The way it's written in my post is the same: the range of a subset cannot be greater than the range of a whole set. This means that the range of a subset is always less than or equal to the range of the whole set.

Solve for an "easier" problem and make up an example to see what's going on in the problem.

Set S = {1,2,3}
Set T = {2,3}

Okay so if we can get an answer that is true, we can eliminate that answer choice.

a) hmm, how to get the mean equal each other? Oh, just remove the 2 instead of 1.
b) same
c) same
d) remove 3 instead of 1

At this point we can choose e) and move on, but to be sure just test some numbers again.

e)
range set S = 3-1 = 2
range set T = 3-2 = 1
range set T = 3-1 = 1

So, this can never be true. --> Bingo

This is basically the same method as Bunuel posted above, but for me it sometimes works better if I have a simpler set to work with.

[quote="Bunuel"]The range of a set is the difference between the largest and smallest elements of a set.

Consider the set S to be {-4, -3, -2, -1, 0, 1, 2, 3, 4} --> \(mean=median=0\) and \(range=8\).

A. Mean of S = mean of T --> remove 0 from set S, then the mean of T still would be 0;
B. Median of S = Median of T --> again remove 0 from set S, then the median of T still would be 0;
C. Range of S = range of T --> again remove 0 from set S, then the range of T still would be 8;
D. Mean of S > mean of T --> remove 4, then the mean of T would be negative -0.5 so less than 0;
E. Range of S < range of T --> the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset be more than the difference between the largest and smallest elements of a whole set.

Answer: E.

Hope it helps.[/quote


If the numbers are all different and positive in the question and S has 8 numbers and T has 7 numbers, then will mean of Set S be ever equal to mean of set T as in option [A]

Hi akadmin,

Yes, it is still possible.

Consider following examples:

T = {2, 4, 6, 8, 10, 12, 21} Mean of T = 63/7 = 9

S = {2, 4, 6, 8, 9, 10, 12, 21} Mean of S = 9

Key idea is that create a set with 7 elements such that the mean is not a member of the set.

For larger set (i.e. set S) you can always add mean as an additional element and mean of the larger set will still be same as smaller set (set T).

Hope it helps.

Bunuel but if i take this set of numbers

S -\(-\frac{0 + 1 +2 +3 +4+5 +6 +7 +8}{9}= 4\)


T --- \(\frac{0 +1 + 2+ 3 +4 +5 + 6 +7}{8} = 4.5\)


mean of set S is 4 and mean of Set T 3.5

median of set S is 4 and median of set T is 3.5


then how should i solve this question pushpitkc

Hi dave13

Though you have written the values down correctly, but while calculating the mean
for T you seem to have made a mistake. Anyways, now that you have the values you
just start by substituting values and you will find out that Option A,B,C,E are incorrect

For instance, We know Mean(S) = 4 and Mean(T) = 3.5

So, Option D is possible and cannot be the answer. You need to choose values for the
two sets, S and T and such that we cab eliminate all but 4 options. The answer to this
question is Option E because it is never going to be possible

Hope that helps!

S has 9 different numbers. T has 8 of these different numbers in it.

Which of the following cannot be true?

A. The mean of S is equal to the mean of T
This is possible. Let's say the mean of set S is a number 20 and one of the numbers in S is 20. If T has all numbers in it except 20, its mean will still be 20.

B. The median of S is equal to the median of T
This is possible. Let's say the median of set S is the middle number 20 and set T does not have 20 but has 19 and 21 in the middle. The median of T will still be 20.

C. The range of S is equal to the range of T
When we read range, think of numbers arranged from lowest to highest. Range is highest - lowest. T could include both the lowest number and the highest number and hence its range will be same as the range of S.

D. The mean of S is greater than the mean of T
Mean of T could be less than or higher than that of S. Again, arrange all elements of S in ascending order. If you pick just the greatest 8 numbers to have in T, mean of T will be more than that of S. If you pick the smallest 8 elements, mean of T will be less than mean of S.

E. The range of S is less than the range of T
Can the range of T be greater than that of S? Arrange all numbers of S in ascending order. Which 8 numbers will you pick to have a higher range? For maximum range, you can pick the smallest and greatest number of S. But that will give just the same range as that of S. T cannot have a range greater than the range of S.

Answer (E)

Bunuel

If the question were changed slightly and Set S were to have even number of elements, say 8, and T were to have 7 elements, I think the answers could change a bit.

Please let me know if the logic below is correct:
a) Median CANNOT be the same for S and T
Set S: if # of elements are even and numbers are distinct, median must be the average of middle numbers and therefore not a number that is actually in the set S.
Set T: Since numbers are odd, median is the middle number in the set and must be in set S by definition.
Thus, Median of S cannot be the same as Median of T

b) Mean CAN be the same for S and T
Mean on the other hand can still be the same as long as the only number that is not included in T is the number that is the same as mean of Set S.

Is that correct?

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