Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

S is a set containing 9 different numbers. T is a set contai [#permalink]
29 Sep 2010, 05:25

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

51% (01:56) correct
48% (01:01) wrong based on 160 sessions

S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. which of the following statements cannot be true?

A. The mean of S is equal to the mean of T B. The median of S is equal to the median of T C. The range of S is equal to the range of T D. The mean of S is greater than the mean of T E. The range of S is less than the range of T

my question : what if the extra number is zero ?? ???

Re: cannot be true . mean median range [#permalink]
29 Sep 2010, 05:47

4

This post received KUDOS

Expert's post

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.

Re: S is a set containing 9 different numbers. [#permalink]
22 Jan 2013, 00:20

fozzzy wrote:

S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. which of the following statements cannot be true?

A) The mean of S is equal to the mean of T B) The median of S is equal to the median of T C) The range of S is equal to the range of T D) The mean of S is greater than the mean of T E) The range of S is less than the range of T

Detailed explanation will be appreciated. Thanks!

Mean of both the sets can be equal. Let us suppose the mean of any 8 number is 10 then the 9th number could also be 10 and mean remains the same. In the same way median can also be same. In set of 9 numbers median will be the 5th number when arranged in ascending order and in set T it will be the mean of 4th and 5th number. If we take S = { 1, 2, 3, 4 ,5, 6, 7, 8, 9 } and T as { 1, 2, 3, 4, 6, 7, 8, 9 } then median in both the cases will be 5. From the above eg range is same in both the cases. If the number which is not the part of set T is greater than mean of T then the mean of set S will be greater than that of set T Range of S will always be greater than or equal to range of T because of an additional number. If that number is greater than the greatest number in set T the range will be more, if that number is smaller than the smallest number in set T again the range will be more since now the new number is the smallest number. If that number lies in between then the range will be equal.

Re: cannot be true . mean median range [#permalink]
22 Jan 2013, 04:40

Bunuel wrote:

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 can not 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.

Re: cannot be true . mean median range [#permalink]
22 Jan 2013, 05:22

Expert's post

fozzzy wrote:

Bunuel wrote:

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 can not 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.

So this is a property of sets?

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

Re: S is a set containing 9 different numbers. T is a set contai [#permalink]
03 Jun 2013, 10:51

@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 ?

Re: S is a set containing 9 different numbers. T is a set contai [#permalink]
04 Jun 2013, 02:53

Expert's post

Alexmsi wrote:

@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.
_________________