Author 
Message 
Senior Manager
Joined: 30 Oct 2004
Posts: 284

The range of a set A is R. A number having a value equal to [#permalink]
Show Tags
19 Oct 2005, 21:51
Question Stats:
0% (00:00) correct
0% (00:00) wrong based on 2 sessions
HideShow timer Statistics
This topic is locked. If you want to discuss this question please repost it in the respective forum. The range of a set A is R. A number having a value equal to R, is included in this set A. Will the range of set A increase?
1) All numbers in set A are positive
2) Mean of the new set is smaller than R
_________________
Vikram



Senior Manager
Joined: 02 Oct 2005
Posts: 297

Answer: D
Stmt 1 indicates all numbers are +ve and range = max  min. Hence R (range) lies between min and max and do not increase (Sufficient)
Stmt 2 indicates the mean of new set is less than R. This indicates, that R was less than the mean of old set. However old mean should be greater than min and less than max. Hence R lies between old min and old max. (Sufficient)



Director
Joined: 21 Aug 2005
Posts: 789

i have a question on A!
Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10.
If I add R=10 to each of these sets,
1. Adding 10 doesn't increase range in {0,...,10}
2. Adding 10 increases the range in {11,...,21}
Is A not insuffient?



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

Using (1), The set could be {1,5,10} and the range is 9. By adding 9 to the set, the range won't increase. Trying out another set {5,10,15}, the range is 10 and adding 10 won't increase the set either. For positive numbers, the set will never increase as the number added will be smaller than the biggest number.
For (2),
Set {1,5,10}: Mean = 16/3, Range = 9. Add in 9, set becomes {1,5,9,10} with mean 9/4 which is smaller than R, but range does not increase.
Set {5,0,10}, Mean = 2.5, Range = 15. Add in 15, set becomes {5,0,10,15}, the range increases to 20, mean = 5 < not feasible
Set {6,2, 1}, mean = 3, Range = 5. Add in 5, the set becomes {6,2,1,5}, the range is now 11, mean = 1. < again not feasible.
It seems once the set invovles a negative number, then the range and mean will increase after adding R.
(2) is sufficient.
Ans: D



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

gsr wrote: i have a question on A! Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10. If I add R=10 to each of these sets, 1. Adding 10 doesn't increase range in {0,...,10} 2. Adding 10 increases the range in {11,...,21} Is A not insuffient?
You're right !! I did not manage to think of this set.



Senior Manager
Joined: 02 Oct 2005
Posts: 297

Good Catch GSR. May be I should go to sleep
I think answer is B. (I hope my explanation for this one is correct). Please correct me, if am wrong.



VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

A for me
statement1 > if all the numbers are +ive, the range can not be superior to the highest number. (dont forget, 0 is neither negative nor positive)
statement 2> consider 2 examples :
40 and 10
mean : 15
R range is : 50
R will increase the range of the set
2 and 8
mean : 5
R range is 6
R will not increase the range of the set



Senior Manager
Joined: 30 Oct 2004
Posts: 284

OA is C
_________________
Vikram



SVP
Joined: 03 Jan 2005
Posts: 2233

Re: DS: Mean/Range [#permalink]
Show Tags
20 Oct 2005, 08:53
vikramm wrote: The range of a set A is R. A number having a value equal to R, is included in this set A. Will the range of set A increase? 1) All numbers in set A are positive 2) Mean of the new set is smaller than R
1) R=maxmin
If R<max and R>min then range would not change.
Since min>0 we know R<max
But we don't know if R>min as gsr showed
2) (n*mean+R)/(n+1)<R
=> R> mean
Therefore R>min
But we don't know if R <max
eg. {1,2,3,4} mean=2.5 R=3 range doesn't change
{1,0,1) mean =0 R=2 Range does change after adding 2 into the set.
Combined, from 1) we know R<max, from 2) we know R>min. Therefore we can determine that range would not change. Therefore C.
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.



VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

gsr wrote: i have a question on A! Consider 2 sets {0,...,10} and {11,...,21} both the cases the range is 10. If I add R=10 to each of these sets, 1. Adding 10 doesn't increase range in {0,...,10}2. Adding 10 increases the range in {11,...,21} Is A not insuffient?
Please note that you can not use 0, from A you know that only +ive number are ok
if you have {5,6} the range will be 1 so including 1 in the new set will increase the range
if you consider {2,3,4,5} the range will be 3 so including 3 in the new set will not increase the range
so i agree A is not suff
HongHu, your algebra explanation was great



SVP
Joined: 03 Jan 2005
Posts: 2233

Antmavel wrote: HongHu, your algebra explanation was great
It didn't look like this mind boggling when I wrote it.
_________________
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.










