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range of set A is R. if a number with value R is added to

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range of set A is R. if a number with value R is added to [#permalink] New post 24 Jul 2007, 21:27
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range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R
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Re: DS: I love ranges [#permalink] New post 24 Jul 2007, 22:34
ArvGMAT wrote:
range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0
mean of the new set is smaller than R


Stmt 1: Range = largest no. - smallest no.
If all numbers in A > 0, then the smallest no. > 0. Therefore, R must be lesser than the largest number. Hence, the range will not change on adding R to the set. Sufficient.
This is of course assuming that sets contain distinct numbers. If the largest and smallest are equal, then R = 0 and this violates stmt 1.

Stmt 2: I think this is not sufficient, but I cannot be sure. :?
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Re: DS: I love ranges [#permalink] New post 24 Jul 2007, 22:58
ArvGMAT wrote:
range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R


Answer: E

stat 1: If the numbers in set A are distinct, then since R=largest no.- smallest no. R will always be smaller than the largest number and therefore, the range will never increase. However if the numbers in set A are the same then the Range can increase.

Eg: Set A = {1,1,1} R=0
New Set A ={0,1,1,1} R=1

Insuff.

Stat 2:

Eg 1:
Set A = {1,2,6} R=5 Mean=3
New Set A= {1,2,5,6} R=5 Mean=3.5
Range remains the same

Eg 2:
set A={-3,-2,-1} R=2 Mean =-2
new set A={-3,-2,-1,2} R=5 Mean = -1
Range increases from 2 to 5

insuff.
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Re: DS: I love ranges [#permalink] New post 04 Aug 2007, 19:59
ArvGMAT wrote:
range of set A is R. if a number with value R is added to the set will the range increase?

(1) all numbers in A are >0

(2) mean of the new set is smaller than R


Range = maxA - minA = R

(1) The range will increase only if R > maxA; otherwise the range would just stay the same.

All #s in A are >0, therefore R = maxA - minA < maxA. Then, the range will not increase. Suff.

(2) The mean does not bring terminating information. All numbers but one could be positive and still we wouldn't have enough grounds to know for sure whether including that R number would increase the range of the set. Insuff.

A.
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Re: DS: I love ranges [#permalink] New post 04 Aug 2007, 21:14
ArvGMAT wrote:
range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R


I think C.
1) Say Set A = {1,2,3}, Range = 2. Inserting 2 will not increase range.
Say Set A = {6,7,8}, Range = 2. Inserting 2 will increase range.

2) Mean of the new set is smaller than R.
Set A = {A1,A2,A3}
Range = A3 - A1
Mean of new set= (A1+A2+A3+A3-A1)/4 = (A2+2*A3) /4
Knowing that mean of new set is smaller than R:
=> (A2+2*A3) / 4 < R
=> (A2+2*A3) / 4 < (A3 - A1)
=> A2 + 2*A3 < 4*A3 - 4*A1
=> 4*A1 + A2 - 2*A3 < 0
=> A2 / 2 < A3 - 2*A1
We want to know if A3-A1 < 0 or A3-A1 > 0. This doesn't tell anything.

If all values are positive, however, this means that A3-2*A1 is positive. This also means that A3-A1 is positive.
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Re: DS: I love ranges [#permalink] New post 05 Aug 2007, 02:53
ArvGMAT wrote:
range of set A is R. if a number with value R is added to the set will the range increase?

all numbers in A are >0

mean of the new set is smaller than R


(1) Suppose A = {2,5}- answer no
Suppose A ={2,3}- answer yes

NOT SUFF

(2) A = {-3,3} yes
A= {0,0,4} no

NOT SUFF

(T) Suppose A' = A U {R}. If all the members of A are positive, R is less than the greatest element.
If the mean of the set A´ is less than R, there is at least one element in A' , and thus in A, that is less than R. Thus R is neither the smallest nor the greatest element in A', and the range of A' = range of A

SUFF
{
Re: DS: I love ranges   [#permalink] 05 Aug 2007, 02:53
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