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

Question

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

sumande · Answer

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.

GK_Gmat · Answer

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.

Andr359 · Answer

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.

bkk145 · Answer

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.

kevincan · Answer

(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
{

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

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