Set S consists of n numbers arranged in ascending order. A

Question

Set S consists of n numbers arranged in ascending order. A new set is created as follows: each element of set S is increased by a value equal to that number's place within the set (i.e. the lowest number is increased by 1, the second lowest is increased by 2, etc.). By how much is the mean of the new set greater than the mean of the original set ?

(1) Set S consists of 10 elements
(2) The sum of the elements in the original set is 100

(1) Set S consists of 10 elements
(2) The sum of the elements in the original set is 100

gmatnub · Answer

A

sum of the original set + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
The average will increase by 5.5

spriya · Answer

(1) says n=10 => increased value is n(n+1)/2 =55 when n=10 
hence increase in average can be obtained.SUFFI
(2)sum is 100 does not say anythin about n hence INSUFFI
IMOA

Youngd8 · Answer

A also.

In order to solve this probem you need to know how many elements are in the set.

st 2 does not show how many elements are in the set so just knowing the sum would not help.

dancinggeometry · Answer

OA is A. Bin 3 problem.

thewind · Answer

By plugging numbers I discovered that the difference (new median - old median) can be calculated from the formula:
(n+1)/2. Experienced mathematicians must know this effect with sets and the formula.

However, if you are an average GMAT test taker, like me, IMO, the best way to solve was found by gmatnub

thewind · Answer

After a while I got the following:

Basically, to obtain a new set we add another set ( 1, 2, 3, 4, 5, ... n )  set N ] to a first set. As the  set N  is a set of consecutive numbers, so we can calculate its median. To locate the median we should find the average of the first number and the last number of the set N:
 (n+1)/2.  
As we know the mean is equal to the median of the same set of consecutive numbers. So, the difference between the mean of a first set and that of a new set can be found if we know the number  n  of elements of either first or last sets.

jlgdr · Answer

Guys remember arranged in ascending order doesn't mean that they are consecutive. Keep that in mind, GMAT sometimes tries to trick you like this Good luck Cheers J

stne · Answer

Just couldn't understand the explanations, here is my small take hope it helps others

average is given by sum of total elements / number of elements

statement 1 : Set S consists of 10 elements

let the sum of the original 10 elements be x , average is  \frac{x}{10} 
the new set is formed and its total will be x+55 . Average of new set  \frac{x+55}{10}

Now average increase will be  \frac{x+55}{10} - \frac{x}{10} = 5.5 
Hence A is sufficient
Hope it helps.

whitehalo · Answer

guys, i have a question.

"Set S consists of n numbers arranged in ascending order."

It didn't mention that each elements are unique so I picked E because was thinking of the possibility of Set S being "1,1,1,1,1,10,10,10,10,10" or something to that effect.

Is it implied that when the question mentions 'ascending order' meant that each element in that set is unique?

Bunuel · Answer

Yes. Ascending order means that each term is greater than the previous one.

atulindia · Answer

Value Qs, (Mean S1-MeanS)=?
Given Info- Set S consist of n no.s in ascending order.
New Set S1 is (element 1+1, element 2+2.....element n+n).
Sum of elements in S1- Sum elements of S2= increased value of each place= (1+2+3+4....+n)
 we need to know n to find of difference in mean.
St-1  n= 10 then Sum of S1- Sum of S= 1+2+3+.....+10= 55
Mean S1 -Mean S= 55/10=5.5  Sufficient

St-2
Sum of the elements of S is 100. we do not know no of elements cant find mean of elements in S1.  Insufficient 
 Answer is A

Kritisood · Answer

we know mean increases by the same number as the increase in every term. 
consider 1 2 3 mean = 2 
add one in all terms 
2 3 4 mean is 3 (2+1)

total increase = 3
no of terms = 3
increase in mean =3/3=1

the same way we know the increase in sum ie 55 (1+2+3...+10 = 55) and we know the number of terms ie 10. Hence, 5.5 is the increase in the mean.

A sufficient.

bumpbot · Answer

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Set S consists of n numbers arranged in ascending order. A

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