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

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Manager
Joined: 04 Jan 2008
Posts: 114
Set S consists of n numbers arranged in ascending order. A  [#permalink]

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05 Sep 2008, 21:59
2
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Difficulty:

55% (hard)

Question Stats:

63% (01:18) correct 37% (01:07) wrong based on 225 sessions

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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
Director
Joined: 23 Sep 2007
Posts: 758

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05 Sep 2008, 22:23
1
dancinggeometry wrote:
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

A

sum of the original set + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
The average will increase by 5.5
VP
Joined: 17 Jun 2008
Posts: 1270

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05 Sep 2008, 22:28
dancinggeometry wrote:
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) 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
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Its Now Or Never

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Joined: 05 Sep 2008
Posts: 13

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05 Sep 2008, 22:48
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.
Manager
Joined: 04 Jan 2008
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07 Sep 2008, 00:06
OA is A. Bin 3 problem.
Intern
Joined: 26 Sep 2012
Posts: 15
Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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29 May 2013, 00:16
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

gmatnub wrote:
Set S consists of n numbers arranged in ascending order. A new set is created as follows: each
sum of the original set + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
The average will increase by 5.5
Intern
Joined: 26 Sep 2012
Posts: 15
Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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29 May 2013, 00:45
After a while I got the following:

Basically, to obtain a new set we add another set (1, 2, 3, 4, 5, ... n) [Let's name this set as 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.
SVP
Joined: 06 Sep 2013
Posts: 1819
Concentration: Finance
Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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12 Oct 2013, 16:35
1
dancinggeometry wrote:
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

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
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Joined: 27 May 2012
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20 Dec 2013, 03:18
gmatnub wrote:
dancinggeometry wrote:
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

A

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

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.
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Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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07 Jul 2015, 00:41
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?
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Joined: 02 Sep 2009
Posts: 49273
Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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07 Jul 2015, 01:12
whitehalo wrote:
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?

Yes. Ascending order means that each term is greater than the previous one.
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Re: Set S consists of n numbers arranged in ascending order. A  [#permalink]

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30 Sep 2017, 04:00
dancinggeometry wrote:
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

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
Re: Set S consists of n numbers arranged in ascending order. A &nbs [#permalink] 30 Sep 2017, 04:00
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