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Set S consists of n numbers arranged in ascending order. A [#permalink]
05 Sep 2008, 20:59

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Difficulty:

35% (medium)

Question Stats:

58% (02:27) correct
42% (01:10) wrong based on 53 sessions

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

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

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

Re: Set S consists of n numbers arranged in ascending order. A [#permalink]
28 May 2013, 23:16

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

Re: Set S consists of n numbers arranged in ascending order. A [#permalink]
28 May 2013, 23:45

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.

Re: Set S consists of n numbers arranged in ascending order. A [#permalink]
12 Oct 2013, 15:35

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

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.