BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Set of n numbers - Mean

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Fri Jul 29, 2011 8:35 pm
Followed by:1 members

Set of n numbers - Mean

by rami26 » Mon Aug 15, 2011 7:35 pm
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 the number's place within the set (i.e., the lowest number is increased by 1, the second lowest number 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.

[spoiler][OA : After discussion][/spoiler]


-----------------------------------
It is never too late to do anything
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2789
Joined: Tue Jul 26, 2011 12:19 am
Location: Chennai, India
Thanked: 206 times
Followed by:43 members
GMAT Score:640

by GmatKiss » Tue Aug 16, 2011 12:48 am
[spoiler]IMO:B[/spoiler]

2)let the original set be {20,25,27,28} (sum=100)
then the set formed will be (21,27,30,32) (sum=110)

Invariably sum of the new set will be 110 (as we add 1+2+3+4 to any number present in the respective positions), Hence B is sufficient
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Fri Jul 29, 2011 8:35 pm
Followed by:1 members

by rami26 » Wed Aug 17, 2011 6:05 am
I chose B too. But the OA is A.

Explanation:

Statement 1:
The mean of Set S = (Sum of elements of S)/n
The mean of new Set = (Sum of elements of S + 1 + 2+ 3 + 4 +.... n)/n
= (Sum of elements of S)/n + (1+2+3+4+....n)/n
= Mean of set S + (1+2+3+4+...n)/n
If we know n , this statement is sufficient. From Statement 1, we know n =10. Therefore, this statement is sufficient.

Statement 2.
Consider Set S1 {0,100} (n elements - sum adds up to 100); Mean = 50
Corresponding new set {1,102} (as the lowest number is increased by 1 and the second lowest is increased by 2) Mean = 51.5
Difference in mean = 1.5

Consider set S2 {100} (set has only one element - hence sum is 100) ; Mean = 100
Corresponding new set {101} Mean = 100
Difference in mean = 1
Hence B alone is insufficient.

A is the OA. This question is from one of the 800score tests. I am still confused how a set containing only one element can be considered in this case.

------------------------------------
It is never too late to do anything
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 312
Joined: Tue Aug 02, 2011 3:16 pm
Location: New York City
Thanked: 130 times
Followed by:33 members
GMAT Score:780

by gmatboost » Wed Aug 17, 2011 8:20 pm
I will try to explain it with less complexity:

From the question:
The amount of the increase will be 1 + 2 + 3 + .... + n
Up to whatever number n is

So, the increase is a sequence of consecutive numbers from 1 to n.
We can find the total amount of increase by using the formula for sum of consecutive numbers:
(first + last)/2 * number of terms
--> the first part gives us the average of the terms in the sequence

first = 1
last = n
number of terms = n

Increase from one set to the other: (n+1)*n/2

That's how much the total goes up by. To find out how much the average goes up by, we need to divide the total increase by the number of terms (n)

[(n+1)*n/2] / n = (n+1)/2

So, the increase depends on the number of terms and has nothing to do with the actual terms themselves.

That is why St 1 is sufficient and St 2 is not.

The error in your example for B is that you have assumed there are 4 terms. If the set was:
18, 19, 20, 21, 22 (sums to 100)
The new set would be
19, 21, 23, 25, 27 (sums to 115)

So the increase depends on the number of terms, not the terms.
In your example, n=4 so (n)(n+1)/2 = 10
In the example above, n=5 so (n)(n+1)/2 = 15
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
It's a total of 20+ hours of expert instruction for an introductory price of just $10.
View sample questions and tips without signing up, or sign up now for full access.

Also, check out the most useful GMAT Math blog on the internet here.
Top
Post new topic Post Reply
• Page 1 of 1