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Sets

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by ricky » Mon Aug 04, 2008 6:01 am
Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?
(a) 4
(b) 9
(c) 13
(d) 17
(e) Cannot be determined
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by sudhir3127 » Mon Aug 04, 2008 6:09 am
IMO its c. 13.. do let me know if its correct... i did it in long way ... if its correct i will post the solution.. otherwise it will be misleading ...
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by sudhir3127 » Mon Aug 04, 2008 6:21 am
this is how i did...

let the numbers of A be 1-9 .. i know they are in Ap series.. so the sum is
9/2*( 1+9) = 45 ..hence the average is 5. range is 9-1 = 8

total 5+ 8 = 13.

its says B is 1+ A1, 2+A2..........9+A9

hence its 2,4,6.....18 ..

As this is 2 times A .. i know the total of mean + range will also be 2 times A.

hence B = 2* 12 = 26.

hence the difference = 26-13 = 13..

i think its the right approach .. please let me know if the answer is right..
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by ricky » Mon Aug 04, 2008 6:44 am
I did same way.But OA is E...i dont understand why !
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by pepeprepa » Mon Aug 04, 2008 6:46 am
I did the same.
With some examples we find that:
The difference of range between A and B is always 8
The difference of mean between A and B is always 5

So the total difference is 13
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Re: Sets

by Ian Stewart » Mon Aug 04, 2008 6:50 am
ricky wrote:Set A is composed of nine numbers, labeled A1 through A9. Set B is also composed of nine numbers, labeled B1 through B9. Set B is defined as follows: B1 = 1 + A1; B2 = 2 + A2; and so on, including B9 = 9 + A9. How much larger is the sum of set B's mean and range than the sum of set A's mean and range?
(a) 4
(b) 9
(c) 13
(d) 17
(e) Cannot be determined
We can certainly work out by how much the mean of B exceeds the mean of A. We cannot, however, compare the range of B with the range of A, unless we have more information about the sets- the range of B might be larger than the range of A, or it might be smaller. We could have:

A = {0,0,0,...,0} --- range = 0
B = {1, 2, 3, 4, ..., 9} --- range = 8

and the range of B > the range of A.

Or we could have:

A = {9,8,7,6,5,4,3,2,1} --- range = 8
B = {10,10,10,10,...,10} --- range = 0

and the range of B < the range of A.

So the answer should be E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by ricky » Mon Aug 04, 2008 7:17 am
Thanx a lot Ian.Its clear now
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