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Range

by gmat009 » Thu Oct 09, 2008 9:13 pm
The range of set A is R. A number having a value equal to R, is added to set A. Will the range of set A increase?
1) All numbers in Set A are positive.
2) The mean of the new set is smaller than R.
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by stop@800 » Thu Oct 09, 2008 11:54 pm
Good one :)

A
let set be all nos from 10 .... 20
range = 10

if we add 10, range no change



let set be all nos from 100 .... 110
range = 10

if we add 10, range will change

so A insuff




B [we can use negative nos also to invalidate this point but let me try with +ve ones]
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

so insufficient



A+B
The example of point B still holds



so IMO ans is E

whats the OA??
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by raju232007 » Fri Oct 10, 2008 2:59 am
I agree with @stop800...E should be the ans..whats the OA?
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by gmat009 » Fri Oct 10, 2008 6:10 am
stop@800 wrote:Good one :)

A
let set be all nos from 10 .... 20
range = 10

if we add 10, range no change



let set be all nos from 100 .... 110
range = 10

if we add 10, range will change

so A insuff




B [we can use negative nos also to invalidate this point but let me try with +ve ones]
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]

so insufficient



A+B
The example of point B still holds



so IMO ans is E

whats the OA??
I did exactly same way and got E but OA is A and it is not wrong.
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by kris610 » Fri Oct 10, 2008 6:23 pm
I'm not sure how A would suffice.

As long as the Largest number in the set is smaller than twice the shortest number, the range will increase.

2 2 2 => add 0 and the new range is 2. range of original set was 0.

2 3 => add 1 and the new range is 2. range of original set was 1

2 2 6 => add 4 and the new range is equal to the old range -- 4.

In both the cases all the numbers are positive and you get a Yes and a No.

How can it be A?
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by Ian Stewart » Fri Oct 10, 2008 7:06 pm
gmat009 wrote: I did exactly same way and got E but OA is A and it is not wrong.
Why are you so convinced the OA is not wrong? It is wrong, quite clearly, as the many examples above demonstrate.
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by youngwolf » Mon Oct 20, 2008 8:17 am
stop@800 wrote:Good one :)
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]
There are few flaws in stop@800 solution.
The problem says “mean is smaller than R” and not “the mean is smaller”
You cannot add 5 nor 14, because they are not the range. Than range in that case is 10.

My answer is C.
“The mean of the new set is smaller than R.” means that R is actually bigger than the mean of the new set. We need to know though if R is in the set or has a value bigger than any element of the set. For later, it means that R will be bigger than the initial range since all elements are positive (and we know from the stem that R equals the range).
We are left with “mean"<R<biggest element of the set which means the range will not change.

Please provide me with an example that proves me wrong.
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by stop@800 » Mon Oct 20, 2008 1:02 pm
youngwolf wrote:
stop@800 wrote:Good one :)
mean is smaller
means added no is less than prev mean

Example
let set be all nos from 10 ... 20
range = 10
mean = 15

added no = 5 [range will change]
added no = 14[range will not change]
There are few flaws in stop@800 solution.
The problem says “mean is smaller than R” and not “the mean is smaller”
Good Catch. Thanks
You cannot add 5 nor 14, because they are not the range. Than range in that case is 10.

My answer is C.
“The mean of the new set is smaller than R.” means that R is actually bigger than the mean of the new set. We need to know though if R is in the set or has a value bigger than any element of the set. For later, it means that R will be bigger than the initial range since all elements are positive (and we know from the stem that R equals the range).
We are left with “mean"<R<biggest element of the set which means the range will not change.

Please provide me with an example that proves me wrong.
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