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The range of set A is r. If a number with a value equal to r

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VP
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The range of set A is r. If a number with a value equal to r [#permalink]  12 Mar 2008, 10:18
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The range of set A is r. If a number with a value equal to r is added to set A,
will the range of set A increase?

(1) All numbers in the set are positive
(2) The mean of the new set is smaller than R
Director
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Re: gprep stats [#permalink]  12 Mar 2008, 19:02
Range of a set is = Maximum Value in set - Minimum Value in set

Statement 1:
Tells us that all the numbers in set are +ve. So in this case Maximum Value - Minimum value will result in a number that is lesser than Maximum value of range but more than minimum value. Any number added to set that is not changing maximum value or minimum value will not change the range of set.
So this alone can answer the question.

Statement 2:
Tells us that the mean of the new set is smaller than R. What about the mean of old set, was that smaller than R as well. Moreover it may also lead to think -ve numbers are involved. So this alone is not sufficient.

Senior Manager
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Re: gprep stats [#permalink]  12 Mar 2008, 21:13
I am getting C

Statement 1:
took two random example 6,7,10 and 3,5,6,7 - in the first case range was increased and in the later case range remained same. so insufficient.

Statement 2:
Got different results for positive numbers and a combination of positive and negative. (eg, 2,6,9 and -2,-1,1)

Combined - for positive numbers, given the second condition, always got same range. Somehow I am not confident though because this is all driven by examples. But I would go with C in GMAT.
VP
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Re: gprep stats [#permalink]  12 Mar 2008, 21:46
sreehari wrote:
I am getting C

Statement 1:
took two random example 6,7,10 and 3,5,6,7 - in the first case range was increased and in the later case range remained same. so insufficient.

Statement 2:
Got different results for positive numbers and a combination of positive and negative. (eg, 2,6,9 and -2,-1,1)

Combined - for positive numbers, given the second condition, always got same range. Somehow I am not confident though because this is all driven by examples. But I would go with C in GMAT.

OA is C in fact. would you mind showing your reasoning with numerical examples?
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Re: gprep stats [#permalink]  13 Mar 2008, 06:50
[quote="marcodonzelli]
OA is C in fact. would you mind showing your reasoning with numerical examples?[/quote]

I picked the series in such a way that when range is added to the series, in one case it increases the range, and in another case it keeps it same.

6,7,10 becomes 4, 6,7,10 - increases the range from 4 to 6
3,5,6,7 becomes - 3,4,5,6,7 - doesn't change the range (4)

for the second statement though it wasn't easy - had to try few different series to come up with ones that satisfy the condition.
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Re: gprep stats [#permalink]  13 Mar 2008, 23:25
sreehari wrote:
[

for example, the second statement could be:

-4 and -6, range 2, which added would give a range of 8, higher than before and mean 8/3, less than new R

anyway:

1 and 4, range 3, new mean 8/3 and range is 3 but range is always the same.

only C is suff, since with positive numbers and the new mean less than the new range , the range would not increase.

how is it possible to answer this one in 2 mins?
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Re: gprep stats [#permalink]  14 Mar 2008, 04:33
Expert's post
C

there are three options:

A) -------0-----------------r---------------[AAAAAAAAAAAAA] the range of set A increases
B) -------0-[AAAAAAAAAArA]------------------------------- the range of set A does not increase
C) --[AA0AAAAAAAAA]--r------------------------------------ the range of set A increases

1. A and B survive. insuff.
2. B and C survive. insuff.
1.&2 only B survives. suff.
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Re: gprep stats   [#permalink] 14 Mar 2008, 04:33
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