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# A series of 5 numbers is 3, 4, 5, 5, x, is the range greater

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Senior Manager
Joined: 08 Nov 2010
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Kudos [?]: 110 [0], given: 161

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater [#permalink]

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06 Jun 2011, 11:53
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A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?
I - the median of the numbers is greater than the mean
II - the median is 4

Hey guys,

Any good way to do it quickly?
[Reveal] Spoiler: OA

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Kudos [?]: 174 [1] , given: 20

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06 Jun 2011, 12:32
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KUDOS
From B it is easy to determine that its not sufficient alone. the value of x can be for example 2, 3 or 4.

For A, i only have one method of solution, that is 2 plug in atleast two different values of x and try to prove the statement otherwise. And the statement doesn't suffice.
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06 Jun 2011, 12:42
Isnt there a more "mathematical" way to increase certainty?
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Kudos [?]: 3 [0], given: 29

A series of 5 numbers is 3, 4, 5, 5, x, is the range greater [#permalink]

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07 Mar 2017, 06:02
(1) Let's pick number 4 for "x"
In this case mean=4,4
R=5-3=2 (equal to 2)
Now pick number 6 for "x"
In this case ,mean=4,6
R=6-3=3 (more than 2)
Insufficient.
(2) Median=4 thus "x" lies in the interval x<=4
Pick number 4, then R=5-3=2 (equal to 2)
Pick number 0, then R=5-0=5 (more than 2)
Insufficient.
(1)+(2)
Median=4 and median should be more than mean
These constrains gives us that x should be less then 3 to conform to both the conditions, in all those cases R will be more than 2.
x=4, mean =4,2 doesn't conform to (1)
x=3, mean=4 doesn't conform to (1)
x=2, mean=3,8; R=5-2=3 more than 2 OK
x=1, mean= 3,6; R=5-1=4 more than 2 OK
Hence both (1) and (2) are sufficient to state that R in subject set would be more than 2. Answer C.
A series of 5 numbers is 3, 4, 5, 5, x, is the range greater   [#permalink] 07 Mar 2017, 06:02
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