A series of 5 numbers is 3, 4, 5, 5, x, is the range greater than 2?

(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.

VeritasPrepKarishma, Bunuel

Would appreciate if you can share your approach to this problem.

In increasing order:

3, 4, 5, 5

x could be placed anywhere - "before 3", "between 3 and 4", "between 4 and 5", "at 5" or "after 5"

The range will be greater than 2 in case x is placed "before 3" or "after 5".

I - the median of the numbers is greater than the mean

Median can only be 4 or 5, no matter where x is placed.
If median is 4, then mean is lower than 4 which means x is lower than 3 (to balance the deviation on the right).
If median is 5, then mean is lower than 5 and x must be 5 or greater.
Not sufficient

II - the median is 4
If median is 4, it means x is either "before 3" or "between 3 and 4".
Not sufficient.

Using both, we know that the median is 4 and mean is lower than 4 which implies that x is lower than 3. So range will be more than 2. Sufficient.

Answer (C)

If you are unsure of the deviations concept, check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... eviations/

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