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I am not pretty sure but i think it is C)
A and B by itself are both insufficient. The third value is missing.
From both A) X=5+Y and B) X=10+Z and 5+Y=10+Z then Y=5+Z and from B) X=10+Z, then the values are Z, 5+Z, 10+Z and the deviation is 5 as it is in the stem.

Statement 1 says , x - y = 5.
But we dont know about z to decide.

Statement 2 says x-z = 10.
But we dont know position of y.

But combing these two,
we know that the numbers come in the order x y z with a difference of 5 each. SD = 5 . [We do not need value of y. We just want to know the difference between other nos and y. ]

Agree with BG.
Think it's C.
Try to pick up numbers
let's say y=15 then x=5+y=15+5=20 and z=x-10=10. So we have 10 15 20 and deviation is the same...moreover in general case as BG has shown we have numbers like Z,Z+5,Z+10 and we know that D(x)=sqrt((X-avg(X,Y,Z))^2+(Y-avg(X,Y,Z))^2+(Z-avg(X,Y,Z))^2)/(n-1) so we can see that the difference in bracket would be always the same if the number follow the pattern Z,Z+5,Z+10....

I am not pretty sure but i think it is C) A and B by itself are both insufficient. The third value is missing. From both A) X=5+Y and B) X=10+Z and 5+Y=10+Z then Y=5+Z and from B) X=10+Z, then the values are Z, 5+Z, 10+Z and the deviation is 5 as it is in the stem.

Great explanation! I guess I fell for the trap.

OA pls? _________________

Don't be afraid to take a flying leap of faith.. If you risk nothing, than you gain nothing...

I am not pretty sure but i think it is C) A and B by itself are both insufficient. The third value is missing. From both A) X=5+Y and B) X=10+Z and 5+Y=10+Z then Y=5+Z and from B) X=10+Z, then the values are Z, 5+Z, 10+Z and the deviation is 5 as it is in the stem.

Great explanation! I guess I fell for the trap. OA pls?

sorry guys i forget to apply range concept. if the range of a given number of observations is equal with the same no of observations, the SDs of these observations are equal and its toooooo late to apply this concept.

i misjudged that SD is higher with higher values....