mean/median ds

Don't know; the sum of the three numbers is equal to three times one number. Do you know a set that fullfills this condition (2) but in which the mean isn't equal to the median?

Hmm. I understand it now sir/madam(?) THANK YOU!!

It will work only if the numbers are of the form you mentioned.
(-n,0,n) or (n,n,n). Hence SUFFICIENT.

Therefor D.

Another classic case of "Answer Biasing" as duttsit would like to call it. I just rejected (2) because I didn't like it

D it is.

Say numbers are x,y,z and these are in ascending order, So median here is y

Range = z-x

St1:

Range = 2 * (z-y)

so z-x = 2z-2y
-x = z-2y
0 = z+x -2y
y = z+x -2y + y
i.e 3y = x+y+z
y = (x+y+z)/3

So median = mean SUFF

St2:
this have three cases

1. x+y+z = 3x
x + (x +a) + (x+b) = 3x
so a + b = 0 (Remember that a and b are +ve)
This means all must be equal to x i.e mean = median
2. x+y+z = 3y
(y-a) + y + y(+b) = 3y
so b-a = 0 i.e a = b (Remember that a and b are +ve)
This means all must be equal to y i.e mean = median

3. x+y+z = 3z
(z-a) + (z-b) + z = 3z
so -a-b = 0 i.e a +b = 0 (Remember that a and b are +ve)
This means all must be equal to z i.e mean = median

SUFF

En contraire, I'm sorry giddi that I haven't made it clear enough.

dahiyas approach is clearer and intuitive. One should strive always for clarity even when the time ticks.

By the way, I'm male.

I would go with D

The nos are a, b, c

i) c-a=2(c-b)=>b=(a+c)/2 =>which is AP which means mean=median
so SUFFICIENT
ii) a+b+c=2a/2b/2c=>Again an AP so SUFFICIENT

So ans is D

the oa is D

great explanation guys

btw how long did it take you to solve?

Close to 1.5 min..
The real trick was to know that the series is an AP..Once you get that its harly a matter of 2 sec

I also got D. Could not fail the second statement. Looks like 3 times one number always means 3 time median.

AP= Arithmetic Progression

example
5 +10 +15 + 20 + 25 +... + 100

AP formula
S = n/2 ((2a + (n-1)*d) = 20/2 (5*2 + 19*5) = 1050