anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}
The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?
The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?
consider this, {-3, 0, 1, 2}. The sum of the largest and the smallest is not 0 (-3 + 2 = 1).
However, the mean of the set is still 0, and multiplying any constant to the set will not change the mean of the set.
If you doubt that, consider -3=x, 1=y, 2=z.
x = y + z
Multiplying ANY constant C to the numbers, the sum of the positives and the negatives will not change.
xC = yC + zC = C(y + z)
Hope this helps that II is not ALWAYS true.