SETS

[goyalsau]

s the range of a combined set (S,T) bigger than the sum of ranges of sets S and T?

(1) The largest element of T is bigger than the largest element of S
(2) The smallest element of T is bigger than the largest element of S

[spoiler]OA is B
How?[/spoiler]

[shovan85]

Smallest of T > Largest of S
Range of combined = (Largest of T - Smallest of S) = R
Range of T = (Largest of T - Smallest of T) = r1
Range of S = (Largest of S - Smallest of S) = r2

r1+r2 = (Largest of T - Smallest of T) + (Largest of S - Smallest of S) = (Largest of T - Smallest of S) - Smallest of T + Largest
of S = R - (something +ve)

Thus r1+r2 < R. (Suff)

Hope this helps.

[shovan85]

r1+r2 = (Largest of T - Smallest of T) + (Largest of S - Smallest of S) = (Largest of T - Smallest of S) - Smallest of T + Largest
of S = R - (something +ve)

Thus r1+r2 < R. (Suff)

- Smallest of T + Largest of S = -ve as Smallest of T > Largest of S

Thus r1+r2= R - diff.