800 score math problem There are two sets A and B

by **Guest** Wed Apr 23, 2008 4:54 pm

There are two sets A and B. Which set contains the maximum value?
(1) The range of A is bigger than that of B
(2) The Minimum value of A is bigger than of B

I got the answer C. Can anyone prove this C is wrong?

by pt Sat Apr 26, 2008 4:18 pm

Unless I am missing something here, C seems right.

by **RonPurewal** Tue Apr 29, 2008 6:35 am

nah, c is correct.

i'll assume that you know why each statement alone is insufficient, and cut directly to the chase.

take the statements together:
let Ma stand for the minimum of set a and Mb the minimum of set b. similarly, let Ra be the range of set a and Rb the range of set b.

then
(1) says Ra > Rb
(2) says Ma > Mb

note that the maximum of set a is Ma + Ra, and the maximum of set 2 is Mb + Rb (because that's what the range is: the distance between the max and min). but we know the former is bigger, by combining the inequalities contained in the 2 statements above.