kkadvent wrote:For Students in Class A the range of height is r cm and the greatest height is g cm, For the students in class B the range of their height is s cm and the greatest height is h cm. Is the least height of student in class A greater than the least height of student in class B?
1) r<s
2) g>h
In a set, if the largest value is L, and the range is R, then from the definition of the range, the smallest element S is equal to L-R.
So here, we want to know if g-r > h - s, or rewriting this, if g+s > h + r. Neither statement is sufficient alone, but if you line up the two inequalities and add them:
r < s
h < g
r+h < g+s
which is exactly what we wanted to prove.
You may also be able to see the answer conceptually. The range is the distance between the largest and smallest elements in a set. If in class A the greatest height is larger than in B, and the range is smaller, then the least height in A certainly must be greater than the least height in B.
