Data Sufficiency

For Students in Class A, the range of their heights is r centimeters and the greatest height is g centimeters. For students in Class B, the range of their heights is s centimeters and greatest height is h centimeters. Is the least height of students in Class A greater than the least height of students in Class B?

1.) r<s
2.) g>h

Please post OA and explanation

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https://www.beatthegmat.com/students-height-t38839.html

Neither statement is sufficient on its own- clearly we need to know about r, s, g and h here. Together we know:

s > r
g > h

These inequalities are in the same direction, so we can add them:

s+g > r+h
g-r > h-s

So we've shown that the smallest height in class A, which is g-r, is larger than the smallest height in class B, which is h-s. C.

A

(g-r),.....................,g


B

(h-s),...................,h


have to show (g-r)>(h-s)
=>(g-h)+ (s-r)>0

hence C it is

Let La be the lowest height of the person in Class A, and Lb be the same for Class B. Then,

s + Lb < r + La ------> La - Lb > r - s > 0

g - La < h - Lb --------> La - Lb > g - h > 0

Since La - Lb > 0, La > Lb always given both conditions.