range and maximum= how did they get the answer?

[coolgirl26]

answer is the square..please help or give your explanation

[scoobydooby]

let the least height in class A be a and the least height in class B be b
given r=g-a, and s=h-b
to find if a>b?

1) r<s
=> g-a<h-b
=>g-h<a-b
we do not know the sign of g-h, if g-h>0, a-b>0 or a>b
if g-h<0; a-b<0 or a<b
not sufficient


2) g>h
we have no information about the range. cant say if a>b.
not sufficient

together,
g>h
g-h>0 or a-b>0 (from statement 1)
=>a>b

hence, C

[vittalgmat]

Excellent explanation Scoobydooby.

Here is my conceptual explanation.

Stmt 1: r < s.

Range is ignorant of actual max and min values. It is knows/tells us the difference between.
So one could have range r < s but the actual min and max values can be different.

eg. 10 - 5 = 500 - 495. If each of the numbers were lengths of some object, (max and min), then with just the value of the range, one cannot say which group had longest object.
However, if we know the one more property (either max or min or a relationship between the max/min with that of other) , we can figure out whch group has longest object.

This is exactly what stmt 2 tells us.
So together we can figure out the answer.

HT helps
-V