GMAT Prep DI question- Experts please reply ASAP

Given

In class A

Greatest height = g
range = r
Since , range = greatest - least
=> least height = g - r

In class B

Greatest height = h
range = s
=> least height = h - s

We are asked
Is g - r > h - s?

Statement 1:
no idea about g and h
Hence insufficient

Statement 2:
no idea about r and s
Hence insufficient

Combining both the statement

let r = 4 and s = 5
and let g = 8 and h = 7

g - r = 8 - 4 = 4
h - s = 7 - 5 = 2

Clearly 4>2
the answer to the question is a definite yes, hence sufficient

The correct answer is A

Note: Range=Greatest-Least

From the given data,
Least height of A=g-r ............(X)
Least height of B=h-s.............(Y)

To prove least height of A class is greater than least height of B class, we prove that
[(Least height of A) - (Least height of B)] > 0

From eqns (X) & (Y)
[(g-r)-(h-s)]>0 ...........(Z)

Taking options
(1) r<s or s-r>0
This does not give complete information.
INSUFFICIENT

(2) g>h or g-h>0
Even this does not give complete information.
INSUFFICIENT

Taking combined, we get
s-r>0 and g-h>0

From Eqn (Z) and given that s-r>0 and g-h>0,
We can rewrite it as,
[(s-r)+(g-h)]>0
SUFFICIENT

[spoiler]Ans: Option C[/spoiler]

anks17 wrote:GMAT Experts,

Can you plz confirm the right way to approach the attached question.Assumed #s to solve it but just checking for a better/shorter method if any.

I would do it this way.

First of all we need to realize that its an inequality question which is asking us.

Is least value of set A < least value of set S.
Now least value of A = Greatest A - Range of A = g-r
And least value of B = Greatest B - Range of B = h-s

So the question becomes, Is g-r > h-s
=> Is g+s > h+r (I rephrased it because I know for most people, + signs are easier to deal with).

Now its easy.

1) r<s => s>r. We don't know anything about g or h. Insufficient.
2) g>h. Again, we now nothing about s and r. Insufficient.

Together:

s > r
g > h
Since left sides of both inequalities are larger than the right sides we can add the two.
s + g > h + r. This is what we sought out to find. Sufficient.

C is correct.