melguy wrote:For students in class A, the range in height is r and the greatest height is g. For students in class B, the range in height is s and the greatest height is h. Is the least height in class A greater than the least height of students in class B?

1) r<s
2) g>h

Range = greatest - least.
Thus:
Least = greatest - range.

In class A, least = greatest - range = g-r.
In class B, least = greatest - range = h-s.

If the least height in A is greater than the least height in B, we get:
g-r > h-s
g+s > h+r.

Question rephrased: Is g+s > h+r?

Statement 1: r < s
No information about g or h.
INSUFFICIENT.

Statement 2: g > h
No information about r or s.
INSUFFICIENT.

Statements combined:
Inequalities can be ADDED TOGETHER.
When we add, the < > must face the SAME DIRECTION in each inequality.
To match g > h in statement 2, rephrase r < s in statement 1 as s > r.
Adding together g > h and s > r, we get:
g+s > h+r.
SUFFICIENT.

The correct answer is C.

melguy wrote:Please help me with a 2 min approach to this problem. I have written a page on my rough work book but still not able to get an answer. I searched on the forum and could not understand the explanations.

Thanks

Please check the solution as attached

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

(1) r < s

(2) g > h

We are given that for the students in class A, the tallest student is g cm and the range in heights is r cm. If we let a = least height in class A, we can create the following equation:

g - r = a

We are also given that for the students in class B, the tallest student is h cm and the range in heights is s cm. If we let b = least height in class B, we can create the following equation:

h - s = b

We need to determine whether the height of the shortest student in class A is greater than that of the shortest student in class B.


That is, we need to determine whether a > b or whether g - r > h - s.

Statement One Alone:

r < s

Since we don't know anything about g and h, we cannot determine whether g - r > h - s.

Statement Two Alone:

g > h

Since we don't know anything about r and s, we can't determine whether g - r > h - s.

Statements One and Two Together:

From the two statements, we know r < s and g > h. We can multiply both sides of r < s by -1 (don't forget to switch the inequality sign) to get: -r > -s.

Adding the two inequalities gives us:

(g > h)
+ (-r > -s)
g - r > h - s

Since we have determined that g - r IS GREATER than h - s, we have answered the question.

Answer: C