Data Sufficiency

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

1.r<S
2.g>h

I am not sure that you need to pick numbers here.

You can look at it logically. With statement 1 you know that the range for class A is smaller than the range for class B. This does not help out enough in telling you which class has the shortest person, because even though class A has a smaller range they could be starting with a tallest person that is not as tall.

When you add statement 2 you see that that the greatest height for class A is larger than that for class B.

So with both statements together you are starting with a taller height for the tallest student in class A and you have a smaller range. That guarantees you a taller shortest person in A when compared to B.

OA C

Of course you could plug in numbers as well!

Just make the tallest student in class A a certain height of 10 (or whatever you choose). Now make the tallest in B a shorter height of 8 (or your choice).

Now make the range of class A smaller than that of B. so the range for A is 4 making the shortest student a height of 6. Make the range for B larger than this...so 5. That makes the shortest person in class B a height of 3. Since 6 is always > 3 this is sufficient and the answer is C.

parulmahajan89 wrote:For the students in class A, the range of their heights is r cm and greatest height is g cm. For students in class B, the range of their height is s cm and greatest height is h cm.Is the least height of a student in class A greater than least height of student in Class B?

1.r<S
2.g>h

Hi Parulmahajan89,
We know that Range is Greatest - Least
So let Least Height in Class A be X
Least Height in Class B be Y

Given: g-X = r ==> X = g-r
h-Y = s ==> Y = h-s

To Find: X>Y (Yes/No Question)

or g-r > h-s ?

Statement1 : r<S
H and G are unsaid. So insufficient.

Statement2 : g>h

R and S are unsaid. So insufficient.

1+2
Lets pick any value such that G>H and S>R
So G = 10 and H = 8
S= 5
R = 3

so 10-3 >8-5 ==> 7>3(Sufficient.)

(You can test for any value.)

Hence sufficient.

Answer is C

Regards,
Uva.

Thanks everyone for your help

Thanks everyone for your help

Here's another quick method:

1.r<S means s = r + k
2.g>h means g = h + t where k and t are positive unknown values

Class A: minimum = a = g - r = h + t - r
Class B: minimum = b = h - s = h - r - k

Comparing a and b, we can delete the red terms to get:

t > -k

Therefore a > b

Answer = yes

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

Alternate approach:

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.