For students in class A, the range in height

[Guest]

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

The answer is c.

[RonPurewal]

remember that
range = greatest - least

which can be arranged to
greatest = least + range
or
least = greatest - range

--

(1)
these data concern ranges only; there is no indication whatsoever of how the heights compare.
insufficient

(2)
the greatest height in class a is taller than its counterpart in class b, but we know nothing about the ranges; if class a has a wider spread, its least height could well be shorter than that of class b.
insufficient

(together)
greatest height in class a = g - r
greatest height in class b = h - s
the given inequalities imply that g - r > h - s
sufficient

--

alternatively, you could have formulated g - r and h - s at the beginning of the problem (i.e., before considering statements (1) and (2) alone); these formulations make it perhaps even easier to see that (1) and (2) individually are insufficient.

[00behzad00]

Can you please explain how you combined the two inequalities to get g-r > h-s ? I tried adding togheter and I get g-s>h-r which isn't what I need. Confused as to how these inequalities were combined.

[lj6871849]

Can you please explain how you combined the two inequalities to get g-r > h-s ? I tried adding togheter and I get g-s>h-r which isn't what I need. Confused as to how these inequalities were combined.

1) r<s
2) g>h

1st make both the inequality point the same direction -

r<s
h<g

Add

r + h < s + g ------- 1

Now we can add / subtract both sides of the inequality (just be careful when multiply or divide - if the variables are negative you need to change the dir of the inequality )

subtract -r-s from both sides of the inequality 1..... we get what we need.....

h - s < g - r

Cheers

[jlucero]

Can you please explain how you combined the two inequalities to get g-r > h-s ? I tried adding togheter and I get g-s>h-r which isn't what I need. Confused as to how these inequalities were combined.

1) r<s
2) g>h

1st make both the inequality point the same direction -

r<s
h<g

Add

r + h < s + g ------- 1

Now we can add / subtract both sides of the inequality (just be careful when multiply or divide - if the variables are negative you need to change the dir of the inequality )

subtract -r-s from both sides of the inequality 1..... we get what we need.....

h - s < g - r

Cheers

Great explanation with one tiny edit- you can add the sides of an inequality, but you can't subtract, multiply or divide:

2<4
1<100

add:
3<104

subtract:
1<-96

Fractions and negative numbers will make multiplying and dividing tricky too. Stick to adding when comparing inequalities.

[sachin.w]

I chose C after finding that A and B alone are insufficient on the basis of following observation.

g-La=r

h-Lb=s

La=least height in A and Lb=least height in B

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

If we use the above and observe the first 2 equations,
La has to be greater than Lb.

[jnelson0612]

I chose C after finding that A and B alone are insufficient on the basis of following observation.

g-La=r

h-Lb=s

La=least height in A and Lb=least height in B

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

If we use the above and observe the first 2 equations,
La has to be greater than Lb.

Yes, correct!

[asharma8080]

I recently got this wrong and wondering how I can think more logically about this?

My approach on this was to plug-in numbers. I started with
A = 102, 103, 104
r, Range of A = 104-102 = 2
Highest height = 104
Lowest Height = 102

B = 5, 6, 8
Highest height = 8
Lowest Height = 5
s, Range of B = 8-5 = 3

For these numbers, r < s and lowest height of A > lowest height of B.

Then, I tried thinking of another case and came up with. During the actual problem, I got stuck here. But afterwards, here is what I produced:

A = 2, 3, 4
r, Range of A = 4-2 = 2
Highest height = 4
Lowest Height = 2

B = 3,4,5,6
Highest height = 6
Lowest Height = 3
s, Range of B = 6-3 = 3

For these numbers, r < s BUT lowest height of B > lowest height of B.

Statement 1 is NOT sufficient.

I did not approach this as an inequalities approach, and I see that knowing that Range = Highest - Lowest is not sufficient but I should be able to massage around that equation to meet my needs.

[RonPurewal]

well, it's good that you know how to test numbers on DS problems -- honestly, that's the most important single piece of strategy that you can have for this exam -- but testing numbers for statement 1 is a total waste of time here.

before you start doing work, LOOK at WHAT YOU WANT and at WHAT YOU HAVE!

in the case of statement 1, all you have is two ranges... but you WANT an answer to a question about specific heights (in different sets).
you should be able to realize (without plugging numbers) that the ranges, alone, are not going to help you answer that question.