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DS: Range

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by parulmahajan89 » Sat Sep 28, 2013 3:47 pm
For students in class A, the range of their heights is r centimeters and greatest height is g centimeters. For students in Class B, their range of heights is s centimeters and greatest height is h centimeters.Is the least height of student in class A greater than least height of student in class B?

1) r< s
2) g > h
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Source: — Data Sufficiency |
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by mevicks » Sat Sep 28, 2013 7:03 pm
Step 1: Simplify:

Do note here that all are positive numbers here!

Class A:
Max = g
Max - Min = r
g - Min = r
Min = (g - r)


Class B:
Max = h
Min = (h - s)

Q: Is (g - r) > (h - s) ?
or Is (g + s) > (h + r) ?

Step 2: Solve:

St1: Gives nothing about g and h, INSUFFICIENT
St1: Gives nothing about r and s, INSUFFICIENT

St1+St2 :
s > r
g > h
(g + s) > (h + r)... Add the above two equations
SUFFICIENT

If you want you can go ahead and verify this by plugging in simple numbers
2 > 1 ... A
2 > 1 ... B
2 + 2 > 1 + 1
etc.

[spoiler]Answer : C[/spoiler]

The key takeaway in such problems is noticing that everything is positive so you can play around with the inequalities easily.

Regards,
Vivek
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by mevicks » Sat Sep 28, 2013 7:08 pm
Similar OG12 problem DS#38 (or DS#43 in OG13)

Regards,
Vivek
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by [email protected] » Sun Sep 29, 2013 11:06 am
Hi parulmahajan89,

This DS question is more about patterns and relationships between variables than about math skills.

mevicks has properly explained the math; I'm going to explain the pattern.

Class A:
Range of heights = R
Max height = G

Class B:
Range of heights = S
Max height = H

We're asked if the LEAST height of Class A > LEAST height of Class B. This is a Yes/No question. To figure out the LEAST height, we're going to need to understand the relationship between the Max height and the range for each class.

Fact 1: Tells us that the Range for Class A < Range for Class B. There's nothing here about the Max heights though.
Fact 1 is INSUFFICIENT

Fact 2: Tells us that the Max height for Class A > Max height for Class B. There's nothing here about the ranges though.
Fact 2 is INSUFFICIENT

Combining Facts:
We know that Class A has a HIGHER Max height and a LOWER Range than Class B. By definition, that would mean that the LEAST height for Class A was greater than the Least height for B (since Class A's heights are "closer together" than Class B's). The answer to the question is YES.

Final Answer: C

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by GMATGuruNY » Sun Sep 29, 2013 1:33 pm
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.
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