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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DS: Range
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parulmahajan89
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mevicks
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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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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GMATGuruNY
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Range = greatest - least.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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