For the students in class A, the range of their heights is r

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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

by melguy » Sat Jun 22, 2013 12:08 am

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

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Source: Beat The GMAT — Data Sufficiency | Sat Jun 22, 2013 12:08 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Jun 22, 2013 2:53 am

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.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Nov 13, 2016 6:00 am

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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Nov 13, 2016 6:04 am

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

1) r < s
2) g > h

Given: For the students in class A , the range of their heights is r cms and the greatest height is g cms.
Range = greatest height - least height.
Rearrange this to get: least height = greatest height - range.
So, for class A, the least height = g - r

Given: For the students in class B, the range of their heights is s cms and the greatest height is h cms.
So, for class B, the least height = h - s

Target question: Is the least height of the students class A greater than the least height of the students in class B?

We can rephrase this as...
REPHRASED target question: Is h - s < g - r

Since it's often easier to deal with sums than with differences, let's rephrase the target question one more time by taking h - s < g - r and adding s and r to both sides to get...
RE-REPHRASED target question: Is h + r < g + s

Perfect!! Now that we've rephrased the target question, this question is relatively easy to solve.

Aside: We have a video with tips on REPHRASINGthe target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: r < s
Since we have no information about h and g, we cannot answer the RE-REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: g > h
Since we have no information about r and s, we cannot answer the RE-REPHRASED target question with certainty.
So, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: If we have two inequalities with the inequality symbols FACING THE SAME DIRECTION, we can add them.

Statement 1: r < s
Statement 2: h < g [I rewrote the inequality so that it's facing the same direction as that in statement 1]
ADD the inequalities to get: h + r < g + s
Perfect!! Since we can answer the RE-REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Thu Nov 17, 2016 1:55 pm

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Thu Nov 17, 2016 7:18 pm

Hi All,

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

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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Rich

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