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

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For the students in class A, the range of their heights is r [#permalink]

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23 Feb 2012, 08:12
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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
[Reveal] Spoiler: OA

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Re: For the students in class A, the range of their heights is r [#permalink]

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23 Feb 2012, 09:32
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BANON wrote:
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

Each statement alone is clearly insufficient. Now, when taken together the question becomes easier if you just visualize it. Given: G>H and R<S:

------------(MIN)----G, red is the range of A, r;
(MIN)------------H, blue is the range of B, s.

You can literally see that the least height of the students in class A is greater than the least height of the students in class B.

Answer: C.

Hope it's clear.
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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jul 2012, 01:39
Hi Bunuel ,

According to me C will not give the answer because , When i plug in the values say

g=15 and h = 10
r= 2 and s = 3

the max value for A is 15 and the minimum value will be 1 (since the range is 2)
The max value for B is 10 and the minimum value will be 1 (since the range is 3)

the min value for both is 1 .. (we will not be able to ans question "Is the least height of the students in class A is greater than the least height of the students in class B"

Here , A=B

In one more instance ,

g=10 and h =9
r=4 and s=5

the min value for A will be 2
the min value for B will be 4

Here,

A < B

One more instance

g=12 and h =10
r=7 and s=8

the min value for A is 5
the min value for B is 2

here A > B

I was getting 3 different values.
So i marked E as my option. Can you please tell me what i am missing here.

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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jul 2012, 02:16
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BANON wrote:
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

QUESTION A>B?........Where A is the smallest hight of class A and B is the smallest hight of class B

we can simply form an equation from this problem
from the question stem we can draw this as per my undestanding G-A=R, H-B=S, G for greatest hight and A for smallest in class A, R for range, H for greatest in B CLASS, B for smallest hight in B class, S for range in B CLASS
from stmnet 1. we can get R-S<0 AND FROM stmnt 2. we can get G-H>0

SO WE have four equations
1.G-A=R
2.H-B=S or H= B+S
3.R-S<0
4.G-H>0
NOW action

Eq.3.------R-S<0 OR G-A-S<0( putting value of R.) or -A<S-G OR A>G-S
Eq 4......... G-H>0 OR G-B-S>0 (putting value of H.) OR -B>S-G OR B<G-S
FROM this two we can easily form this
B<G-S<A..................WHERE ALL OF THE ACRONYMES ARE POSITIVE NOT NEGATIVE SO B MUST BE LESS THAN A

THAT directs us to combine these two statements for the solution

hence C

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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jul 2012, 05:34
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Desperate123 wrote:
Hi Bunuel ,

According to me C will not give the answer because , When i plug in the values say

g=15 and h = 10
r= 2 and s = 3

the max value for A is 15 and the minimum value will be 1 (since the range is 2)
The max value for B is 10 and the minimum value will be 1 (since the range is 3)

the min value for both is 1 .. (we will not be able to ans question "Is the least height of the students in class A is greater than the least height of the students in class B"

Here , A=B

In one more instance ,

g=10 and h =9
r=4 and s=5

the min value for A will be 2
the min value for B will be 4

Here,

A < B

One more instance

g=12 and h =10
r=7 and s=8

the min value for A is 5
the min value for B is 2

here A > B

I was getting 3 different values.
So i marked E as my option. Can you please tell me what i am missing here.

The red parts above are not correct. How did you get those values there? Anyway:

The range of a set is the difference between the largest and smallest elements in the set.

Which means that if: g=15, h = 10, r= 2 and s = 3, then:

For A: {Largest}-{Smallest}={Range} --> 15-{Smallest}=2 --> {Smallest}=13, not 1 as you've written.
For B: {Largest}-{Smallest}={Range} --> 10-{Smallest}=3 --> {Smallest}=7, not 1 as you've written.

13>7.

The same for the second example in your post.

Hope it's clear.
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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jul 2012, 13:40
Bunuel wrote:
Desperate123 wrote:
Hi Bunuel ,

According to me C will not give the answer because , When i plug in the values say

g=15 and h = 10
r= 2 and s = 3

the max value for A is 15 and the minimum value will be 1 (since the range is 2)
The max value for B is 10 and the minimum value will be 1 (since the range is 3)

the min value for both is 1 .. (we will not be able to ans question "Is the least height of the students in class A is greater than the least height of the students in class B"

Here , A=B

In one more instance ,

g=10 and h =9
r=4 and s=5

the min value for A will be 2
the min value for B will be 4

Here,

A < B

One more instance

g=12 and h =10
r=7 and s=8

the min value for A is 5
the min value for B is 2

here A > B

I was getting 3 different values.
So i marked E as my option. Can you please tell me what i am missing here.

The red parts above are not correct. How did you get those values there? Anyway:

The range of a set is the difference between the largest and smallest elements in the set.

Which means that if: g=15, h = 10, r= 2 and s = 3, then:

For A: {Largest}-{Smallest}={Range} --> 15-{Smallest}=2 --> {Smallest}=13, not 1 as you've written.
For B: {Largest}-{Smallest}={Range} --> 10-{Smallest}=3 --> {Smallest}=7, not 1 as you've written.

13>7.

The same for the second example in your post.

Hope it's clear.

Thanks . It cleared my confusion.
I mistakenly thought range as a Common difference and pulled out AP concept here.

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Re: DS question , plz explain the answer [#permalink]

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02 Nov 2012, 22:46
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pramodkg wrote:
For students in class A, the range of heights is r and the greatest height is g. For students in class B, the
range of heights is s and the greatest height is h. Is the least height in class A greater than the least height in
class B?
(1) r < s (2) g > h

$$Shortest_A = g-r$$

$$Shortest_B = h-s$$

So question is is g-r>h-s or is g>h+(r-s)

1) r-s<0, Not sufficient. We dont know whether g is greater than h or not.
2) g>h, Not sufficient. We dont know if (r-s) is positive and when added to h is less than g or positive and when added to h is greater than g or negative.

1 & 2,
g>h, and r-s is negative. So, h+r-s < h

So, g>h + r -s.

Sufficient.

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Re: DS question , plz explain the answer [#permalink]

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02 Nov 2012, 23:13
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Class A:
Smallest height=g-r
Range of heights=r
Greatest height=g
Class B:
Smallest height=h-s
Range=s
Greatest height=h

Question is asking whether g-r>h-s? or whether g+s>h+r?
Statement 1: S>r Not sufficient. Since we don't know about g & h.
Statement 2: g>h Not sufficient. Since we don't know about s & r.
On adding the two inequalities,
We get: g+s>h+r. Hence sufficient.

Please note that we can add or multiply the inequalities but we can't divide or subtract.
Hope that helps.
-s
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Re: For the students in class A, the range of their heights is r [#permalink]

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23 May 2015, 04:58
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Assume smallest in class A as a
=> g - a = r
=> a = g - r

Assume smallest in class B as b
=> h - a = s
=> a = h - s

Question is whether g - r > h - s

(1) just says that r < s
Since we don't know anything about g and h, this is insufficient.

(2) says that g > h
Since we don't know anything about r and s, this is insufficient.

Combining,

s > r
g > h

Reversing the inequality r < s to s > r, so that now we have both inequalities pointing in the same direction.

Once that's the case, we can simply add the two inequalities

=> s + g > r + h
=> g - r > h - s

Hence, sufficient.

So, C.

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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jun 2015, 19:22
Bunuel,

Pls explain how you concluded:
------------(MIN)----G, red is the range of A, r;
(MIN)------------H, blue is the range of B, s.

You can literally see that the least height of the students in class A is greater than the least height of the students in class B.

How come minimumof A is smaller then minimum of B?

Thanks,

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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Jun 2015, 22:18
For class A
Range= r
Greatest= g
Smallest assume = x

For class B
Range= s
Greatest= h
Smallest assume = y

Combining both conditions
r<s
g-x<s
As , g>h
x> h-s
x>y. Sufficient

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For the students in class A, the range of their heights is r ...... [#permalink]

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25 Feb 2016, 06:54
For the students in class A, the range of their heights is r centimeters and the greatest height is h 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

A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) Both statements together are not sufficient, but neither statement alone is sufficient.
D) Each statement alone is sufficient.
E) Statements (1) and (2) together are not sufficient.

Two questions in order to help me with my review:

1) How would one come to answer this correctly, and with what method?
2) What underlying concept is applicable? I assume the underlying concept is Algebra, but I might be wrong. Please help.

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Re: For the students in class A, the range of their heights is r [#permalink]

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25 Feb 2016, 08:22
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aadirenpronk wrote:
For the students in class A, the range of their heights is r centimeters and the greatest height is h 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

A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
C) Both statements together are not sufficient, but neither statement alone is sufficient.
D) Each statement alone is sufficient.
E) Statements (1) and (2) together are not sufficient.

Two questions in order to help me with my review:

1) How would one come to answer this correctly, and with what method?
2) What underlying concept is applicable? I assume the underlying concept is Algebra, but I might be wrong. Please help.

Please follow posting guidelines (link in my signatures), especially search for a question before you start a new thread. Topics merged. Make sure to transcribe the problem completely as you are mentioning incorrectly that for class A the greatest height is h cm while it should be g cm.

Two questions in order to help me with my review:

1) How would one come to answer this correctly, and with what method?
For these questions, you need to stick to a step by step process or else you will end up making a mistake by getting confused. Concepts getting involved here are inequalities, number line and definition of range (=maximum value in the set - minimum value). For a detailed solution refer below.

2) What underlying concept is applicable? I assume the underlying concept is Algebra, but I might be wrong. Please help.
Refer above for the underlying concepts.

Solutions is as follows:

Class B: range r= g-b (a being the smallest height in class A) ---> b=g-r

Similarly, for Class A: s=h-a ---> a=h-s

The question asks whether b>a ---> g-r>h-s ---> is g-h>r-s?

Lets look at the statements:

Statement 1, r<s . Not sufficient without relative values of g and h.

Statement 2, g>h. Not sufficient without relative values of r and s.

When combined you get, r<s and g>h ---> you can do some algebraic manipulations:

r<s ---> r-s<0 and g>h --> g-h>0. Thus g-h>r-s (a positive quantity > a negative quantity), which is what we had to prove. Hence C is the correct answer.

Hope this helps.

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Re: For the students in class A, the range of their heights is r [#permalink]

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25 Feb 2016, 08:24
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j_shreyans wrote:
For the students in class A, the range of their height is r cm and the greatest heights is g cm. For the students in class B , the range of their heights is s cm and the greatest heights is h cm. Is the least height of the students in class A greater than the least height of the students in class B?
Statement 1) r < s
Statement 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 free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?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
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Re: For the students in class A, the range of their heights is r [#permalink]

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15 Mar 2016, 08:23
GMATPrepNow wrote:
j_shreyans wrote:
For the students in class A, the range of their height is r cm and the greatest heights is g cm. For the students in class B , the range of their heights is s cm and the greatest heights is h cm. Is the least height of the students in class A greater than the least height of the students in class B?
Statement 1) r < s
Statement 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 free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?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

You have to smile for some seconds at this solution. this is neat out-of-the-box thinking on a cutting-edge level.
Would someone mind bumping us several related questions to hone in on this skill? Please gmatclubxperts like Engr2012 and chetan2u you contributions as regards this request will receive kudos from me.
Bunuel your method was great as well. Please Bunuel in number picking to test the statements, how many number of elements would you suggest is the GMAT-wise number. I used 3 {2, 2, 4} but i wasnt quite satisfied like something might change if it were to be say 10 elements inside the set? Is there a minimum advisable?

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Re: For the students in class A, the range of their heights is r [#permalink]

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14 Jul 2016, 08:21
Pls help with clarifying my doubts:

Qsn says g-Min(A)=r and h-min(B)=s.
Option A says r<s,
so following can be possible 5-1=4<6-1=5;here Min height of class A and B is equal however range r is< range s.Also another possibility is 6-4=2<6-3=3 .In this case although g=h but Min height of class A>Min height of class B. So we cannot say this option is sufficient
Option B says g>h
Likewise in this case, not sufficient as we know nothing about ranges or min heights
Together, we would be able to say whether min height of class a is greater than min height of class b
e.g
7-3=4<6-1=5;where r<s and g>h

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Re: For the students in class A, the range of their heights is r [#permalink]

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13 Nov 2016, 06:53
BANON wrote:
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

Answer: Option C

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Re: For the students in class A, the range of their heights is r [#permalink]

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09 Apr 2017, 11:50
A = Smallest height in Class A => g-r
B = Smallest height in Class B => h-s

1. r<s
2. g>h

Subtracting 2 from 1

r-g < s-h
Multiply by -1

g-r>h-s
A>B

Option: C

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Re: For the students in class A, the range of their heights is r [#permalink]

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18 Apr 2017, 16:20
BANON wrote:
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 = the height of the shortest student 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 = the height of the shortest student 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 reverse 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
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Re: For the students in class A, the range of their heights is r [#permalink]

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10 Sep 2017, 22:12
BANON wrote:
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

Very tricky question- but becomes much clearer when you just plug in numbers - one such question where plugging in numbers is the preferred strategy, IMO.

Set A [4,5,6]

Set B [1,2 ,5]

C

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Re: For the students in class A, the range of their heights is r   [#permalink] 10 Sep 2017, 22:12

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