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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]  23 Feb 2012, 07:12
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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]  23 Feb 2012, 08:32
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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.

Hope it's clear.
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Re: For the students in class A, the range of their heights is r [#permalink]  15 Jul 2012, 00:39
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]  15 Jul 2012, 01:16
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This post was
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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]  15 Jul 2012, 01:32
heygmat wrote:
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

gud method thanks
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Re: For the students in class A, the range of their heights is r [#permalink]  15 Jul 2012, 04:34
Expert's post
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]  15 Jul 2012, 12:40
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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DS question , plz explain the answer [#permalink]  02 Nov 2012, 19:07
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
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Re: DS question , plz explain the answer [#permalink]  02 Nov 2012, 21:46
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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.

Kudos Please... If my post helped.
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Re: DS question , plz explain the answer [#permalink]  02 Nov 2012, 22:13
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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.
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: DS question , plz explain the answer [#permalink]  02 Nov 2012, 22:16
Expert's post
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

Merging similar topics. Please refer to the solutions above.

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Re: For the students in class A, the range of their heights is r [#permalink]  27 Mar 2014, 08:52
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Re: For the students in class A, the range of their heights is r [#permalink]  11 Apr 2015, 02:57
Hello from the GMAT Club BumpBot!

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Re: For the students in class A, the range of their heights is r [#permalink]  23 May 2015, 03:58
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]  15 Jun 2015, 18:22
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]  15 Jun 2015, 21:18
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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Re: For the students in class A, the range of their heights is r   [#permalink] 15 Jun 2015, 21:18
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