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

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For the students in class A, the range of heights is "r [#permalink] New post 22 Oct 2011, 22:26
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A
B
C
D
E

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93% (01:45) correct 7% (01:39) wrong based on 14 sessions
For the students in class A, the range of heights is "r cm" and the greatest height is "g cm" for the students in class B
the range of their heights is "S" cm and the greatest height is "h" cm, Is the least height of students in class A greater than least height of students in class B ?

1) r<s
2)g>h

I got the answer as A, but it is wrong can anyone plz help.....
[Reveal] Spoiler: OA

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Re: Height problem frm Gmat prep [#permalink] New post 23 Oct 2011, 03:26
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Least height of Class A is g-r
Least height of Class B is h-s

Question is is g-r > h-s ??

With 1 – r is < s but g could be less than h and hence it is not sufficient
With 2 – g > h but r could be large enough to make g-r<h-s

With both 1 and 2, g-h > h-s. Greatest height in g is greater than h and also because the range is class A is less than range in class B, least height in class A is geater than least hight in class B
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Re: Height problem frm Gmat prep [#permalink] New post 24 Oct 2011, 06:30
Hi prakhag,

Can you please explain how you got option C?
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Re: Height problem frm Gmat prep [#permalink] New post 24 Oct 2011, 08:29
kotela wrote:
Hi prakhag,

Can you please explain how you got option C?


Given: Range of A = r, Greatest of A = g, Range of B = s, Greatest of B = h
Say, least of A = a and least of B = b

r = g - a
s = h - b

The question is whether a > b or not.

Statement 1: r < s
Implies (g - a) < (h - b)
No information about g and h.

Not sufficient.

Statement 2: g > h
Implies (r + a) > (s + b)
No information about r and s.

Not sufficient.

1 & 2 Together: We have information about r, s, g and h. We can easily determine whether a > b or not. In fact from statement 2 (r + a) > (s + b). Now from statement 1, r < s. Thus a must be greater than b.

Sufficient.
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Re: Height problem frm Gmat prep [#permalink] New post 25 Oct 2011, 02:25
kotela wrote:
For the students in class A, the range of heights is "r cm" and the greatest height is "g cm" for the students in class B
the range of their heights is "S" cm and the greatest height is "h" cm, Is the least height of students in class A greater than least height of students in class B ?

1) r<s
2)g>h

I got the answer as A, but it is wrong can anyone plz help.....


Ans - 'C'

Let least height of class A = La
Let least height of class B = Lb

Given,
Range of A = R and max height of A = G
Range of B = S and max height of B = H

Therefore,
G - La = R => La = G - R
H - Lb = S => Lb = H - S

We have to find La > Lb or G - R > H - s

1. R < S ...Not Suff.
2. H < G ...Not Suff.

Combined, Add eq. 1 and eq. 2

H + R < G + S => H - S < G - R


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Re: Height problem frm Gmat prep [#permalink] New post 25 Oct 2011, 22:32
Thanks prakhag for the explanation :)
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Re: Height problem frm Gmat prep   [#permalink] 25 Oct 2011, 22:32
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