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Students Height

by BlindVision » Tue Jun 16, 2009 4:29 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


OA = C
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by mehravikas » Tue Jun 16, 2009 7:08 pm
You can pick number for these problems:

Start from statement 2: g > h, no other information is given about r, s and least height.

Answer can be: A, C, E

Statement 1: r < s, let r = 8, s = 10
r = 14 - 6
s = 15 - 5 or 17 - 7

Not sufficient.

combine both the statements and pick numbers satisfying both the answer choices.
r = 8, s = 10, g = 14, h = 12
r = 14 - x1
s = 12 - x2

we know that r < s therefore, x1 is greater than x2
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by BlindVision » Tue Jun 16, 2009 7:53 pm
Thanks for the help but I got lost on the combining part. Can you please help me better understand that last part?

P.S. When I combine, I get: r < s < h < g . Is that right?

P.S.S. Maybe I'm not understanding the question stem: Is it asking 'Which of the two classes has the most shortest students'?
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by tohellandback » Tue Jun 16, 2009 8:18 pm
BlindVision wrote:Thanks for the help but I got lost on the combining part. Can you please help me better understand that last part?

P.S. When I combine, I get: r < s < h < g . Is that right?

P.S.S. Maybe I'm not understanding the question stem: Is it asking 'Which of the two classes has the most shortest students'?
you already have got the individual parts. so lets see what happens when we combine both
plug in numbers
let r=15
g=20
so least height in class A is 5
now plug in numbers for B
r<s so lets say s is 16
g>h
so lets say h=19
lest height in B is 3 i.e less than 5
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by aj5105 » Tue Jun 16, 2009 11:58 pm
Combining both, least element in ClassB has to be less than ClassA.

(C)
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by aj5105 » Wed Jun 17, 2009 12:03 am
Ian's post:

dragonxiam- when you chose numbers here, you made r larger than s, when it should be smaller than s, which is why you've arrived at the wrong answer.

Neither statement is sufficient on its own- clearly we need to know about r, s, g and h here. Together we know:

s > r
g > h

These inequalities are in the same direction, so we can add them:

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

So we've shown that the smallest height in class A, which is g-r, is larger than the smallest height in class B, which is h-s. C.
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