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Range of heights

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Range of heights

by ostrowskiamy » Mon Feb 18, 2013 5:10 pm
"For kids in Class A, the range of heights is r, and the greatest height is g centimeters. For students in B, the range is s, and the height is h. Is the least height of kids in A greater than the least height of kids in B?

(1) r < s
(2) g>h

My answer was "E." The correct answer is "C." How do I obtain sufficiency when combining both statements?
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by Anurag@Gurome » Mon Feb 18, 2013 10:49 pm
ostrowskiamy wrote:"For kids in Class A, the range of heights is r, and the greatest height is g centimeters. For students in B, the range is s, and the height is h. Is the least height of kids in A greater than the least height of kids in B?

(1) r < s
(2) g > h
I assume it'll be "...the greatest height is h."

Now, let us assume that least height of kids in A and B are respectively a and b.

Hence, r = (g - a) and s = (h - b)
Hence, a = (g - r) and b = (h - s)

We need to determine whether a > b or not, i.e. (g - r) > (h - s) or not.

Clearly none of the statements are individually sufficient.

1 & 2 Together: We know r < s and g > h and r, s, g, and h all are positive quantities.
Hence, (g - r) > (h - r) and (h - r) > (h - s)
Hence, (g - r) > (h - s)
Hence, a > b

Sufficient

The correct answer is C.
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