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by kkadvent » Wed Feb 13, 2013 5:55 am
For Students in Class A the range of height is r cm and the greatest height is g cm, For the students in class B the range of their height is s cm and the greatest height is h cm. Is the least height of student in class A greater than the least height of student in class B?
1) r<s

2) g>h
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Source: — Data Sufficiency |

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by Ian Stewart » Wed Feb 13, 2013 6:30 am
kkadvent wrote:For Students in Class A the range of height is r cm and the greatest height is g cm, For the students in class B the range of their height is s cm and the greatest height is h cm. Is the least height of student in class A greater than the least height of student in class B?
1) r<s

2) g>h
In a set, if the largest value is L, and the range is R, then from the definition of the range, the smallest element S is equal to L-R.

So here, we want to know if g-r > h - s, or rewriting this, if g+s > h + r. Neither statement is sufficient alone, but if you line up the two inequalities and add them:

r < s
h < g
r+h < g+s

which is exactly what we wanted to prove.

You may also be able to see the answer conceptually. The range is the distance between the largest and smallest elements in a set. If in class A the greatest height is larger than in B, and the range is smaller, then the least height in A certainly must be greater than the least height in B.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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