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DS-height question

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by [email protected] » Mon May 13, 2013 12:15 am
For the students in class A, the range of their heights is r centimeters and the greatest height is g gentimeters. For the students in class B, the range of their heights is s centimeters and thr greatest is h centimeters. Is thr least height of the students in class A greater than least height of thr least height of the students in class B?

1)r<s
2)g>h

Pheww!! out of my scope!Please explain
OA is C
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by mkdureja » Mon May 13, 2013 2:31 am
Range of a set is difference between highest and lowest.
In this case, for Class A, 'g' is highest; 'r' is range; therefore, least is: g-r.
Similarly, for Class B, least height is: h-s.
Question asks you to compare 'g-r' and 'h-s'
Now, consider statement 1, r<s; Since you dont have any information about g and h in this statement, so it alone is not sufficent to answer the question.
Similarly, Statement 2 alone is also not sufficient to answer the question.
Now, if you combine the two statements,
If r<s and g>h; then you can surely say that 'g-r' > 'h-s'.
So, using both statements together, you can answer the question.
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by lunarpower » Mon May 13, 2013 4:18 am
remember that
range = greatest - least

which can be arranged to
greatest = least + range
or
least = greatest - range

--

(1)
these data concern ranges only; there is no indication whatsoever of how the heights compare.
insufficient

(2)
the greatest height in class a is taller than its counterpart in class b, but we know nothing about the ranges; if class a has a wider spread, its least height could well be shorter than that of class b.
insufficient

(together)
greatest height in class a = g - r
greatest height in class b = h - s
the given inequalities imply that g - r > h - s
sufficient

--

alternatively, you could have formulated g - r and h - s at the beginning of the problem (i.e., before considering statements (1) and (2) alone); these formulations make it perhaps even easier to see that (1) and (2) individually are insufficient.
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