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Ms. Big Fat Panda
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Is the range of numbers {a, b, c, d, e} greater than 10 [#permalink]
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11 Oct 2010, 14:50
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So, I was preparing a list of important properties to include in the flashcards I was making for the competition and when I was looking for illustrative examples, I came across this one question. I believe this is a good question to test your knowledge of sets and ranges and to really think smartly. I will post the answer tomorrow, so you guys will have a day to try the question! Quote: Is the range of numbers {a, b, c, d, e} greater than 10.
Statement 1: b  d > 10 Statement 2: b is the greatest number in the set.



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Re: Sets and Ranges  Challenge Question [#permalink]
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11 Oct 2010, 15:35
whiplash2411 wrote: Is the range of numbers {a, b, c, d, e} greater than 10.
Statement 1: b  d > 10 Statement 2: b is the greatest number in the set.
Range = Max(set)Min(set) (1) bd>10 ... max(set)>=b & min(set)<=d by definition, hence range>10. Sufficient (2) doesnt tell us anything much at all about the set. Insufficient Answer is (a)
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Re: Sets and Ranges  Challenge Question [#permalink]
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12 Oct 2010, 02:00
Range=The distance between two extreme points on the number line XpqrY range= distance between X and Y
Stmnt1: bd > 10 ===> the distance between b and d on the number line is > 10 hence the range must surely be > 10 even if the rest (a,c and e are kept between b and d)  SUFF.
stmnt2: b is the grtst # among them; as per the definition of range, two points (extreme points) are required to calculate the range ===> NOT SUFF.
ANSWER "A"
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Re: Sets and Ranges  Challenge Question [#permalink]
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12 Oct 2010, 09:49
Its E....
From 1... I am not sure the order of a,b,c,d so i can not say whether the smalllest number and largest numbers possible from 1 ...
from 2 clearly, it is not sufficient....
even if i club together... we can not get the value of range > 10 ....
So my ans is : E
guys, please reply me if i m wrong....



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Re: Sets and Ranges  Challenge Question [#permalink]
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12 Oct 2010, 10:52



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Re: Sets and Ranges  Challenge Question [#permalink]
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12 Oct 2010, 12:17
There are many ways to define the range of a set. Most people learn that: range = largest  smallest which is a perfectly good way to understand the range for most questions. That definition is equivalent to the following: range = largest distance between any two elements in a set So if you know b and d are in your set, and you know that bd > 10, then the largest distance between any two elements in the set clearly must be greater than 10, and the range is thus greater than 10.
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Re: Sets and Ranges  Challenge Question [#permalink]
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14 Oct 2010, 03:05
It must be A.Range=largest  smallest



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Re: Sets and Ranges  Challenge Question [#permalink]
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14 Oct 2010, 08:22
Easy A. whiplash2411 wrote: Is the range of numbers {a, b, c, d, e} greater than 10.
Statement 1: b  d > 10 Statement 2: b is the greatest number in the set.
(1) b  d > 10. So the range must be, at the very least, 10. If b and d are the absolute extremes of the set (so a, c, and e all fall between them), then b  d is the range. If any of a, c, or e are larger or smaller than b or d, then the range will be bigger than b  d. The other three numbers are irrelevant because they can't shrink the range. Quick examples, let b = 21 and d = 9, so b  d = 11: {9, 10, 11, 12, 21}  range = 11 {5, 9, 10, 11, 21}  range = 16 {5, 9, 10, 21, 25}  range = 20 Sufficient. (2) Clearly insufficient, as we have no information about the other numbers.




Re: Sets and Ranges  Challenge Question
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