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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, 13:50

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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.

Re: Sets and Ranges - Challenge Question [#permalink]

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12 Oct 2010, 01:00

Range=The distance between two extreme points on the number line -----X---p---q---r--Y----- range= distance between X and Y

Stmnt1: b-d > 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.

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 b-d > 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, 07:22

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.

gmatclubot

Re: Sets and Ranges - Challenge Question
[#permalink]
14 Oct 2010, 07:22

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