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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.

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 -----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.

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

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12 Oct 2010, 12:17

Expert's post

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. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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.

gmatclubot

Re: Sets and Ranges - Challenge Question
[#permalink]
14 Oct 2010, 08:22

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