Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Is the range of numbers {a, b, c, d, e} greater than 10 [#permalink]
11 Oct 2010, 13:50

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

50% (01:26) correct
50% (00:37) wrong based on 8 sessions

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]
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.

Re: Sets and Ranges - Challenge Question [#permalink]
12 Oct 2010, 11:17

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 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. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

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