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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

18 Oct 2010, 10:57

21

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

54% (02:52) correct
46% (02:00) wrong based on 414 sessions

HideShow timer Statistics

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

12 17 18 19 20

Range = e-a. d-b=3 or d=b+3

Average = 6 thus a+b+c+d+e=30

To maximize range, we need to minimize a and maximize e. Minimum a is 1, so we choose that. Since sum is fixed, we should choose minimum possible values for b,c,d to maximize e. b>a, minimum choice is 2 c>b, minimum choice is 3 d=b+3 so d=5 So e(max) = 30 - a(min) -b(min) -c(min) - d(min) = 30-1-2-3-5 = 19 Range(max) = e(max)-a(min) = 19-1 =18

Well it's basic logic. If you want maximize one of the numbers you should minimize all other numbers if you're given the average or sum of the series. An example would be there are five numbers the sum of the five numbers add to 20. All the numbers are positive what is the largest possible number in the set. The smallest positive number is 1. 20-1-1-1-1 =16. If other numbers were not minimize then the answer would be less than 16. 20-1-2-1-2 = 14.

For the above question, the smallest positive integer is 1. Therefore A=1. Since they can't be the same number the next smallest integer is 2. B = 2. We know D-B = 3, so 2+3 = 5. D=5. C has to be between 2 and 5. 3 is the smallest number. Finally the last number should be 30-5-3-2-1=19.

Let's say you didn't choose the smallest number a = 3, then b = 4, c = 5, d = 7. E would be only be 11. The range would only be 8.

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

18 Sep 2013, 07:31

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

30 Sep 2013, 11:24

a<b<c<d<e

As all these integers are +ve then minimum value of a=1.

Furthermore, to maximize the range we will have to minimize the value of "a" and maximize the value of "e".

a=1 b=2 c=3 d= 5 (Since d=b+3) e=19

Range = e - a = 19 -1 Range = 18 !
_________________

Rgds, TGC! _____________________________________________________________________ I Assisted You => KUDOS Please _____________________________________________________________________________

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

17 Feb 2014, 07:51

1

This post received KUDOS

My way:: let's say that 'a' the smallest integer is 'x' and then we have that b=x+1, c=x+2, d=x+4 and e=x+k. We then have that the sum 5x+7+k = 30, and that k = 23-5x. Since the smallest value of x can be 1. Therefore k = 18 which is also the range is the maximum value. C is the correct answer

Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

02 Jul 2014, 04:42

shrouded1 wrote:

shrive555 wrote:

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

12 17 18 19 20

Range = e-a. d-b=3 or d=b+3

Average = 6 thus a+b+c+d+e=30

To maximize range, we need to minimize a and maximize e. Minimum a is 1, so we choose that. Since sum is fixed, we should choose minimum possible values for b,c,d to maximize e. b>a, minimum choice is 2 c>b, minimum choice is 3 d=b+3 so d=5 So e(max) = 30 - a(min) -b(min) -c(min) - d(min) = 30-1-2-3-5 = 19 Range(max) = e(max)-a(min) = 19-1 =18

Answer is (c)

I have some inference like you, but

a + b + c + d + e = 30 d-b =3 => a + 2b + c + e = 27 => e = 27 - a - 2b - c range = e - a = 27 - 2a - 2b - c

range is max when a, b, e are min => a=1, b=2, c=3 (as a,b,c are positive integers and a<b<c)

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

08 Jul 2015, 00:01

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e [#permalink]

Show Tags

09 Sep 2016, 07:26

shrive555 wrote:

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

A. 12 B. 17 C. 18 D. 19 E. 20

IMO B

Attachment:

1.JPG [ 34.38 KiB | Viewed 1792 times ]

_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos ¯\_(ツ)_/¯

gmatclubot

Re: Positive integers a, b, c, d and e are such that a<b<c<d<e
[#permalink]
09 Sep 2016, 07:26

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...