Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 08:15

### GMAT Club Daily Prep

#### 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

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

# A set consists of 5 distinct positive integers a, b, c, d, e, ........

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2942
A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

09 Jan 2019, 02:24
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:59) correct 32% (02:13) wrong based on 164 sessions

### HideShow timer Statistics

A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

Updated on: 09 Jan 2019, 03:41
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 19 and b is least can be 1
so 19-1= 18
IMO C

EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 09 Jan 2019, 03:13.
Last edited by Archit3110 on 09 Jan 2019, 03:41, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2942
A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

09 Jan 2019, 03:38
Archit3110 wrote:
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 20 and b is least can be 0
so 20-0 = 20
IMO E

EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

Hi Archit3110,

Please note that a, b, c, d and e are positive integers

Regards,
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

09 Jan 2019, 03:40
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?

EgmatQuantExpert
in that case b =1 and d = 19
and d-b = 18
IMO C

EgmatQuantExpert wrote:
Archit3110 wrote:
given
b is least integer and d is highest no
and sum of a,b,c= 24
mean of b+24+d/5 =8.8
b+d=20
since d is the highest no it can be 20 and b is least can be 0
so 20-0 = 20
IMO E

EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

Hi Archit3110,

Please note that a, b, c, d and e are positive integers

Regards,

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2942
A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

09 Jan 2019, 03:53
Archit3110 wrote:
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?

Yes, 0 is neither a positive integer nor a negative integer.
It will be included in a set of non-negative and non-positive integers but it must be excluded from the set of positive or negative integers

Though, 0 is an even integer, it cannot be considered as a positive even integer. Since, 0 is not a positive integer

Regards,
_________________
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4237
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

09 Jan 2019, 03:57
EgmatQuantExpert

thanks

EgmatQuantExpert wrote:
Archit3110 wrote:
EgmatQuantExpert

there is a confusion regarding usage of 0 ;
what i know is that 0 is neither +ve or -ve integer

if a statement says n is a set of +ve integers then we begin set n from (1,2,3...)

and if statement says n is a set of non negative integer then we begin set from ( 0,1,2,3,..)

will 0 be considered in set of +ve even integers? i.e (0,2,4,6,.) or not?

Yes, 0 is neither a positive integer nor a negative integer.
It will be included in a set of non-negative and non-positive integers but it must be excluded from the set of positive or negative integers

Though, 0 is an even integer, it cannot be considered as a positive even integer. Since, 0 is not a positive integer

Regards,

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2942
Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

11 Jan 2019, 07:12

Solution

Given:
• A set of 5 distinct positive integers, {a, b, c, d, e}
• b is the least number and d is the highest number of the set
• a + c + e = 24
• Mean of the set = 8.8

To find:
• The maximum value of (d – b)

Approach and Working:
• a + c + e = 24 ………………………….………………………………… (1)
• $$\frac{(a + b + c + d + e)}{5} = 8.8$$
o Implies, a + b + c + d + e = 5 * 8.8 = 44 …………… (2)

(2) – (1), we get,
• b + d = 44 – 24 = 20
• For d – b to be maximum, b must be minimum
o The minimum value b can take is 1, since b is a positive integer

• If b = 1, then d = 20 – 1 = 19

Therefore, the maximum value of (d – b) = 19 – 1 = 18

Hence, the correct answer is option C.

_________________
CEO
Joined: 12 Sep 2015
Posts: 3848
Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

19 Jan 2019, 06:35
Top Contributor
EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

The mean of all 5 numbers is 8.8
(a + b + c + d + e)/5 = 8.8
Multiply both sides by 5 to get: a + b + c + d + e = 44

The sum of a, c and e is 24
(a + c + e) = 24
So, take a + b + c + d + e = 44 and rewrite as: (a + c + e) + b + d = 44
We get: (24) + b + d = 44
So, b + d = 20

b is the least number and d is the highest number
Since b and d are POSITIVE INTEGERS, and since we're tying to MAXIMIZE the value of (d - b), we want to MAXIMIZE d and MINIMIZE b
This is accomplished when d = 19 and b = 1

What is the maximum value of (d – b)?
d - b = 19 - 1 = 18

Cheers,
Brent

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........  [#permalink]

### Show Tags

27 Jan 2019, 11:03
EgmatQuantExpert wrote:
A set consists of 5 distinct positive integers a, b, c, d, e, where b is the least number and d is the highest number. If the sum of a, c and e is 24, and the mean of all 5 numbers is 8.8, then what is the maximum value of (d – b)?

A. 16
B. 17
C. 18
D. 19
E. 20

We know that a + c + e = 24. Because the mean of the 5 numbers is 8.8, we see that their sum must be 5 x 8.8 = 44. Thus, a + b + c + d + e = 44.

Subtracting the first equation from the second equation, we obtain:
b + d = 44 - 24 = 20.

To maximize the difference of b and d, we will choose b to be as small as possible and d to be as large as possible. Thus, if b = 1 then d = 19, and the maximum value of (d - b) is 18.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: A set consists of 5 distinct positive integers a, b, c, d, e, ........   [#permalink] 27 Jan 2019, 11:03
Display posts from previous: Sort by