If the average of 5 positive integers is 40 and the : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 08 Dec 2016, 11:08
GMAT Club Tests

Close

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
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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the average of 5 positive integers is 40 and the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 18 Feb 2011
Posts: 41
GPA: 3.91
Followers: 8

Kudos [?]: 43 [1] , given: 26

If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 04 Feb 2012, 03:15
1
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:38) correct 38% (01:56) wrong based on 292 sessions

HideShow timer Statistics

If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

A. 50
B. 52
C. 49
D. 48
E. 44
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 May 2013, 03:37, edited 2 times in total.
Added the OA
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35912
Followers: 6853

Kudos [?]: 90055 [1] , given: 10402

Re: Averages – Descriptive Statistics problem solving [#permalink]

Show Tags

New post 04 Feb 2012, 03:42
1
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
nafishasan60 wrote:
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
A. 50
B. 52
C. 49
D. 48
E. 44


The average of 5 positive integers is 40 --> the sum of these 5 integers is 5*40=200;
The difference between the largest and the smallest of these 5 numbers is 10 --> let the smallest integer be x and the largest x+10;

Now, we want to maximize x+10.

General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

Hence, in order to maximize x+10 we should minimize all other terms, thus make them equal to the smallest integer x. We would have: x+x+x+x+(x+10)=200 --> x=38 --> x+10=48.

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12895
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 30 Jun 2014, 04:39
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 44

Kudos [?]: 1834 [0], given: 193

If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 01 Jul 2014, 02:00
Let the 5 integers be as follows:

To have maximum value of a+10, let all others be "a"

a+10 ............ a ............... a .............. a .............. a

Addition = 200

5a + 10 = 200

\(a = \frac{190}{5} = 38\)

a+10 = 48 (Maximum Value)

Answer = D
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
avatar
Joined: 18 Mar 2014
Posts: 8
Concentration: International Business
GMAT 1: Q V
Followers: 0

Kudos [?]: 3 [0], given: 58

Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 12 Aug 2014, 18:59
My method was,

x + (x+1) + (x+2) + (x+3) + (x+4) / 5 = 40

Thus 5x + 10 = 200
and x = 38

Since we know the range is 10, that is ( x + 4 ) - x = 10

so, ( x + 4) - 38 = 10

(x + 4) = 48

** Take (x + 4) as a whole number.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 12895
Followers: 561

Kudos [?]: 158 [0], given: 0

Premium Member
Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 02 Dec 2015, 04:37
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
VP
VP
User avatar
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1341 [0], given: 42

Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 02 Dec 2015, 06:25
nafishasan60 wrote:
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

A. 50
B. 52
C. 49
D. 48
E. 44


Sum of 5 Integer (a, b, c, d, e) = 5*40 = 200

e - a = 10
i.e. e = a+10

For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers


i.e. a+a+a+a+(a+10) = 200
i.e. 5a = 190
i.e. a = 38

i.e. Largest e = 38+10 = 48

Answer: option D
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html



Feel free to give a Kudos if it is a useful post .

Manager
Manager
avatar
Joined: 08 Oct 2015
Posts: 80
Followers: 0

Kudos [?]: 0 [0], given: 7

Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 02 Dec 2015, 07:49
GMATinsight wrote:
nafishasan60 wrote:
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

A. 50
B. 52
C. 49
D. 48
E. 44


Sum of 5 Integer (a, b, c, d, e) = 5*40 = 200

e - a = 10
i.e. e = a+10

For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers


i.e. a+a+a+a+(a+10) = 200
i.e. 5a = 190
i.e. a = 38

i.e. Largest e = 38+10 = 48

Answer: option D



why cant we solve taking a=e-10
Expert Post
VP
VP
User avatar
Joined: 08 Jul 2010
Posts: 1432
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 65

Kudos [?]: 1341 [0], given: 42

Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 02 Dec 2015, 08:02
rahulkashyap wrote:
GMATinsight wrote:
nafishasan60 wrote:
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

A. 50
B. 52
C. 49
D. 48
E. 44


Sum of 5 Integer (a, b, c, d, e) = 5*40 = 200

e - a = 10
i.e. e = a+10

For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers


i.e. a+a+a+a+(a+10) = 200
i.e. 5a = 190
i.e. a = 38

i.e. Largest e = 38+10 = 48

Answer: option D



why cant we solve taking a=e-10


We can solve it like that too

in that case the equation will look like

(e-10)+(e-10)+(e-10)+(e-10)+e = 200
i.e. 5e - 40 = 200
i.e. 5e = 240
i.e. e = 48

I hope this helps
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html



Feel free to give a Kudos if it is a useful post .

SVP
SVP
User avatar
Joined: 17 Jul 2014
Posts: 2088
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
WE: General Management (Transportation)
Followers: 18

Kudos [?]: 248 [0], given: 124

GMAT ToolKit User Premium Member Reviews Badge
Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 05 Oct 2016, 06:37
I solved it the same way bunuel explained.
sum is 200.
x is the smallest
x+10 is the greatest
to maximize x+10, suppose all numbers are the same
x+x+x+x+x+10=200
5x=190
x=190/5
x=38
x+10=48.
Intern
Intern
avatar
Joined: 27 Sep 2016
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: If the average of 5 positive integers is 40 and the [#permalink]

Show Tags

New post 05 Oct 2016, 06:59
nafishasan60 wrote:
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

A. 50
B. 52
C. 49
D. 48
E. 44


It average of 5 integers is 40, then their sum is \(40 *5=200\)
Let max value be \(x\) .
Therefore smallest value is \(x -10\)
for one value to be maximum (i.e. x ) , all others have to be minimum (i.e. x- 10 ) .
So, \(4(x -10) + x = 200\)
\(x =48\)
Ans. D
Re: If the average of 5 positive integers is 40 and the   [#permalink] 05 Oct 2016, 06:59
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic The average (arithmetic mean) of 20, 40, and 60 is 5 more than the ave Bunuel 1 31 May 2016, 01:35
3 Experts publish their posts in the topic The average (arithmetic mean) of 4 positive integers is 50. iyersu 3 21 Dec 2013, 03:31
15 Experts publish their posts in the topic If the average (arithmetic mean) of 5 positive temperatures Madelaine88 11 06 Mar 2011, 08:31
18 Experts publish their posts in the topic The average (arithmetic mean) of the 5 positive integers ajit257 16 28 Dec 2010, 16:54
5 Experts publish their posts in the topic If the average (arithmetic mean) of positive integers x, y, shamimshariq 12 21 Jul 2009, 21:25
Display posts from previous: Sort by

If the average of 5 positive integers is 40 and the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.