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

 It is currently 19 Jan 2017, 13:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If the average of 5 positive integers is 40 and the

Author Message
TAGS:

### Hide Tags

Intern
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

04 Feb 2012, 03:15
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:42) correct 37% (01:57) wrong based on 314 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.
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93198 [0], given: 10553

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

### Show Tags

04 Feb 2012, 03:42
Expert's post
6
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.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

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

### Show Tags

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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1931 [0], given: 193

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

### Show Tags

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

5a + 10 = 200

$$a = \frac{190}{5} = 38$$

a+10 = 48 (Maximum Value)

_________________

Kindly press "+1 Kudos" to appreciate

Intern
Joined: 18 Mar 2014
Posts: 8
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

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
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

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

### Show Tags

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.
_________________
VP
Joined: 08 Jul 2010
Posts: 1443
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 68

Kudos [?]: 1408 [0], given: 42

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

### Show Tags

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

_________________

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
Joined: 08 Oct 2015
Posts: 79
Followers: 0

Kudos [?]: 1 [0], given: 7

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

### Show Tags

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

why cant we solve taking a=e-10
VP
Joined: 08 Jul 2010
Posts: 1443
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 68

Kudos [?]: 1408 [0], given: 42

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

### Show Tags

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

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
Joined: 17 Jul 2014
Posts: 2188
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (S)
GMAT 1: 560 Q42 V26
GMAT 2: 550 Q39 V27
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 20

Kudos [?]: 270 [0], given: 140

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

### Show Tags

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
Joined: 27 Sep 2016
Posts: 3
Followers: 0

Kudos [?]: 2 [0], given: 0

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

### Show Tags

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
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1897
Followers: 49

Kudos [?]: 363 [0], given: 453

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

### Show Tags

17 Dec 2016, 20:23
Excellent Question
Here is what i did in this Question =>

Using =>

$$Mean=\frac{Sum}{#}$$

Sum(5)=40*5=200

Now to maximise the largest quantity,we must minimise all other quantities.
Let a be the smallest element
The series would be -> a,a,a,a,a+10

Hence 5a+10=200
a=38

Helen the largest element = 38+10 = 48

Hence D

_________________

Mock Test -1 (Integer Properties Basic Quiz) ---> http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1676182

Mock Test -2 (Integer Properties Advanced Quiz) --->http://gmatclub.com/forum/stonecold-s-mock-test-217160.html#p1765951

Give me a hell yeah ...!!!!!

If the average of 5 positive integers is 40 and the   [#permalink] 17 Dec 2016, 20:23
Similar topics Replies Last post
Similar
Topics:
The average (arithmetic mean) of 20, 40, and 60 is 5 more than the ave 6 31 May 2016, 01:35
3 The average (arithmetic mean) of 4 positive integers is 50. 4 21 Dec 2013, 03:31
17 If the average (arithmetic mean) of 5 positive temperatures 12 06 Mar 2011, 08:31
19 The average (arithmetic mean) of the 5 positive integers 17 28 Dec 2010, 16:54
5 If the average (arithmetic mean) of positive integers x, y, 15 21 Jul 2009, 21:25
Display posts from previous: Sort by