GMAT Changed on April 16th - Read about the latest changes here

 It is currently 26 May 2018, 12:52

### 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

# What is the average (arithmetic mean) of eleven consecutive

Author Message
TAGS:

### Hide Tags

Manager
Joined: 27 Feb 2010
Posts: 101
Location: Denver
What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

23 Apr 2010, 18:05
2
KUDOS
34
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:43) correct 28% (00:46) wrong based on 690 sessions

### HideShow timer Statistics

What is the average (arithmetic mean) of eleven consecutive integers?

(1) The average of the first nine integers is 7
(2) The average of the last nine integers is 9
Math Expert
Joined: 02 Sep 2009
Posts: 45455
What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

24 Apr 2010, 06:10
18
KUDOS
Expert's post
20
This post was
BOOKMARKED
What is the average (arithmetic mean) of eleven consecutive integers?

Consecutive integers represent evenly spaced set. For every evenly spaced set mean=median, in our case $$mean=median=x_6$$.

(1) The average of the first nine integers is 7 --> $$x_1+x_2+...+x_9=63$$ --> there can be only one set of 9 consecutive integers to total 63. Sufficient.

If you want to calculate: $$(x_6-5)+(x_6-4)+(x_6-3)+(x_6-2)+(x_6-1)+x_6+(x_6+1)+(x_6+2)+(x_6+3)=63$$ --> $$x_6=8$$.

OR: Mean(=median of first 9 terms=5th term)*# of terms=63 --> $$x_5*9=63$$ --> $$x_5=7$$ --> $$x_6=7+1=8$$

(2) The average of the last nine integers is 9 --> $$x_3+x_4+...+x_{11}=81$$ --> there can be only one set of 9 consecutive integers to total 81. Sufficient.

If you want to calculate: $$(x_6-3)+(x_6-2)+(x_6-1)+x_6+(x_6+1)+(x_6+2)+(x_6+3)+(x_6+4)+(x_6+5)=81$$ --> $$x_6=8$$.

OR: Mean(=median of last 9 terms=7th term)*# of terms=81 --> $$x_7*9=81$$ --> $$x_7=9$$ --> $$x_6=9-1=8$$

_________________
Director
Joined: 29 Nov 2012
Posts: 821
Re: If 11 consecutive integers are listed from least to [#permalink]

### Show Tags

08 Mar 2013, 05:51
so its not possible to have a list of numbers with positive and negative numbers?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
Joined: 02 Sep 2009
Posts: 45455
Re: If 11 consecutive integers are listed from least to [#permalink]

### Show Tags

08 Mar 2013, 06:02
fozzzy wrote:
What is the average (arithmetic mean) of eleven consecutive integers?

(1) The average of the first nine integers is 7.
(2) The average of the last nine integers is 9.

so its not possible to have a list of numbers with positive and negative numbers?

How it is possible? From both statements it follows that the set is {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 620
Re: What is the average (arithmetic mean ) of eleven consecutive [#permalink]

### Show Tags

12 Aug 2013, 04:39
10
KUDOS
18
This post was
BOOKMARKED
zz0vlb wrote:
What is the average (arithmetic mean ) of eleven consecutive integers?

(1) The avg of first nine integers is 7
(2) The avg of the last nine integers is 9

Here is a neat little trick for such kind of problems:

Will be better illustrated using a numerical example: take the set {2,3,4,5,6}. Here the common difference (d)=1. The initial average = 4. Now, the averge of the set, after removing the last integer of the set(i.e. 6)will be reduced by exactly $$\frac{d}{2} units \to$$ The new Average = $$4-\frac{1}{2} = 3.5$$

Again, for the new set of {2,3,4,5} the average is 3.5 . Now, if the last integer is removed, the new average will again be = 3.5-0.5 = 3.

Similarly, for the same set {2,3,4,5,6}, if we remove the first integer from the given set, the average increases by 0.5 and so on and so forth.

Back to the problem:

From F.S 1, we know that the average of the first 9 integers is 7. Thus, the average with the original 11 integers must have been 7+0.5+0.5 = 8. Sufficient.

From F.S 2, we know that the average of the last 9 integers is 9, thus the average with the initial 11 integers must have been 9-0.5-0.5 = 8. Sufficient.

D.
_________________
Intern
Joined: 26 May 2010
Posts: 10
Re: What is the average (arithmetic mean ) of eleven consecutive [#permalink]

### Show Tags

12 Aug 2013, 23:15
6
KUDOS
7
This post was
BOOKMARKED
zz0vlb wrote:
What is the average (arithmetic mean ) of eleven consecutive integers?

(1) The avg of first nine integers is 7
(2) The avg of the last nine integers is 9

As a general rule whenever there is a AP the average of the series is always the median of the series. Here it is a AP with difference 1

1. First 9 integers average is 7 . So the median that is the 5th digit is 7. Hence we can easily find the series and the average of the 11 consecutive digit series. Sufficient
2. Average of last 9 integers is 9 hence we know that for this subset of 9 integers the 5th integer would be 9 and we can find the series on the basis of this and the average. Sufficient

And is D
Manager
Joined: 24 Jun 2014
Posts: 52
Concentration: Social Entrepreneurship, Nonprofit
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

09 Mar 2015, 19:15
I considered following approach

if the smallest number in set is x , then sum of 11 consecutive numbers = 11x+(1+2+...10)=11x+55--->A
if largest number in set is x ,then sum of 11 consecutive numbers=11x-(1+2+10)=11x-55

Now as per statement 1 , average of first 9 numbers is 7 i.e sum =63
sum of 11 numbers =63+x+9+x+10----->B

Equating A& B
11X+55=63+X+9+10 ,which can be solved to get x=3

statement I is sufficient
similar approach for Statement II
11X-55=8+2X-19 ,can be solved to get X=13

statement 2 is sufficient

OA=D
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11670
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

09 Mar 2015, 19:26
5
KUDOS
Expert's post
5
This post was
BOOKMARKED
Hi All,

When you look at this question, if you find yourself unsure of where to "start", it might help to break down everything that you know into small pieces:

1st: We're told that we have 11 consecutive integers. That means the 11 numbers are whole numbers that are in a row. If we can figure out ANY of the numbers AND it's place "in line", then we can figure out ALL of the other numbers and answer the question that's asked (the average of all 11 = ?)

2nd: Fact 1 tells us that the average of the FIRST 9 integers is 7. For just a moment, ignore the fact that there are 9 consecutive integers and let's just focus on the average = 7.

What would have to happen for a group of consecutive integers to have an average of 7?

Here are some examples:

7

6, 7, 8

5, 6, 7, 8, 9

Notice how there are the SAME number of terms below 7 as above 7. THAT'S a pattern.

With 9 total terms, that means there has to be 4 above and 4 below:

3, 4, 5, 6,.......7.......8, 9, 10, 11

Now we have enough information to figure out the other 2 terms (12 and 13) and answer the question. So Fact 1 is SUFFICIENT

With this same approach, we can deal with Fact 2.

The key to tackling most GMAT questions is to be comfortable breaking the prompt into logical pieces. Don't try to do every step at once and don't try to do work in your head. Think about what the information means, take the proper notes and be prepared to "play around" with a question if you're immediately certain about how to handle it.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 11 Apr 2016
Posts: 3
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

29 Jun 2016, 03:10
1
KUDOS
wow such complex explanations for such a simple problem?

given :

11 consec integers

let them be x,x+1,x+2,...,x+10

Q: what is their mean?

mean is (11x+55)/11 = x+5.
Q becomes what is x+5

1) mean first 9 is 7.

so (9x+36)/9 = x+4 = 7 , so x+5 =8 ,--> sufficient A or D

2) mean of last 9 is 9.

so (9x+54)/9 = x+6= ---> x+5=8, sufficient . so D

D
Director
Joined: 04 Jun 2016
Posts: 611
GMAT 1: 750 Q49 V43
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

15 Jul 2016, 00:10
zz0vlb wrote:
What is the average (arithmetic mean) of eleven consecutive integers?

(1) The average of the first nine integers is 7
(2) The average of the last nine integers is 9

For odd number of consecutive integer the mean and median both is the middle value. Use this property to solve th question
(1) The average of the first nine integers is 7
7 will be the middle value; there will be 4 consecutive integers to the left and also to the right of 7
we will have {3,4,5,6,7,8,9,10,11}
now we can add last two consecutive integer after 11, they will be 12,13
our new set will become = {3,4,5,6,7,8,9,10,11,12,13}
again since the number of total elements in the set is odd, Mean will simply be the middle value = 8
SUFFICIENT

(2) The average of the last nine integers is 9
Again number of element in the set are odd, 9 will be the middle value; 4 consecutive integers will lie to its left and right
Middle value will be
{5,6,7,8,9,10,11,12,13}
Add 3,4 at the start of the set
new set = {3,4,5,6,7,8,9,10,11,12,13}
Mean will be 8
Sufficient

_________________

Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly.
FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2606
GRE 1: 323 Q169 V154
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

20 Dec 2016, 17:37
Nice Official Question>
Here is my solution to this one =>
Set of consecutive integers =>
N
N+1
N+2
.
.
.
N+10

AP series with D=2
Hence Mean = Median = Average of the first and the last terms= N+5

So we just ned the value of N

Statement 1
N
N+1
.
.
N+8

Mean => N+4=7
Hence N+5=> 8
So the mean of the original set will be 8
Hence Sufficient

Statement 2-->
p
p+2
p+3
.
.
p+8
Mean = p+4=9
p=5
Hene p+8=>13
So N+10=>13
Hence N+5=>8
Hence the mean of the original data set must be 8

Hence Sufficient

Hence D

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Director
Joined: 26 Oct 2016
Posts: 668
Location: United States
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

26 Jan 2017, 05:52
3
KUDOS
The key is that the integers are consecutive. So, if we can determine any one of the 11 (and know where it falls), we can answer the question.

(1) The average of the first 9 consecutive integers is 7.

We know that avg = sum of terms / # of terms.

So, 7 = sum of terms/9
sum of terms = 63.

Well, there's only going to be one set of 9 consecutive integers that add up to 63. If we can determine the first 9, we can certainly determine the last 2: sufficient.

(2) The average of the last 9 terms is 9.

Exact same reasoning as (1): sufficient.

Both (1) and (2) are sufficient: choose (D).
_________________

Thanks & Regards,
Anaira Mitch

Intern
Joined: 04 Dec 2016
Posts: 2
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

13 Mar 2017, 05:39
The trick here is to catch the phase "11 consecutive integers". We know that an odd set of consecutive integers have the same median and mean {i.e. set 1,2,3 has a median and mean of 2}.

Based on this we can say the same for the statements:

s1) Represent the first 9 integers as: A+B+C+D+E+F+G+H+I. If the mean of this set is 7 then the median is also 7 so we found that the 7th number in the total set. We know they are consecutive and therefore we could count forward and backward to get the unknown numbers. Therefore statement is sufficient.

s2) Same concept as above. Statement is sufficient.
SVP
Joined: 12 Sep 2015
Posts: 2477
Re: What is the average (arithmetic mean) of eleven consecutive [#permalink]

### Show Tags

24 Mar 2018, 07:32
1
KUDOS
Expert's post
Top Contributor
zz0vlb wrote:
What is the average (arithmetic mean) of eleven consecutive integers?

(1) The average of the first nine integers is 7
(2) The average of the last nine integers is 9

There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."

Since the consecutive integers are equally-spaced, their mean and median will be equal.

Target question: What is the average of eleven consecutive integers?

Statement 1: The average of the first nine integers is 7.
This also tells us that the MEDIAN of the first nine integers is 7.
In other words, the MIDDLEMOST value is 7.
This means, the first nine integers are 3, 4, 5, 6, 7, 8, 9, 10, 11
So, ALL 11 integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Since we've identified all 11 integers, we can DEFINITELY find their average.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The average of the last night integers is 9
This also tells us that the MEDIAN of the last nine integers is 9.
In other words, the MIDDLEMOST value is 9.
This means, the last nine integers are 5, 6, 7, 8, 9, 10, 11, 12, 13
So, ALL 11 integers must be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Since we've identified all 11 integers, we can DEFINITELY find their average.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Re: What is the average (arithmetic mean) of eleven consecutive   [#permalink] 24 Mar 2018, 07:32
Display posts from previous: Sort by