It is currently 17 Jan 2018, 19:38

### 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 arithmetic mean of n consecutive odd integers is 20, what is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139331 [1], given: 12783

If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

19 Aug 2015, 02:05
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

64% (01:06) correct 36% (01:07) wrong based on 177 sessions

### HideShow timer Statistics

If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139331 [1], given: 12783

Manager
Joined: 21 Jan 2015
Posts: 149

Kudos [?]: 121 [0], given: 24

Location: India
Concentration: Strategy, Marketing
WE: Marketing (Other)
Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

19 Aug 2015, 02:13
Bunuel wrote:
If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Ans: D

Solution: consecutive odd integers sequence with avg 20 means 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31,33 and so on. but to keep the average 20 we need to keep 19,21 at the centre of the series.

now Statement 1: range 18 means (difference of least and greatest element of sequence = 18) for a fix pattern sequence we can get the largest value. [Sufficient]
Statement 2: once again this statement is also sufficient [Sufficient]
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Kudos [?]: 121 [0], given: 24

Senior RC Moderator
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1084

Kudos [?]: 1715 [5], given: 283

Location: India
GMAT 1: 680 Q47 V34
GRE 1: 321 Q164 V157
WE: General Management (Aerospace and Defense)
Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

19 Aug 2015, 02:16
5
KUDOS
4
This post was
BOOKMARKED
Bunuel wrote:
If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Kudos for a correct solution.

For any evenly spaced set, the average is the average of 1st and last term in the sequence.

So $$\frac{(X1 +Xn)}{2}= 20$$. So $$(X1 +Xn)= 40$$.

1. Gives us the value of Xn-X1= 18 So we have 2 equations and 2 variable. So we can solve for Xn. So sufficient.

2. Gives us the value of X1=11. So Xn= 40-11= 29. Sufficient.

_________________

Kudos [?]: 1715 [5], given: 283

Manager
Joined: 14 Mar 2014
Posts: 148

Kudos [?]: 181 [3], given: 124

GMAT 1: 710 Q50 V34
Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

19 Aug 2015, 04:49
3
KUDOS
Bunuel wrote:
If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Kudos for a correct solution.

IMO : D

AM = 20
$$\frac{1st Term + Last term}{2}$$= 20
$$T_1 + T_n$$= 40 ---(i)

Statement 1 : Range = 18
$$T_n - T_1$$ = 18
Solving Eq (i) & (ii)
$$T_n$$= 29
Sufficient

Statement 2 : The least of the n integers is 11

$$T_1$$ = 11
Thus $$T_n$$ = 29
Sufficient
_________________

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

Kudos [?]: 181 [3], given: 124

Director
Joined: 21 May 2013
Posts: 566

Kudos [?]: 57 [0], given: 509

Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

21 Aug 2015, 10:10
Bunuel wrote:
If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Kudos for a correct solution.

Statement 1: Range of n integers is 18-The nos are 11,13,15,17,19,21,23,25,27,29. Range=29-11=18. Sufficient
Statement 2: Least of n integers is 11. Again use same set of numbers. Sufficient

Kudos [?]: 57 [0], given: 509

Intern
Joined: 13 Nov 2014
Posts: 49

Kudos [?]: 11 [0], given: 105

GMAT 1: 590 Q42 V29
GMAT 2: 630 Q47 V29
Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

23 Aug 2015, 02:54
IMO D,reading the term 'Arithmetic Mean' is really important, I somehow took some more time to read that
_________________

-----------------------------------------
Consider Cudos if you like this post.
-----------------------------------------

Kudos [?]: 11 [0], given: 105

Intern
Joined: 14 Apr 2014
Posts: 19

Kudos [?]: 2 [1], given: 49

Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

23 Aug 2015, 04:15
1
KUDOS
pretty simple

statement one says range is 18. so we can get actual value of n which turns out to be even and 20 is arithmetic mean so 20 is middle number between 19 & 21...

statement two says least is 11 and we have already got the value of n.so we can say with conviction about the final number in the series.

Kudos [?]: 2 [1], given: 49

Math Expert
Joined: 02 Sep 2009
Posts: 43312

Kudos [?]: 139331 [1], given: 12783

Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

23 Aug 2015, 11:38
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
If the arithmetic mean of n consecutive odd integers is 20, what is the greatest of the integers?[/b]

(1) The range of the n integers is 18.

(2) The least of the n integers is 11.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

We have discussed mean in case of arithmetic progressions in the previous posts. If mean of consecutive odd integers is 20, what do you think the integers will look like?

19, 21 or
17, 19, 21, 23 or
15, 17, 19, 21, 23, 25 or
13, 15, 17, 19, 21, 23, 25, 27 or
11, 13, 15, 17, 19, 21, 23, 25, 27, 29
etc.

Does it make sense that the required numbers will represent one such sequence? The numbers in the sequence will be equally distributed around 20. Every time you add a number to the left, you need to add one to the right to keep the mean 20. The smallest sequence will have 2 numbers 19 and 21, the largest will have infinite numbers. Did you notice that each one of these sequences has a unique “range,” a unique “least number” and a unique “greatest number?” So if you are given any one statistic of the sequence, you will know the entire desired sequence.

Statement 1: Only one possible sequence: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 will have the range 18. The greatest number here is 29. This statement alone is sufficient.

Statement 2: Only one possible sequence: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 will have 11 as the least number. The greatest number here is 29. This statement alone is sufficient too.

_________________

Kudos [?]: 139331 [1], given: 12783

Retired Moderator
Joined: 12 Aug 2015
Posts: 2331

Kudos [?]: 995 [0], given: 680

GRE 1: 323 Q169 V154
Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

13 Dec 2016, 09:48
Excellent Quality Question.
Here is my approach ->

Given data -->
N consecutive odd integers.
Consecutive odd integer set is an AP set with common difference =2
Hence Mean=Median=Average of the first and the last terms.
Thus,Median=20.
As median =Even => The number of terms must be even.So,the set will have two middle terms.

Statment 1->
Range =18
Let p be the first element.
Hence the last element must be p+18 so that the range is 18.
Thus the average = p+p+18/2 => p+9
Hence p+9=20 => p=11
Hence the first term =11
And the median =20
The number of terms to the left of the median = number of terms to the right of the median.
Hone we can get the last term.
Hence sufficient

Statement 2-->
The first term =11
As we have the median and the first term -> we can get the last term by using the principle =>The number of terms to the left of the median = number of terms to the right of the median.
Hence Sufficient

Hence D

_________________

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

Kudos [?]: 995 [0], given: 680

Non-Human User
Joined: 09 Sep 2013
Posts: 14256

Kudos [?]: 291 [0], given: 0

Re: If the arithmetic mean of n consecutive odd integers is 20, what is [#permalink]

### Show Tags

21 Dec 2017, 19:32
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.
_________________

Kudos [?]: 291 [0], given: 0

Re: If the arithmetic mean of n consecutive odd integers is 20, what is   [#permalink] 21 Dec 2017, 19:32
Display posts from previous: Sort by