NEW HERE? LEARN MORE
closeclose
Last visit was: 03 May 2024, 02:27 It is currently 03 May 2024, 02:27
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If the average of 10 consecutive odd integers is 224, what is the leas

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93024
Own Kudos [?]: 620878 [2]
Given Kudos: 81741
Send PM
CAT Tests Forum Quiz Mode
If the average of 10 consecutive odd integers is 224, what is the leas [#permalink] New post   26 Oct 2020, 07:48
1
Kudos
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

70% (01:26) correct 30% (02:06) wrong based on 27 sessions
Hide Show timer Statistics
If the average of 10 consecutive odd integers is 224, what is the least of these integers?

A. 211

B. 213

C. 215

D. 217

E. 219
ShowHide Answer
Official Answer
C
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9257 [2]
Given Kudos: 91
 Q51  V47
Send PM
Re: If the average of 10 consecutive odd integers is 224, what is the leas [#permalink] New post   26 Oct 2020, 08:08
2
Kudos
Expert Reply
Consecutive odd integers are equally spaced, so their average equals their median. If 224 is their median, then 223 and 225 are the two odd numbers in the middle of our list. Since it only takes a few seconds, there's no need to do anything more complicated than list the five smallest integers in the list, the five consecutive odd integers ending with 223:

215, 217, 219, 221, 223

So 215 is the answer.
User avatar
D
Hoozan
Director
Director
Joined: 28 Sep 2018
Posts: 732
Own Kudos [?]: 560 [1]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
Reviews Badge
Re: If the average of 10 consecutive odd integers is 224, what is the leas [#permalink] New post   26 Oct 2020, 08:14
1
Bookmarks
Method 1

We know that there are 10 consecutive odd numbers. Leaving thr first number in the list ( the least one) we have 9 consecutive numbers. And we are given that the average is 224. Thus, 224-9 = 215 will be the least number in the list of odd numbers.


Method 2

10 consecutive odd numbers can be represented as a, a+2, a+3.... a+18 with "a" as the first number in the list.

The sum of these 10 numbers is 224×10 = 2240.

Thus we can say 10a + 90 = 2240. By solving we get a = 215.

Posted from my mobile device
avatar
satubus
Intern
Intern
Joined: 28 Oct 2020
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 2
Send PM
Re: If the average of 10 consecutive odd integers is 224, what is the leas [#permalink] New post   28 Oct 2020, 04:18
Hoozan wrote:
Method 1

We know that there are 10 consecutive odd numbers. Leaving thr first number in the list ( the least one) we have 9 consecutive numbers. And we are given that the average is 224. Thus, 224-9 = 215 will be the least number in the list of odd numbers.


Method 2

10 consecutive odd numbers can be represented as a, a+2, a+3.... a+18 with "a" as the first number in the list.

The sum of these 10 numbers is 224×10 = 2240.

Thus we can say 10a + 90 = 2240. By solving we get a = 215.

Posted from my mobile device


Could you please eloborate more on your methods, thanks :please:
User avatar
L
Abhishek009
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6070
Own Kudos [?]: 4696 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
GMAT ToolKit User
Re: If the average of 10 consecutive odd integers is 224, what is the leas [#permalink] New post   28 Oct 2020, 08:04
satubus wrote:
Hoozan wrote:
Method 1

We know that there are 10 consecutive odd numbers. Leaving thr first number in the list ( the least one) we have 9 consecutive numbers. And we are given that the average is 224. Thus, 224-9 = 215 will be the least number in the list of odd numbers.


Method 2

10 consecutive odd numbers can be represented as a, a+2, a+3.... a+18 with "a" as the first number in the list.

The sum of these 10 numbers is 224×10 = 2240.

Thus we can say 10a + 90 = 2240. By solving we get a = 215.

Posted from my mobile device


Could you please eloborate more on your methods, thanks :please:

\(n + ( n + 2 ) + ( n + 4 ) + ( n + 6 ) + ( n + 8 ) + ( n + 10 ) + ( n + 12 ) + ( n + 14 ) + ( n + 16 ) + ( n + 18 ) = 2240\)

Or, \(10n + 90 = 2240\)

Or, \(n + 9 = 224\)

Or, \(n = 215\)

Hope this helps.....

Welcome to gmatclub and for your first post, happy learning!!
GMAT Club Bot
gmatclubot
Re: If the average of 10 consecutive odd integers is 224, what is the leas [#permalink]
28 Oct 2020, 08:04
Moderators:
Bunuel
Math Expert
93017 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions