GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Oct 2019, 05:59

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

Confirm Cancel

For positive integers n and m (n>m), is the average (arithmetic mean)

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

Hide Tags

Find Similar Topics 
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1348
Location: Malaysia
GMAT ToolKit User
For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 25 Mar 2017, 15:41
2
26
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

16% (02:29) correct 84% (02:28) wrong based on 220 sessions

HideShow timer Statistics

For positive integers n and m \(n>m\), is the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) an integer?

1) \(m<6\)
2) \(n=10\)

_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8023
Re: For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 25 Mar 2017, 22:48
4
3
ziyuen wrote:
For positive integers n and m \(n>m\), is the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) an integer?

1) \(m<6\)
2) \(n=10\)



Hi

Few important points to solve this Q..
1) n>m, so lowest term \(4*10^{n-m}\) will be ATLEAST 4*10 or 40
2) Therefore each term will be multiple of 40 or 2,4,5,8,10,20,40
3) Average of the terms is " INTEGER or Not" depends on number of elements.
4) number of elements depends on 'm' and is m+1
5) since each term multiple of 40, so if m is multiple of the factors of 40, answer is YES, otherwise it has to be checked


Let's see the statements:-
1) m<6
Therefore m can be 1 to 5
So number of terms can be 1 to 5+1..
We already know if number of elements are factors of 40, and is YES..
So 1,2,4,5 will have answer as YES..
Let's check for 3 and 6..

Each number in series consists of digits 4 and 0.... 40,400,4000 etc
So if there are 3 or 6 numbers, the SUM of digits of total of these numbers will be 3*4 or 6*4, which will be divisible by 3, thus we will have an integer here too..
Example:- 40+400+4000=4440.. sum of digits is 12, so number is div by 3
Or 400000+40000+4000=444000, again SUM of digits is 12

6 numbers will have total div by 3 and the numbers being EVEN, total will be div by 6, thus an integer again

Ans is YES always
Sufficient

2) n=10..
We are concerned about m only
Insufficient

A
_________________
General Discussion
Manager
Manager
avatar
S
Joined: 22 Mar 2014
Posts: 99
Location: United States
Concentration: Finance, Operations
GMAT 1: 530 Q45 V20
GPA: 3.91
WE: Information Technology (Computer Software)
Re: For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 26 Mar 2017, 13:23
Hi Chetan,

I did not understand your explanation.
Intern
Intern
avatar
B
Joined: 10 Jul 2017
Posts: 30
Schools: ISB '20
For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 19 Aug 2018, 19:16
Ques: Arithmetic mean an integer?
we can simply take common from the expression 4∗10^n , 4∗10^n−1, ......, and 4∗10^n−m
=> 4*10^n (1+1/10 +1/10^2+......+1/10^m)---------(1)

so here we can see that the value of 'n' doesn't matter...it can be 40,400,40000.....
The only information you need is the value of 'm' , hence A sufficient !

Further: you can take the LCM of equation 1
4*10^n-m (10^m+10^m-1.....+1) => 4*10^n-m (11111.....m times)
Senior Manager
Senior Manager
avatar
S
Joined: 15 Jan 2017
Posts: 340
Re: For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 12 Sep 2018, 01:06
How did we assume m to be between 1 to 5? if M< 6 then can't m be negative, like say m = -6?
Manager
Manager
User avatar
G
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 08 Nov 2018, 07:32
Madhavi1990 wrote:
How did we assume m to be between 1 to 5? if M< 6 then can't m be negative, like say m = -6?

Stem mentions n and m are positive integers
_________________
Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

GMAT 1 - 620 .... Disappointed for 6 months. Im back Im back. Bhai dera tera COMEBACK !!!
SVP
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1755
Location: India
Premium Member Reviews Badge CAT Tests
For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 25 Aug 2019, 09:54
hazelnut wrote:
For positive integers n and m \(n>m\), is the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) an integer?

1) \(m<6\)
2) \(n=10\)


Asked: For positive integers n and m \(n>m\), is the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) an integer?
Number of terms = n - (n-m) +1 = m+1
the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) = \(\frac{4*10^n + 4*10^{n-1} + ......+4*10^{n-m}}{(m+1)}\)

1) \(m<6\)
Let us take m=0
\(4*10^n/1 = 4*10^n\) Integer
Let us take m=1
\(\frac{4*10^n + 4*10^{n-1}}{2} = \frac{4*10^{n-1} ( 1+10)}{2} =\frac{4*10^{n-1} *11}{2}\) Integer
Let us take m=2
\(\frac{4*10^n + 4*10^{n-1} + 4*10^{n-2}}{3} = \frac{4*10^{n-2} ( 1+10+100)}{3} =\frac{4*10^{n-2} *111}{3}\) Integer
Let us take m=3
\(\frac{4*10^n + 4*10^{n-1} + 4*10^{n-2} + 4*10^{n-3}}{4} = \frac{4*10^{n-3} ( 1+10+100+1000)}{4} = \frac{4*10^{n-3} *1111}{4}\) Integer
Let us take m=4
\(\frac{4*10^n + 4*10^{n-1} + 4*10^{n-2} + 4*10^{n-3} + 4*10^{n-4}}{5} = \frac{4*10^{n-4} ( 1+10+100+1000+10000)}{5} = \frac{4*10^{n-4} *11111}{5}\) Integer
Let us take m=5
\(\frac{4*10^n + 4*10^{n-1} + 4*10^{n-2} + 4*10^{n-3} + 4*10^{n-4} + 4*10^{n-5}}{6} = \frac{4*10^{n-5} ( 1+10+100+1000+10000 +10^5)}{6} =\frac{4*10^{n-5} *111111}{6}\) Integer
SUFFICIENT

2) \(n=10\)
Since if we take n=10 and m=6
The expression will not be divisible by 7
NOT SUFFICIENT

IMO A
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Intern
Intern
avatar
B
Joined: 14 Jun 2015
Posts: 15
Re: For positive integers n and m (n>m), is the average (arithmetic mean)  [#permalink]

Show Tags

New post 28 Aug 2019, 20:16
hazelnut wrote:
For positive integers n and m \(n>m\), is the average (arithmetic mean) of \(4*10^n\), \(4*10^{n-1}\), ......, and \(4*10^{n-m}\) an integer?

1) \(m<6\)
2) \(n=10\)



Hi.....

Not convinced with the OA..... Let us consider n=10, m=3, which gives Avg as an Integer. However, if we consider n=10, m=5, its Avg will not be an integer. I had opted for Optn E.... Please clarify.

Bunuel chetan2u request your help
GMAT Club Bot
Re: For positive integers n and m (n>m), is the average (arithmetic mean)   [#permalink] 28 Aug 2019, 20:16
Display posts from previous: Sort by

For positive integers n and m (n>m), is the average (arithmetic mean)

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne