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

It is currently 19 Jul 2018, 17:56

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

After multiplying a positive integer A, which has n digits,

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

Hide Tags

4 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 120
After multiplying a positive integer A, which has n digits,  [#permalink]

Show Tags

New post 15 Feb 2013, 12:04
4
14
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

36% (01:11) correct 64% (01:08) wrong based on 286 sessions

HideShow timer Statistics

After multiplying a positive integer A, which has n digits, by (n+2), we get a number with (n+1) digits, all of whose digits are (n+1). How many instances of A exist?

A. None
B. 1
C. 2
D. 8
E. 9

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.

Most Helpful Expert Reply
Expert Post
16 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
P
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: After multiplying a positive integer A, which has n digits,  [#permalink]

Show Tags

New post 15 Feb 2013, 19:05
16
2
emmak wrote:
After multiplying a positive integer A, which has n digits, by (n+2), we get a number with (n+1) digits, all of whose digits are (n+1). How many instances of A exist?

A. None
B. 1
C. 2
D. 8
E. 9



The question seems convoluted but it's not. You have to take the first step in the right direction. The only definitive thing given here is that we get a number with (n+1) digits, all the digits being (n+1). What will such a number look like?

22
333
4444
55555 etc

We obtain this number by multiplying A with (n+2). This means that our number should be divisible by (n+2). Now, ask yourself:
Is 22 divisible by 3? No.
Is 333 divisible by 4? No
We know that no odd number will be divisible by an even number. So we can ignore 333, 55555, 7777777 etc

Only consider even numbers:

Is 4444 divisible by 5? No

Is 666666 divisible by 7? Yes! Check: 666666/7 = 95238 (5 digit number). SO when you multiply 95238 by 7, you get 666666

Is 88888888 divisible by 9? No

Use divisibility rules to quickly rule out the numbers not divisible.

Answer (B)
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

General Discussion
Expert Post
MBA Section Director
User avatar
D
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5186
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
GMAT ToolKit User Premium Member
Re: After multiplying a positive integer A, which has n digits,  [#permalink]

Show Tags

New post 15 Feb 2013, 12:56
emmak wrote:
After multiplying a positive integer A, which has n digits, by (n+2), we get a number with (n+1) digits, all of whose digits are (n+1). How many instances of A exist?

None

1

2

8

9


Constraint 1) when we put a sequence of multiples of (n+2) atleast one multiple should have its unit digit same as that of (n+1)
Constraint 2) N+1 can not greater than 9 since it is a single digit.
Constraint 2) N can not be 0

n(n+1)(n+2)
8---9----10------ Units digit zero always. so out
7---8----9-------- 9X2=18 so 2323232X9 = .......2988 or 2222222 x 9 = ......98 out
6---7----8-------- units digits 8,6,4,2,4,8,6,4,2,0,8,6.... No 7 so out
5---6----7-------- 7x8=56 so 83838 x 7 = .......5866 or 88888 x 7 = ....216 out
4---5----6-------- units digits 6,2,8,4,0,6,2,8,4,0...... No 5 so out
3---4----5-------- 5,0,5,0 out
2---3----4-------- 4,8,2,6,0,4.... out
1---2----3-------- only possible pair is 3 x 4 = 12 so out

Bunuel, Can you Pls help?
_________________

Chances of Getting Admitted After an Interview [Data Crunch]


Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates

Expert Post
MBA Section Director
User avatar
D
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 5186
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
WE: Business Development (Manufacturing)
GMAT ToolKit User Premium Member
Re: After multiplying a positive integer A, which has n digits,  [#permalink]

Show Tags

New post 16 Feb 2013, 09:14
VeritasPrepKarishma wrote:
emmak wrote:
After multiplying a positive integer A, which has n digits, by (n+2), we get a number with (n+1) digits, all of whose digits are (n+1). How many instances of A exist?

A. None
B. 1
C. 2
D. 8
E. 9



The question seems convoluted but it's not. You have to take the first step in the right direction. The only definitive thing given here is that we get a number with (n+1) digits, all the digits being (n+1). What will such a number look like?

22
333
4444
55555 etc

We obtain this number by multiplying A with (n+2). This means that our number should be divisible by (n+2). Now, ask yourself:
Is 22 divisible by 3? No.
Is 333 divisible by 4? No
We know that no odd number will be divisible by an even number. So we can ignore 333, 55555, 7777777 etc

Only consider even numbers:

Is 4444 divisible by 5? No

Is 666666 divisible by 7? Yes! Check: 666666/7 = 95238 (5 digit number). SO when you multiply 95238 by 7, you get 666666

Is 88888888 divisible by 9? No

Use divisibility rules to quickly rule out the numbers not divisible.

Answer (B)


You said correctly Karishma.
It is important to take first step in right direction.

Regards,

Abhijit
_________________

Chances of Getting Admitted After an Interview [Data Crunch]


Must Read Forum Topics Before You Kick Off Your MBA Application

New GMAT Club Decision Tracker - Real Time Decision Updates

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7300
Premium Member
Re: After multiplying a positive integer A, which has n digits,  [#permalink]

Show Tags

New post 10 Nov 2017, 15:10
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: After multiplying a positive integer A, which has n digits, &nbs [#permalink] 10 Nov 2017, 15:10
Display posts from previous: Sort by

After multiplying a positive integer A, which has n digits,

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

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.