N is positive integer and hundredth digit of 10N is 6 : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 02:12

### 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

# N is positive integer and hundredth digit of 10N is 6

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

### Hide Tags

Manager
Joined: 14 Mar 2010
Posts: 82
Followers: 2

Kudos [?]: 134 [0], given: 44

N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

30 Apr 2012, 20:13
3
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:33) correct 27% (01:59) wrong based on 131 sessions

### HideShow timer Statistics

N is positive integer and hundredth digit of 10N is 6.If N and N+13 is multiple of 13 then N+13 tenth digit is 7. Now what is the unit digit of N.

A.7
B.5
C.8
D.4
E.0
[Reveal] Spoiler: OA

_________________

MGMAT CAT MATH http://gmatclub.com/forum/mgmat-cat-math-144609.html
MGMAT SC SUMMARY: http://gmatclub.com/forum/mgmat-sc-summary-144610.html

VP
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1126
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 124

Kudos [?]: 540 [3] , given: 19

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

30 Apr 2012, 20:52
3
KUDOS
This question should be re-framed by specifying that N is a two digit positive integer.

1) If the hundred's digit of 10N is 6 => the ten's digit of N is 6.
2) The ten's digit of N+13 is 7 => the one's digit of N is 5

The one's digit of N is 5 because for the ten's digit of N to be 6, and the ten's digit of N+13 to be 7, the addition of 13 to N must be causing a carry of 1 to the ten's column. Therefore 3 must be getting added to the ten's column. Now, if the one's digit is X, we must choose X in such a way that 60+X and 70+(X+3) are both divisible by 13. This is possible when X=5.

Option (B), provided that this number is two digit number (not given in the question).

If this is not a two digit number, then the numbers 260 and 273 will also satisfy this criteria and in that case the units digit will be 0, 364 and 377 will also satisfy with the units digit being 4, 663 and 676 will also satisfy with the units digit being 3....... so there is no unique answer for the units digit in that case.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Last edited by GyanOne on 30 Apr 2012, 20:58, edited 2 times in total.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 80

Kudos [?]: 1117 [1] , given: 136

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

28 Aug 2013, 20:40
1
KUDOS
kassim wrote:
monir6000 wrote:
N is positive integer and hundredth digit of 10N is 6.If N and N+13 is multiple of 13 then N+13 tenth digit is 7. Now what is the unit digit of N.

A.7
B.5
C.8
D.4
E.0

Hello,

I didn't understand why the tens digit 6 if the hundredth digit of 10N is 6.

For me I assumed that it's a 3 digit number and the hundredth digit of N is 6

Can anyone please explain more?

Best,
Kassim

We know that N is an integer. Let N = abc.Now, 10*N = abc0. As you can notice, the value of the each of the digit shifts place wise. Initially, the units digit of N was c, which is now 0. The tens unit of N was b, which is now at the hundred's place.Thus, when we know that the hundred's digit after multiplication by 10 is 6, then by similar analogy, we can say that the tens place of N must be 6.
You can actually pick up numbers with tens digit as 6, and multiply by 10 to get an idea. Also, for this particular thing, it doesn't matter if N is a 2 digit number or a 10 digit number.

Hope this helps.
_________________
Intern
Joined: 25 Apr 2012
Posts: 16
Followers: 0

Kudos [?]: 12 [0], given: 1

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

30 Apr 2012, 20:57
My take:
Hundredth digit of 10N is 6 => tenth digit of N is 6
N+13 tenth digit is 7 => unit digit of N shall be between 0 and 6 (inclusive of 0,6)
The only answer options possible are 0,4,5
We know that 65 is divisible by 13. And no other additional clue is given we can conclude the unit digit to be '5'
_________________

Ravi Sankar Vemuri

Senior Manager
Joined: 03 Sep 2012
Posts: 338
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 16

Kudos [?]: 179 [0], given: 31

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

01 Oct 2012, 20:12
From the information given :

N = multiple of 13 ...

N + 13 = Multiple of 13 , with the tenth place being 7 ...

10N has a 100th unit as 6 ...

Multiples of 13 = ( 13 x 2 = 26 , 13 x 3 = 39, 13x4 = 52 , 13x5 = 65, 13x6 = 78, 13x9 = 78, 13x10 = 130...) ..

Out of these we need to find a number which when added to 13 yields a unique number whose tenth place is occupied by a 7.. We have 65 as that number so will select it to test it out ..

65+13 = 78 , tenth place is 7 .. So 1 condition is met ...

Lets multiply 10 by N we get 10 x 65 = 650 ..The hundredth unit is 6 , so the second condition has been met...

after satisfying 1 and 2 we know that n = 65 , the units digit of n is 5 (B)
_________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Intern
Joined: 11 Jul 2012
Posts: 46
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

03 Nov 2012, 12:24
N = tu, 10N = tu0, t = 6, N = 6u; N + 13 = 6u + 13 = 73 + u =13k (because N+13 is multiple of 13)
u = 13k - 73 = 5 for k= 6
Brother Karamazov
Intern
Joined: 07 Jan 2013
Posts: 39
GMAT 1: 570 Q43 V26
GMAT 2: 610 Q47 V28
Followers: 0

Kudos [?]: 6 [0], given: 24

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

28 Aug 2013, 13:25
monir6000 wrote:
N is positive integer and hundredth digit of 10N is 6.If N and N+13 is multiple of 13 then N+13 tenth digit is 7. Now what is the unit digit of N.

A.7
B.5
C.8
D.4
E.0

Hello,

I didn't understand why the tens digit 6 if the hundredth digit of 10N is 6.

For me I assumed that it's a 3 digit number and the hundredth digit of N is 6

Can anyone please explain more?

Best,
Kassim
Intern
Joined: 07 Jan 2013
Posts: 39
GMAT 1: 570 Q43 V26
GMAT 2: 610 Q47 V28
Followers: 0

Kudos [?]: 6 [0], given: 24

Re: N is positive integer and hundredth digit of 10N is 6 [#permalink]

### Show Tags

31 Aug 2013, 12:48
mau5 wrote:
We know that N is an integer. Let N = abc.Now, 10*N = abc0. As you can notice, the value of the each of the digit shifts place wise. Initially, the units digit of N was c, which is now 0. The tens unit of N was b, which is now at the hundred's place.Thus, when we know that the hundred's digit after multiplication by 10 is 6, then by similar analogy, we can say that the tens place of N must be 6.
You can actually pick up numbers with tens digit as 6, and multiply by 10 to get an idea. Also, for this particular thing, it doesn't matter if N is a 2 digit number or a 10 digit number.

Hope this helps.

Hi,

Thank you for your help. I don't know why I assumed that 10N is 3 digit number or more as one hundred and N not 10 times N.

Now it's Crystal clear

Thank you
Re: N is positive integer and hundredth digit of 10N is 6   [#permalink] 31 Aug 2013, 12:48
Similar topics Replies Last post
Similar
Topics:
1 What is the largest value of non negative integer N for which 10N is a 2 17 Jan 2017, 11:38
8 If 200!/10^n is an integer, what is the largest possible value of n? 7 28 Apr 2016, 02:36
6 If 10^(n-1)< 0.000125 <10^n, what is the value of an integer n? 8 04 Apr 2016, 00:01
12 n represent the hundredths digit in the number shown above. 9 12 Jul 2012, 08:31
17 If the two-digit integers M and N are positive and have the 7 12 Dec 2009, 08:04
Display posts from previous: Sort by

# N is positive integer and hundredth digit of 10N is 6

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.