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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

30 Apr 2012, 20:52

3

This post received 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.
_________________

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

Show Tags

28 Aug 2013, 20:40

1

This post received 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.

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' Answer option 'B'
_________________

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

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

gmatclubot

Re: N is positive integer and hundredth digit of 10N is 6
[#permalink]
31 Aug 2013, 12:48

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...

The words of John O’Donohue ring in my head every time I reflect on the transformative, euphoric, life-changing, demanding, emotional, and great year that 2016 was! The fourth to...