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Divisibility and Bases
by Software Engineer - Sunday, 5 July 2009, 04:08 AM
  cat 2009 cat 2010 divisibility and basesA few days ago, I was telling Dagny how a car changed our lives. When we started our first TathaGat center at Kailash Colony in Delhi in December, 2007, we intended to continue there for a couple of years. But within a few months, we realized that we should be operating in Connaught Place (CP), the heart of Delhi and one of the costliest places in India. We did not realize how costly CP was until we started searching for an office space in April, 2008. Day after day, we traveled on foot from one building to another, trying to find a less expensive place for our center. We spoke with property brokers, office owners, shopkeepers, etc. and slowly we realized that operating in CP was out of our budget. After 10- 15 days, we had found a lot more places empty for rent in CP than what the property brokers knew about, but we were nowhere near our goal. One day, Riddler and I traveled on foot in the middle circle of CP, entering every building and asking the guard or the owners if they had a small place for us to teach students. I do not remember how many kilometers we walked on foot that day but by the end of the day, we found that our dream was impossible. And then we gave up. We decided to open in CP once we had the money to afford it.

That night, after having meal in a restaurant, we went to have coffee at twenty-four seven at Satyam Cineplex, Nehru Place. We were dusty, sweaty and tired. And we were dejected. When we reached our destination, we were already discussing in Riddler’s car how we have saved some money by not opening at CP. When you know you are beaten and licked, your mind adapts fairly quickly to defeat. At that particular moment, the miracle we have been trying for the last 15 days happened. The moment Riddler stopped the car, he exclaimed in disbelief; right in front of his car was parked a gleaming new Carrera, a 2- 3 crore car from Porsche. I am not a car fan but Riddler is, and when he told me the price, I was also impressed. Then the owner of the car, a nondescript chap in simple jeans and a teeshirt, came, sat into the car, and drove away. But our surprise hadn’t ended still. The moment the Carrera started, lights from a car parked behind us turned on. There was an S-class Mercedes parked behind us, inside which were sitting 2-3 bodyguards of the Carrera owner. Imagine, a guy traveling in a car worth 2- 3 crores and his bodyguards traveling in a car worth 40- 60 lakh. We sat watching both the cars drive away slowly. The moment they were out of our sight, Riddler and I exclaimed simultaneous, “Yaar, Kholte hain CP Center.” In a matter of minutes, a car had changed our attitude.

The rest is history. We doubled our efforts to find a center, and we were not going to stop till we find it. On April 26th that month itself, our first batch started at our new CP center. And we learnt an important lesson about victory or defeats in life- It’s all in your mind.

And here comes another article from Software Engineer whose recent tag line in our CAT CBT Club also bolstered our attitude- TG Wale IIMs Le Jayenge! When Dagny and I read it, only thing we said was “Yesssss.” So those of you who believe in it as hard as I do, please do let us know. Come hell or high water, CAT being CBT or PBT, TG WALE IIMs LE JAYENGEEEEEE!- Total Gadha

divisibility 1

divisibility 2

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divisibility 4

divisbility 5

divisibility 6

divisibility 7

divisbility 8

divisbility 9

 

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Re: Divisibility and Bases
by yogesh bansal - Sunday, 5 July 2009, 08:55 AM
  Bravo....u stole my heart..smilesmile
Re: Divisibility and Bases
by amit kheterpal - Sunday, 5 July 2009, 11:04 AM
  AWESOME ARTICLE..WAITING FOR MORE ARTICLES..smile
Re: Divisibility and Bases
by piyush jain - Sunday, 5 July 2009, 12:24 PM
 

tg u r saving lot of money of students by providing these kinds of article, no need of coaching,

thank you

Re: Divisibility and Bases
by Badboy Skeletor - Sunday, 5 July 2009, 12:49 PM
  hello sir....gr8 article....

I would like to ask one thing though...

I have just started my preps so my knowledge is very scarce...

u ppl devise these beautiful formulae or I can read some books and garner them....If there is a book..Plz suggest me...

Thanks....
Re: Divisibility and Bases
by Saurav Modi - Sunday, 5 July 2009, 04:26 PM
 

great article...

but have a doubt..

In divisibility rule #3(last n digits)..in the third example which u have provided it is given that n is a factor of 30.that means 30 to the power 1.

so we should divide last 1 digit of the given number but why we are dividing the last 2 digits and doing it.

Please clarify..

Thank you.

Re: Divisibility and Bases
by Software Engineer - Sunday, 5 July 2009, 04:55 PM
  Saurav,

Yes, that's a mistake. sad

As n is a factor of 30^1, just divide the last digit.

- SE
Re: Divisibility and Bases
by himanshu mishra - Monday, 6 July 2009, 08:58 AM
 

Hi badboy......

Read all the TG's lessons on site+buy no system and geometry ebook published by TG+grammer lesson by dagny and daily grammer posts by dagny is enough for first stage.

If you need TG's advice .............Please read old posts.

You will find yr answer................

 

 

 

 

 

 

 

 

 

Re: Divisibility and Bases
by Anish Nambisan - Monday, 6 July 2009, 01:03 PM
  Thank You! smile
Re: Divisibility and Bases
by William Wallace - Monday, 6 July 2009, 02:24 PM
  Great Article SE....Thanks and keep up the good work smile
Re: Divisibility and Bases
by CATching CAT - Monday, 6 July 2009, 03:01 PM
  TG sir ,
SE may turn out to be  your competitor.Beware evil

SE,
U can start another forum called "Total Engineer"
Re: Divisibility and Bases
by kavi Mani Kumar K S - Tuesday, 7 July 2009, 10:12 AM
  Hi TGites,

The Positive Integer n divides (3030)30.Find the total number of possible values of n if n is a factor of 30.

The solution posted was:

The last 2 digits = 30. The factors of 30 are 1,2,3,5,6,10,15 and 30. All the factors divide the last two digits of (3030). hence Number of possible values is 8.

Query:

The factors 1,2,3,5,6,10,15,30 are factors of 301. Ideally, only last digit of (3030) '0' should have been considered. Why are we considering the last two digits here?

Please explain.

Thanks,
Kavi.K.S.


Re: Divisibility and Bases
by Software Engineer - Tuesday, 7 July 2009, 10:22 AM
  Kavi,

This bug has been already reported by Saurav Modi; and I've corrected the mistake in my above post. Please read Saurav's and my previous posts.

- SE
Re: Divisibility and Bases
by sanjeeb panda - Tuesday, 7 July 2009, 12:12 PM
 

Hi SE>>>>GRT

Indeed this is too much informative.

 

regards

sanjeeb

Re: Divisibility and Bases
by Ronak kabani - Tuesday, 7 July 2009, 04:57 PM
  Hi SE
thnx a ton 4 such an informative article
TG rocks so does SE !!!!!!
Re: Divisibility and Bases
by raja chava - Tuesday, 7 July 2009, 11:13 PM
 

Thanks for the article SE.

One correction....The remainder when 8484 in base 12 is divided by 13 is 5 (not 8). As the answer we get is -8, the effective remainder is 5.

Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 12:06 AM
  Raja,

You are welcome. smile

That's the 'positive diffrence'; so whether we do (8-16) or (16-8), the positive diffrence is 8 in both cases. Is it clear?

- SE
Re: Divisibility and Bases
by raja chava - Wednesday, 8 July 2009, 01:27 AM
 

Dear SE,

I don't think the positive difference concept is correct. Let's convert 8484 in base 12 to base 10 and get the remainder when divided by 13. We will get a remainder of 5.

As a simple example, let's take 184 in base 10 get the remainder when divided by 11 manually. We will get a remainder of 8. Now, let's take the +ve difference of the sums of digits in odd and even places and divide it by 11. We will get a remainder of 3 which is not correct.

The +ve difference concept can be applied for checking the divisibility, but not to find remainder. For remainder, we have to consider the signed difference.

Correct me if I am wrong.

Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 01:48 PM
  Raja,

Had a blast in mind after reading your post.

Thanks for the correction. smile

Please check the updated article.

- SE
Re: Divisibility and Bases
by A. SINGH - Wednesday, 8 July 2009, 02:24 PM
 

hello SE..

great article man.

reading such articles makes me feel , subconciously we know all these things , but when they come together as collected facts , its looks jst amazing.

so thanks 4 th article.

but, i hav also hav th same doubt as raja's.

plz clarify it.

thanks

anjan

 

Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 02:51 PM
  Anjan,

It does not matter whether you consider signed or unsigned difference while testing the divisibility; BUT consider the signed difference while finding the remainder.
Signed Difference = sum of the digits in ODD places - sum of the digits in EVEN places

- SE
Re: Divisibility and Bases
by just iim - Wednesday, 8 July 2009, 03:03 PM
  hi se sir!
great article! hats off
as for raja's post in my view the remainder 8 comes when 8484 is divided by
13 in base 12 and not in base 10 as done by you!
(8+8)-(4+4)=8! so remainder when 8484 in base 12 div by 13 is 8 and not 5!
as for your next query 184 in base 10 when divided by 11 gives remainder 8!
its like this  [(4+1)-8]=-3 so  remainder = -3+11=8!
we dont have to make this diff +ve it has to remain as it is!
well previously i also thought dat dis alternate diff concept can only be use for checking divisibility but after reading the article i came to know that remainders can also be found by dis method!
and sir dis digitally divisble concept is slightly unclear as in 14325, 143 is not divisble by 3 and in 54321, 54321 is not divisible by 5!
and u hv said dat each no formed by the leftmost k digits is divisible by k!
so how they are digitally divisible????????????
please correct me wherever i m wrong!
thanks!
Re: Divisibility and Bases
by CATster . - Wednesday, 8 July 2009, 03:04 PM
  Simply awesome
Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 03:07 PM
  Just IIM,

Thank You. smile

"14325, 143 is not divisible by 3"
Can you please read the problem and Div. Rule 3 again?

14325 is written in base 6.
The number formed by the leftmost 3 digits is 143. 3 is a factor of base 6. Apply 'Last n Digit' rule. The last digit 3 is divisible by 3. Therefore, (143)_6 is divisible by 3.

(54321)_6 is divisible by 5, because 5+4+3+2+1 is divisible by 5.

Correct me if I'm wrong.

- SE

             P.S.:- There is EXACTLY ONE Sir on the site, - TG. Don't address me as Sir.
Re: Divisibility and Bases
by just iim - Wednesday, 8 July 2009, 03:10 PM
  oh sorry man!
i just forgot dat it is in base 6!sad
i take d base 10 and checked it!
now its clear!
but  can you solve d above query i had in my previous post!
Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 03:18 PM
  Just IIM,

I've already updated the article. Have a look.

It does not matter whether you consider signed or unsigned difference while testing the divisibility of a number N by (b+1) in base b; BUT consider the signed difference while finding the remainder.
Signed Difference = sum of the digits in ODD places - sum of the digits in EVEN places

- SE

Re: Divisibility and Bases
by just iim - Wednesday, 8 July 2009, 03:23 PM
  se 8484 in base 12 when divided by 13 should give the remainder 8!
its like (8+8)-(4+4)=8! even by your below given result!
so the remainder should be 8!
but you have written 5 in the article!
correct it se!
Re: Divisibility and Bases
by Software Engineer - Wednesday, 8 July 2009, 03:29 PM
  Just IIM,

The rightmost digit of a number is in ODD place.

Signed Difference
= sum of the digits in ODD places - sum of the digits in EVEN places
= (4+4) - (8+8) mod 13
= 8 - 16 mod 13
= -8 mod 13
= 5 mod 13

- SE
Re: Divisibility and Bases
by just iim - Wednesday, 8 July 2009, 03:34 PM
  thanks for the clarification!
Re: Divisibility and Bases
by vishnu madhavan - Wednesday, 8 July 2009, 05:15 PM
  Thanku so much SE for this grt stuff smile
Re: Divisibility and Bases
by Total Gadha - Wednesday, 8 July 2009, 06:04 PM
  SE smile 'Sir' is a term for respect. And you ARE worth a lot of respect. smile
Re: Divisibility and Bases
by vishal shah - Thursday, 9 July 2009, 03:23 PM
  Superb article SE..keep up the good work & keep updating more articles like these...smile
Re: Divisibility and Bases
by Parag Paratkar - Saturday, 11 July 2009, 03:15 PM
  Just two words.........SIMPLY AWESOME!!!!!!!!!!!
Re: Divisibility and Bases
by Ashish Kumar - Friday, 17 July 2009, 05:37 AM
 

What I like about TG is that they are making it interesting and inspiring their users by their stories which is really helping for those who love to learn ;)
Naaaaaaaaaaaaaice
Ashish!!!

Re: Divisibility and Bases
by - SK - Tuesday, 21 July 2009, 01:20 PM
 

Ultimate !!!!

We all ekalavyas owe u a lot TG..
 
Earnestly request you to post different types of questions from DI too..
I am very weak in DI sad .. plss help me

Thank u soo mchsmile
shiva

Re: Divisibility and Bases
by vivek ghiria - Wednesday, 22 July 2009, 08:47 AM
  Until today I knew all the divisibility rules. Today I know how that rules were formulated.
Thanks SE for sharing the concept of most basic things we learn in school. And how can they be applied to number of other bases.
I have older version of TG Number System book. So requesting to please post more problems for us to practice.

Keep it up... and TGwale pakka IIM le jayenge smile smile
Re: Divisibility and Bases
by Prateek Goyal - Friday, 24 July 2009, 01:37 AM
  Thank you se for such a beautiful article.

but i m having little problem in understanding(129)base 6 can you use 9 in a base 6 number?
I think you can not
and one more problem how to treat A'sand B's used in hexadecimal system
correct me if i am wrong

Re: Divisibility and Bases
by Software Engineer - Friday, 24 July 2009, 11:35 AM
  Prateek,

Thanks for the correction. smile  I'll update the article soon.

In base b, where b>10, A=10, B=11, C=13, D=14 and so on. And in base b only 0 to (b-1) numbers are considered as single-digits.

- SE


Re: Divisibility and Bases
by ramireddy avinash - Friday, 24 July 2009, 08:44 PM
  pls help me to solve this question

what is the maximum value of n such that 157! is perfectly divisible by 18^n?
a) 38 b)38 c)39 )40

if u have solution pls explain it logic.

ty
Re: Divisibility and Bases
by sankalp bansal - Saturday, 25 July 2009, 12:38 AM
  Hi SE

Lets say we need to check (345)6 divisible by 9: By the rule given, 9 divides 62, therefore we check 45(mod 9) = 0(mod 9) as 9*5 = 45.

But this is not true as we should not check 45(mod 9) but [4*(6) + 5](mod 9) as the base is not 10 but 6. i.e. in base 6, 45 is not divisible by 9 as it actually is 29 which is not exactly divisible by 9.

Am i making some mistake here. Please explain...
Re: Divisibility and Bases
by sankalp bansal - Saturday, 25 July 2009, 04:02 PM
  Hi ramireddy avinash

Please read another superb article by SE called "FACTORIALS". That will answer your question and explain the logic too.
Sankalp
Re: Divisibility and Bases
by ramireddy avinash - Monday, 27 July 2009, 07:32 AM
  ty fr ur help! but pls explain it to me here. please
Re: Divisibility and Bases
by Software Engineer - Monday, 27 July 2009, 11:12 AM
  Sankalp,

Thanks for the correction. I'll update the article soon. smile

- SE
Re: Divisibility and Bases
by Sujith menon - Monday, 27 July 2009, 04:01 PM
 

Answer for the penultimate problem.

Since the number is divisible by 10, the last digit should be 0

As Y=0, the number which is divisible by 5 should have 5 as its last digit => T=5

T=5 => U=4 (since it TU divisible by 6)

U=4 => V=2  or V =9 (since UV is divisible by 7)

V=2  = > W=4 ( since VW is divisible by 8 . But U=4 so W cant be 4 as they got to be distinct. So V cant be 2)

V=9 => W=6

W=6 => X=3(since WX is divisible by 9)

Now P Q R S can take one of 1 2 7 8

As PQ is divisible by 2 Q can take either  2 or 8 . If Q takes 2 then we cant get an RS such that its divisible by 4. So Q is 8.

Q=8 => R S = [ 7 2] or [1 2] and both [8 1]  and [8 7] are divisible by 3.

Hence 2 possibilities ?

Re: Divisibility and Bases
by sankalp bansal - Monday, 27 July 2009, 08:35 PM
  hi avinash
here is the solution....
18 = 2 * (3^2)
now since in (157)! maximum power of 2 will be less than maximum power of 3 (because every 2nd number gives a 2 while every 3rd gives 3)...we need to find out max power of 3^2 and that wud be the answer......

Lets find that out....
now we will get a 3 fro every 3rd number like from 3 then 6 then 9 and so on.
we will get two 3's from every 9th number like from 9 then 18 then 27 and so on.
we will get three 3's from every 27th number and so on.....



therefore first divide 157 by 3 = 52 and keep the integral part.
this removes all the 3's which are xisting alone like in 3,6,12 etc...and remove one 3 from all other like from 9,18,27 etc...

now out of these 52 numbers i.e.(3,6,9,12,.....so on) every 3rd number will have one more 3...i.e.(9,18,...so on) therefore divide 52 again by 3 = 17 and keep the integral part...

keep doing this to get:
157/3 +157/(3*3) +157/(3*3*3) + ... = 52 + 17 + 5 + 1 = 75 = max power of 3 in 157!

now max power of 9 wud be 75/2 = 37(because two 3's multiply to give one 9)


therefore max power of 18 wud be 37....

cor blimey!....did tht clear ur doubt...[:|][:|]
sankalp
Re: Divisibility and Bases
by Dinesh Mohan - Friday, 7 August 2009, 05:20 PM
 

Hi SE,

Thanks, I liked the article.

I'm new to TG and had a problem understanding the factors of a number.

1,2,4,5,...20 are factors of 20 in base 10 is it true of other bases (base 19) too??

Can you refer me to anyother post that explains this, please

Dinesh

Re: Divisibility and Bases
by Software Engineer - Saturday, 8 August 2009, 06:29 PM
  Dinesh,

The factors of N stay same in every base.
A prime is prime no matter what base is used to represent it.

- SE
Re: Divisibility and Bases
by A S - Wednesday, 12 August 2009, 05:28 AM
 

Hi Sujith,

I got the same answer, too

Re: Divisibility and Bases
by abhishek tripathi - Wednesday, 12 August 2009, 01:25 PM
  sir i would like 2 know how come 8 is a multiple of 10 to the power 3 as u wrote in the question of cat 1998 do let me know
Re: Divisibility and Bases
by Software Engineer - Wednesday, 12 August 2009, 02:05 PM
  Abhishek Tripathi,

The article says 8 is a factor, NOT multiple, of 103.

- SE
Re: Divisibility and Bases
by abhishek tripathi - Wednesday, 12 August 2009, 04:24 PM
  yaa sir how can b 8 is a multiple of 10 to the power 3 i can not understand dis point...will b very grateful if u help me in understanding dis...sir dat is more elaborated with the help of example dat 16 is a factor of 12 square dats the thing i cant understand..
Re: Divisibility and Bases
by aditya vyas - Saturday, 22 August 2009, 04:00 PM
  thanks tg..gr8 help
Re: Divisibility and Bases
by rajat sharma - Thursday, 3 September 2009, 10:52 PM
 

hello

the property u xplain that if a number in base b is dived by (b-1) leaves the same remainder as the sum of the digit divided by (b-1) has a flaw.

like (3456) in base10 divided by 9,gives remainder 3+4+5+6=18 so 18/9 leaves remainder 2 on the other hand if 3456 is divided by 9 leaves remainder as 0.
plz clarify thanks in advance!!!!! 
Re: Divisibility and Bases
by Software Engineer - Friday, 4 September 2009, 11:18 AM
  Rajat,

like (3456) in base10 divided by 9,gives remainder 3+4+5+6=18 so 18/9 leaves remainder 2 on the other....

2 is the quotient, not remainder.

- SE
Re: Divisibility and Bases
by Praveen M - Friday, 4 September 2009, 05:35 PM
  Thanks for the article, its taught a lot funda smile
Riping e: Divisibility and Bases
by Anand K R - Sunday, 6 September 2009, 09:53 AM
  well i have not completed the enrire post as well..But I cant resist thanking SE for this wonderfull work on fundas...hats off se and thanks again for equiping us..
Re: Divisibility and Bases
by bllitz blitz - Sunday, 6 September 2009, 06:52 PM
  Hi SE,
A beautiful Article indeed.
I have a question.
(8484) to base 12 is divisible by 13 since ( 12+1) = 13  and alternate digits rule.
Now how to do if the question asks, Is it divisible by 14 ,15, and so on.... since the above rule concerns to b+1 only ... In case of add the digits, (b-1) only...  Is power residues the only way ?
Re: Divisibility and Bases
by vikash kumar - Monday, 7 September 2009, 01:53 PM
  sir,
i m having a confusion in a question having 4-digit amro bank pin no. n the digit reshuffled to form hdfc bank pin no.
n the differnce of digit was 2,3 n 9 n we have to find last digit of difference.

as u stated that sum of the difference should be divisible by 9 which gives answer 4

but the sum of the difference should also be divisible by 3(as same formula applies for divisibilty test of 9 n 3) which will give answer "1"
Re: Divisibility and Bases
by Software Engineer - Monday, 7 September 2009, 06:14 PM
  Bllitz,
Please refer the Summary part and pick the most appropriate rule. smile

Vikash,
The sum of digits of difference D must be divisible by both 3 and 9(or LCM of 3 and 9). Therefore, a=4.

- SE
Re: Divisibility and Bases
by santhana lakshmanan - Tuesday, 15 September 2009, 07:38 PM
  Is the answer for the last question "600"?
Re: Divisibility and Bases
by Saurabh - confusion fused - Tuesday, 10 November 2009, 06:32 PM
  Hi Sujit,

Yes your answer is correct. I also got n=2 but I solved it a little bit different method. First, obviously y=0 and hence T=5. I then started solving for values from P,Q,R...till X. Kept P blank, Q can have 2,4,6,8..and went on forming numbers and deleted those where we need to duplicate digits to proceed. This process left me with only two numbers which are 7812549630 and 1872549630.

Regards,
$aurabh
Re: Divisibility and Bases
by ganesh p - Tuesday, 17 November 2009, 04:58 AM
  simply awesome !!
Re: Divisibility and Bases
by sunil meharia - Friday, 27 November 2009, 09:01 AM
  Thanks a lot.

Re: Divisibility and Bases
by King Gadha - Sunday, 11 July 2010, 12:12 AM
  thanx a lot for such  stuff!!!
Re: Divisibility and Bases
by Kunal Chauhan - Sunday, 11 July 2010, 03:17 PM
  legendary......cool
Re: Divisibility and Bases
by Ritesh Raman - Thursday, 15 July 2010, 05:50 PM
 

Awesome Sir!!!

Do you have any compiled notes or correspondence course as such.

Re: Divisibility and Bases
by nancy agrawal - Saturday, 18 September 2010, 12:40 AM
 

cn nebdy pllzzz send me the detailed solution for the problem...rem(123123123.....300 digits)/504?

reply asap!!

Re: Divisibility and Bases
by TG Team - Saturday, 18 September 2010, 01:50 PM
 

504 = 7*8*9 and all three are coprime.

Given number N = 0 mod7 = 3 mod8 = 6 mod9 = 42 mod63 = 483 mod504. smile

Re: Divisibility and Bases
by saurabh tibrewal - Sunday, 19 September 2010, 11:10 PM
  please xplain in detail..
where from this 483 has come...??
Re: Divisibility and Bases
by nancy agrawal - Monday, 20 September 2010, 12:12 AM
  please tell me...hw did u get 42 mod 63...???m stuck frm dis point onwards...
Re: Divisibility and Bases
by nancy agrawal - Monday, 20 September 2010, 12:36 AM
 

please try solving this ques too...

rem of 7777.....(2n+1)times/1232

Re: Divisibility and Bases
by TG Team - Monday, 20 September 2010, 02:11 PM
 

Dear Saurabh and Nancy smile

We need to look for smallest number N which gives 0, 3 and 6 as remainder when divided by 7, 8 and 9 respectively.

Or N = 7a = 8b + 3 = 9c + 6

First I looked in multiples of 7 which are of the form 9c + 6 and smallest such number is 42. Next will be 42 + 63 and then 42 + 2*63 or in general 63d + 42 or 42 mod63. smile

Now we need to look in all numbers of 42 mod63 which are of the form 8b + 3 and 483 is smallest such number. Or in general 504e + 483 or 483 mod504. smile

We can also use Chinese Remainder Theorem. If you have doubts in that then look for it in quant lessons.

Now 1232 = 7*11*16

And N = 777...2n + 1 times = 0 mod7 = 7 mod11 = 1 mod16

Now among multiples of 7, 49 is the smallest number of the form 16a + 1 and next number will be 49 + 112 and so on or say 49 mod112.

And writing all these numbers of 49 mod112 i.e. 49, 161, ..we get 161 which is of the form 7 mod11. So our answer is N = 161 mod1232. smile      

Re: Divisibility and Bases
by nancy agrawal - Monday, 20 September 2010, 11:40 PM
  thanks a tonne kamal...
Re: Divisibility and Bases
by swayam aahuja - Sunday, 10 October 2010, 03:00 AM
  hi Nancy it's very simple sum...
1232=2*2*2*2*7*11.
777777.....(2n+1)time can be written as
77777777.....00000+77777
now 77777777.....00000 is divisible by 2*2*2*2*7*11
so you get the remainder by 77777(mod 1232)=161(mod1232).
Re: Divisibility and Bases
by cat 2012 - Saturday, 8 October 2011, 09:16 PM
  Kamal Sir,
Can you please explain when do we take positive difference and when normal difference?

Rule2 :A no. in base b divided by (b+1) leaves the same remainder as the positive difference b/w the sum of the digits at odd places and those at even places is divided by (b+1)

But, in an example it is written 8484(base 12) divided by 13.
Shouldn't it be +8 in place of -8?

Please revert. Thanks n advance. smile
 
Re: Divisibility and Bases
by Arpit Jain - Wednesday, 12 October 2011, 07:03 PM
  for second last question in article i am getting 2 possible values of N which are 7812549630 and 1872549630

but i am not able to solve the last question of article,please SE sir post the solution,method,how to approach it.

~Arpit
Re: Divisibility and Bases
by Aakash Gupta - Saturday, 31 May 2014, 10:52 PM
  Hey TG..

I came to know of Total Gadha from a cousin of mine. The first image that came to my mind about this was that of a typical site providing that old and repeated study matter. Still, I thought of giving it a shot. And after few months, I think that was one of the best shot I fired aiming for CAT.

Quant is my strong point compared to verbal and I didn't think that TG will offer anything new here. But I must say that the question specific material you offer here is outstanding. The study material and the approach you describe here hit right at the center of problem.

As far as this topic is concerned, I haven't read it yet but the introduction itself fills me with confidence. Is baar TG wale IIM le hi jayengee...!!