Divisibility and Bases  
A 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 twentyfour 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 Sclass Mercedes parked behind us, inside which were sitting 23 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 26^{th} 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

Re: Divisibility and Bases  
Bravo....u stole my heart.. 
Re: Divisibility and Bases  
AWESOME ARTICLE..WAITING FOR MORE ARTICLES.. 
Re: Divisibility and Bases  
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  
Saurav, Yes, that's a mistake. As n is a factor of 30^1, just divide the last digit.  SE 
Re: Divisibility and Bases  
Thank You! 
Re: Divisibility and Bases  
Great Article SE....Thanks and keep up the good work 
Re: Divisibility and Bases  
TG sir , SE may turn out to be your competitor.Beware SE, U can start another forum called "Total Engineer" 
Re: Divisibility and Bases  
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  
Hi SE>>>>GRT Indeed this is too much informative.
regards sanjeeb 
Re: Divisibility and Bases  
Hi SE thnx a ton 4 such an informative article TG rocks so does SE !!!!!! 
Re: Divisibility and Bases  
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  
Raja, You are welcome. That's the 'positive diffrence'; so whether we do (816) or (168), the positive diffrence is 8 in both cases. Is it clear?  SE 
Re: Divisibility and Bases  
Raja, Had a blast in mind after reading your post. Thanks for the correction. Please check the updated article.  SE 
Re: Divisibility and Bases  
Simply awesome 
Re: Divisibility and Bases  
oh sorry man! i just forgot dat it is in base 6! 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  
thanks for the clarification! 
Re: Divisibility and Bases  
Thanku so much SE for this grt stuff 
Re: Divisibility and Bases  
SE 'Sir' is a term for respect. And you ARE worth a lot of respect. 
Re: Divisibility and Bases  
Superb article SE..keep up the good work & keep updating more articles like these... 
Re: Divisibility and Bases  
Just two words.........SIMPLY AWESOME!!!!!!!!!!! 
Re: Divisibility and Bases  
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  
ty fr ur help! but pls explain it to me here. please 
Re: Divisibility and Bases  
Sankalp, Thanks for the correction. I'll update the article soon.  SE 
Re: Divisibility and Bases  
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  
Hi Sujith, I got the same answer, too 
Re: Divisibility and Bases  
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  
Abhishek Tripathi, The article says 8 is a factor, NOT multiple, of 10^{3}.  SE 
Re: Divisibility and Bases  
thanks tg..gr8 help 
Re: Divisibility and Bases  
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  
Thanks for the article, its taught a lot funda 
Riping e: Divisibility and Bases  
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  
Is the answer for the last question "600"? 
Re: Divisibility and Bases  
simply awesome !! 
Re: Divisibility and Bases  
Thanks a lot. 
Re: Divisibility and Bases  
thanx a lot for such stuff!!! 
Re: Divisibility and Bases  
legendary...... 
Re: Divisibility and Bases  
Awesome Sir!!! Do you have any compiled notes or correspondence course as such. 
Re: Divisibility and Bases  
cn nebdy pllzzz send me the detailed solution for the problem...rem(123123123.....300 digits)/504? reply asap!! 
Re: Divisibility and Bases  
504 = 7*8*9 and all three are coprime. Given number N = 0 mod7 = 3 mod8 = 6 mod9 = 42 mod63 = 483 mod504. 
Re: Divisibility and Bases  
please xplain in detail.. where from this 483 has come...?? 
Re: Divisibility and Bases  
please tell me...hw did u get 42 mod 63...???m stuck frm dis point onwards... 
Re: Divisibility and Bases  
please try solving this ques too... rem of 7777.....(2n+1)times/1232 
Re: Divisibility and Bases  
thanks a tonne kamal... 
Re: Divisibility and Bases  
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. 