We’ll just look at a few quick tricks, not go for too advanced problems as of now 🙂 The thing is that base systems have not been that frequently asked in CAT so I don’t plan to concentrate much on the topic for now…
Gud afternoon sir…
sir please explain the last part of today’s blog. the number of the form (2abc) to the base 6 lies between 432 and 647… it is a 4 digit number then it shud lie between 6^3 and 6^4 -1
Girish, it is not just a 4-digit number but a 4-digit number starting with 2. So the highest power (in this case 6^3) is occurring exactly twice. Think about it: (2000)6 = 2 * 216 = 432, while (3000)6 is 3*216 = 648. So any number of the form (2abc)6 will be >= 432 but < 648 i.e. between 432 and 647 inclusive.
This is just like saying any number of the form (5abc) in our usual base 10 must be between 5*10^3 and (6*10^3-1) i.e. between 5000 and 5999….
Nice one sir..waiting for more advanced base system concepts.
By Rnishant on June 11, 2013 at 12:13 PM
Hi Nishant,
We’ll just look at a few quick tricks, not go for too advanced problems as of now 🙂 The thing is that base systems have not been that frequently asked in CAT so I don’t plan to concentrate much on the topic for now…
regards
J
By catcracker on June 11, 2013 at 12:19 PM
Gud afternoon sir…
sir please explain the last part of today’s blog. the number of the form (2abc) to the base 6 lies between 432 and 647… it is a 4 digit number then it shud lie between 6^3 and 6^4 -1
By Girish on June 11, 2013 at 12:27 PM
Girish, it is not just a 4-digit number but a 4-digit number starting with 2. So the highest power (in this case 6^3) is occurring exactly twice. Think about it: (2000)6 = 2 * 216 = 432, while (3000)6 is 3*216 = 648. So any number of the form (2abc)6 will be >= 432 but < 648 i.e. between 432 and 647 inclusive.
This is just like saying any number of the form (5abc) in our usual base 10 must be between 5*10^3 and (6*10^3-1) i.e. between 5000 and 5999….
regards
J
By catcracker on June 11, 2013 at 12:33 PM
THANK YOU SIR….
By Girish on June 11, 2013 at 1:34 PM
The last part is the best
By Ratish on June 11, 2013 at 2:49 PM
one more thing: no of p digit nos in n base system= n^p-n^p-1.
Eg: 4 digit nos in binary system=2^4-2^3=8
By kronos on November 26, 2016 at 7:29 PM