We’ll just look at a few quick tricks, not go for too advanced problems as of now ðŸ™‚ 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.

Hi Nishant,

We’ll just look at a few quick tricks, not go for too advanced problems as of now ðŸ™‚ 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

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….

regards

J

THANK YOU SIR….

The last part is the best

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