P&C - Count of numbers divisible by 3

Saurabh123 · Joined: 28 Jun 2006 Posts: 4 Location: Fbd

Hi,

how to approach for solving such problems:
- How many 4 digit numbers are there which r divisible by 3

when we know that no. divisible by 3 has sum of all its digits divisible by3?

thnks

apgo2000 · Joined: 13 Jul 2006 Posts: 15

[quote="Saurabh123"]Hi,

how to approach for solving such problems:
- How many 4 digit numbers are there which r divisible by 3

when we know that no. divisible by 3 has sum of all its digits divisible by3?

thnks[/quote]

The way i do such questions is that the first four digit number divisible by 3 is 1002 (999 + 3; we all know 999 is div by 3, or else u cud divide 1000/3 and multiply 3 by the next highest integer than the divisor. for eg, u get 333.something so multiply 334 with 3 and u get 1002).
the largest 4 digit number is 9999 which is very apparent.

so u have an a.p. where 1st term =a= 1002
last term=l =9999
common difference = d= 3

therefore l=a+(n-1)d
9999=1002+(n-1)*3
u get 3000

this is a very concise process requiring u to write only the equation. rest is mental cal and wont take much time.

do post a better method if anyone can.

regards,
anshu

CZ@@@H@@@R · Serious about CAT Joined: 14 Jan 2006 Posts: 64