Question

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APTITUDE / ANALYTICAL
Question No. 1 of 10 | 1 Marks
How many numbers smaller than 2.10% and are divisible by 3 can be written by means of the digits 0,1
and 2 (exclude single digit and double digit numbers)?​

Answer 1

Answer:

How many numbers smaller than 2x10^8 are divisible by 3 can be written by means of the digits 0, 1, and 2?

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2×108=200,000,000

First digit must be 0 or 1

All other digits can be 0,1, or 2

Since we are allowing leading zeros, this will help to include all integers less than 200,000,000. (1digit numbers up to 9digit numbers).

First digit =0 or 1

Second to eighth digits =0,1, or 2

Last digit = whichever of 0,1, or 2 will make number divisible by 3.

Note that no matter what digits you enter in first 8 positions, choosing exactly one of 0,1, or 2 as the last digit will make the number divisible by 3. That’s because for any 3 consecutive numbers, one and only one will be divisible by 3.

So this just comes down to the number of ways of placing 0,1, and 2 into first 8 positions, and placing the appropriate one in last position.

=2×37×1=4,374