Aptitude - Numbers - Discussion

We can do this as:

The number should be divisible by 6.

We can write 6 as (2*3).

Then,

A) 149 -- (1+4+9) = 14 (which is divisible by 2 but not 3 so it is not divisible by 6).

B) 150 --(1+5+0) = 6(which is divisible by both 2 and 3).

C) 151 --(1+5+1) = 7(which is not divisible by both 2 and 3).

D) 166 --(1+6+6) = 13(which is not divisible by both 2 and 3).


So the answer is (b) which is divisible by both 2 and 3 i..e(2*3=6).

Another method:

Add those 3 digit numbers which are given in the options if that answer is divisible by 3 then it will divisible by 6. Once see 1+5+0=6 it is divisible by 3 so it is divisible by 6. Remaining options are not divisible by 3 after adding.

Simple answer : A number is divide by 6 if that number was divisible by 2 and 3.

149 = Not divide by by 2 answer 3.

150 = Divide by 2 and 3.

151 = Not divide by by 2 answer 3.

166 = Not divide by by 2 answer 3.

So answer is B.

Total 3 digit number=999.
Counting of 2 digit numbers(i.e 0-99)=100,
Counting of 3 digit numbers=999-100=899,
(899+1)/6=150.

What is the meaning of A.P here?

A.P is arithmetic progression.

((last term-first term)/difference) +1.

The question is about how many 3 digit numbers. So we must COUNT the numbers divisible by 6 right?

- if any amount of nos. Is divisible by 6,

Then the equal amount of nos. Is also divisible by 6.

Hence, option B is correct.