# Aptitude - Numbers - Discussion

### Discussion :: Numbers - General Questions (Q.No.36)

36.

How many 3 digit numbers are divisible by 6 in all ?

 [A]. 149 [B]. 150 [C]. 151 [D]. 166

Explanation:

Required numbers are 102, 108, 114, ... , 996

This is an A.P. in which a = 102, d = 6 and l = 996

Let the number of terms be n. Then,

a + (n - 1)d = 996 102 + (n - 1) x 6 = 996 6 x (n - 1) = 894 (n - 1) = 149 n = 150.

 Sree said: (Oct 1, 2012) 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.

 Moni said: (Jul 17, 2013) 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).

 Pvk said: (Nov 24, 2015) 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.

 Imran said: (Sep 7, 2018) 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.

 Yogesh Panchal said: (Mar 6, 2019) What is the meaning of A.P here?

 Shreyash Itankar said: (Jun 5, 2019) A.P is arithmetic progression. ((last term-first term)/difference) +1.

 Mamatha said: (Apr 28, 2020) The question is about how many 3 digit numbers. So we must COUNT the numbers divisible by 6 right?

 Vivek Singh said: (Sep 10, 2021) - 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.