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

Answer: Option B

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.

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