Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.33)

33. 

How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?

[A]. 8
[B]. 11
[C]. 12
[D]. 13
[E]. None of these

Answer: Option D

Explanation:

Required numbers are 24, 30, 36, 42, ..., 96

This is an A.P. in which a = 24, d = 6 and l = 96

Let the number of terms in it be n.

Then tn = 96    a + (n - 1)d = 96

24 + (n - 1) x 6 = 96

(n - 1) x 6 = 72

(n - 1) = 12

n = 13

Required number of numbers = 13.


Mahesh Patil said: (Aug 1, 2011)  
Total numbers between 23 to 100 = 100-23+1 = 78

Numbers Divisible by 6 = 78 / 6 =13 (consider Only Quotient ....not Remainder)

Sallick said: (Apr 21, 2012)  
24+(n-1)6=96
=n-1=12
=n=13

Goms said: (Aug 21, 2013)  
4*6 = 24
5*6 = 30
6*6 = 36
7*6 = 42
8*6 = 48
9*6 = 54
10*6 = 60
11*6 = 66
12*6 = 72
13*6 = 78
14*6 = 84
15*6 = 90
16*6 = 96
TOTAL = 13.

Avinash said: (Sep 16, 2013)  
24+(n-1)6 = 96.

= n-1 = 12.

= n = 13.

Shiv said: (Jan 3, 2015)  
Any other method please.

Anil Sarode said: (Feb 8, 2015)  
@Shiv here is the method for you.

Here total 78 numbers are here, check by AP formula.

Tn = a+(n-1) d where a = 23, d =1, Tn = 100, so n = 78. Now simply divide 78/6 = 13.

Ramskittu said: (Feb 14, 2015)  
Max number which or completely divisible by 6 below 100 is 96.

So 96/6 = 16.

Remove before divisible numbers of 23. i.e. 3.

So finally 16-3 = 13.

Nano_Desu said: (Sep 11, 2015)  
How about this one?

100-23 = 77 divided it by 6 77/6 = 12.83 round off 13.

Rehana said: (Mar 10, 2016)  
For example,

Number b/w 15 to 180 divided by 5 are,

180-15+1 = 166.

166/5 = 33.xxx.

Then 33 is the right answer?

Vijay said: (Jun 19, 2016)  
@Ramskittu.

I am not understanding your method for getting solution. Please explain it again.

Haseeb said: (Aug 1, 2016)  
The number between 1 to 100 number which a are divisible by 6 is;

6 (100(16
___
96
___
4.

Hence, the number which is divisible between 1 to 100 by 6 are "16".

Now we will find the number which is divisible between 1 to 23.

6)23(3
18
_
5.

Hence the number which is divisible between 1 and 23 are "3".
Now the number between (1 to 100 ) - ( 1 to 23).
16 - 3 = 13 => Answer.

Abdul Hasib Laskar said: (Apr 19, 2017)  
Thanks for explaining this.

Sarbarth said: (Jul 20, 2017)  
How can we know which number is perfectly divisible by 78?

9944 or 9988.

Can anyone sole it?

Bhuvana Ram said: (Jun 24, 2019)  
It was a difficult one to remember the numbers which are divisible by 6.

So, I recommended you to solve this by the following method.

Formula: n=(l-a)/d+1.
For the above question l=100,a=23, d=6.
n=((100-23)/6)+1.
=(77/6)+1.
=77+6/6.
= 83/6 = 13 (consider only the quotient, not the remainder).

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