# Aptitude - Numbers - Discussion

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

33.

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

Answer: Option

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 t_{n} = 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.

Discussion:

14 comments Page 1 of 2.
Bhuvana ram said:
4 years ago

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).

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).

Sarbarth said:
6 years ago

How can we know which number is perfectly divisible by 78?

9944 or 9988.

Can anyone sole it?

9944 or 9988.

Can anyone sole it?

ABDUL HASIB LASKAR said:
6 years ago

Thanks for explaining this.

Haseeb said:
7 years ago

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.

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.

(2)

Vijay said:
7 years ago

@Ramskittu.

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

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

Rehana said:
7 years ago

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?

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

180-15+1 = 166.

166/5 = 33.xxx.

Then 33 is the right answer?

Nano_Desu said:
8 years ago

How about this one?

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

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

Ramskittu said:
8 years ago

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.

So 96/6 = 16.

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

So finally 16-3 = 13.

Anil sarode said:
8 years ago

@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.

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.

SHIV said:
8 years ago

Any other method please.

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