# 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

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).