Latest Elitmus Aptitude Question SOLUTION: Q. consider a series 1,2,3,....N, is divisible by 10, where N

Sn=n(n+1)/2
Therefore, n(n+1)/2 must be divisible by 10
Or, n(n+1) must be divisible by 20

CASE 1: take the following consecutive numbers
4,5,6 [4*5 divisible by 20]
14,15,16 [15*16 divisible by 20]
24,25,26 [24*25 divisible by 20]
34,35,36 [35*36 divisible by 20]
44,45,46 [44*45 divisible by 20]
.
.
.
984,985,986 [984*985 divisible by 20]
994,995,996 [995*996 divisible by 20]
From above steps it is clear that there is
an alternative number around the 5's multiple
which is producing the combination to
produce a number divisible by 20.
COUNT_1=100

CASE 2: take the following consecutive numbers
19,20,21 [19*20 and 20*21 both are divisible by 20]
39,40,41 [39*40 and 40*41 both are divisible by 20]
59,60,61 [59*60 and 60*61 both are divisible by 20]
79,80,81 [79*80 and 80*81 both are divisible by 20]
.
.
.
979,980,981 [979*980 and 980*981 both are divisible by 20]
From above steps it is clear that both the numbers
around the 20's multiple are producing the combination to produce a number divisible by 20.
COUNT_2= 49*2=98

CASE 3:
The series 1 to 999 is divisible by 20
COUNT_3=1

Total Count = Count_1 + Count_2 +Count_3 = 100+98+1 = 199

complete question is a series 1,2,3,4...n is divisible by 10 and n is less than 1000.for example 1,2,3,4. sum is divisible by 10,how many search series are possible?

Sn=n(n+1)/2 ;n

Today's Ques.
consider a series 1,2,3,....N, is divisible by 10
where N

consider a series 1,2,3,....N, is divisible by 10 where N

this question is only solved by option.

options are
1-> 199
2-> 249
3-> 399

Sn=n(n+1)/2 ;n

Sn=n(n+1)/2 ;n

1,2,3.......15
sum:n(n+1)/2 must be divisble by s10
15*16/2=60 is divisble by 10
answers are n=15,20,24,...

its answer is 199, 249-50 = 199;

sum of n terms of an series 1,2,3,4...........n is
n^2+n/2 for divisible by 10 it must produce value of type 10*k
hit and trail
n=4,15,20 and so on...

Sn=n(n+1)/2 ;n

Ans:-199
Approach:-
Sn=n(n+1)/2 for n