Even i did the same way,arora007 wrote:n^2 =(24x + 1) where x is an integer.
(n^2 -1) = 24x
(n+1)(n-1) =24x
1/thus n has to be an odd number
2/ either n+1 or n-1 should be a multiple of 3
now start plugging in numbers... we for sure know
n=1
n=5
n=7
n=13
n=17
n=19
n=23
n=25
n=29
now we see the repitition
as
n=31
n=35
n=37
thus we should have 30 natural numbers....
I dont know my answer... but i hope my logic is correct.
I know there should be a better answer!!
But my series was. 
arora007.arora007 wrote:n^2 =(24x + 1) where x is an integer.
(n^2 -1) = 24x
(n+1)(n-1) =24x
1/thus n has to be an odd number
2/ either n+1 or n-1 should be a multiple of 3
now start plugging in numbers... we for sure know
n=1
n=5
n=7
n=13
n=17
n=19
n=23
n=25
n=29
now we see the repitition
as
n=31
n=35
n=37
thus we should have 30 natural numbers....
I dont know my answer... but i hope my logic is correct.
I know there should be a better answer!!
The series you have written is follows 6x+1 pr 6x-1 (AND n=1 is not valid otherwise n-1 = 0 which is one of the factor).goyalsau wrote:Even i did the same way,arora007 wrote:n^2 =(24x + 1) where x is an integer.
(n^2 -1) = 24x
(n+1)(n-1) =24x
1/thus n has to be an odd number
2/ either n+1 or n-1 should be a multiple of 3
now start plugging in numbers... we for sure know
n=1
n=5
n=7
n=13
n=17
n=19
n=23
n=25
n=29
now we see the repitition
as
n=31
n=35
n=37
thus we should have 30 natural numbers....
I dont know my answer... but i hope my logic is correct.
I know there should be a better answer!!
1
5
7
11
13
17
19
23
25
29
31
35
37
41
43
47
49
53
55
59
61
65
67
71
73
77
79
83
85
89
91
95
97
I formed this series with the similarity in the first few number of the series.
Like difference between 1 to 5 is 4
difference between 5 to 7 is 2
again 7 to 11 is 4
like this i formed the series and checked it for the first new number as i remember the square of them. but the problem is answer that i am getting is 33 while the OA is 32, Now i don't think it will be valid do the square of all the number to check..
There is a pattern as well 1 to 10 - 3 numbers
11 to 20 - 4 numbers
21 to 30 - 3 numbers.
31 to 40 - 3 numbers.
again 41 to 50 - 4 numbers ....
Please suggest what i am doing wrong..............
Anshu, well... i missed 11 in my calculations...anshumishra wrote:arora007.arora007 wrote:n^2 =(24x + 1) where x is an integer.
(n^2 -1) = 24x
(n+1)(n-1) =24x
1/thus n has to be an odd number
2/ either n+1 or n-1 should be a multiple of 3
now start plugging in numbers... we for sure know
n=1
n=5
n=7
n=13
n=17
n=19
n=23
n=25
n=29
now we see the repitition
as
n=31
n=35
n=37
thus we should have 30 natural numbers....
I dont know my answer... but i hope my logic is correct.
I know there should be a better answer!!
Your method is right.
Also, you can see the pattern it follows is 6x+1 or 6x-1
So, the number should be = (100/6)*2 = 16*2 = 32
arora007 wrote:Anshu, well... i missed 11 in my calculations...anshumishra wrote:arora007.arora007 wrote:n^2 =(24x + 1) where x is an integer.
(n^2 -1) = 24x
(n+1)(n-1) =24x
1/thus n has to be an odd number
2/ either n+1 or n-1 should be a multiple of 3
now start plugging in numbers... we for sure know
n=1O
n=5
n=7
n=13
n=17
n=19
n=23
n=25
n=29
now we see the repitition
as
n=31
n=35
n=37
thus we should have 30 natural numbers....
I dont know my answer... but i hope my logic is correct.
I know there should be a better answer!!
Your method is right.
Also, you can see the pattern it follows is 6x+1 or 6x-1
So, the number should be = (100/6)*2 = 16*2 = 32
and as per saurabh's brute-force method the count is 33,
32 is off the track!
I hope there is a simpler more accurate way!
so answer should be 33.anshumishra wrote:Also, the only reason that 1 is treated separately is that sequence 6x+-1 will also include -1 when x=0.
Yes !goyalsau wrote:so answer should be 33.anshumishra wrote:Also, the only reason that 1 is treated separately is that sequence 6x+-1 will also include -1 when x=0.
