24

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!!

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!!

Even i did the same way, But my series was.
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..............

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!!

arora007.
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

goyalsau wrote:

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!!

Even i did the same way, But my series was.
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..............

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).
Hence instead of 33 it is 32.
here is how you calculate it => k = 100/6 = 16 (so, each k+1 and k-1 will have 16 values, total 32).

anshumishra wrote:

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!!

arora007.
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

Anshu, well... i missed 11 in my calculations...
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!

yes, my fault . 1 is a valid solution.
However besides that the method is not terrible.
6x+-1 less than 100 , where x is integer
quite straight foward.

arora007 wrote:

anshumishra wrote:

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!!

arora007.
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

Anshu, well... i missed 11 in my calculations...
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!

Also, the only reason that 1 is treated separately is that sequence 6x+-1 will also include -1 when x=0.

anshumishra wrote:Also, the only reason that 1 is treated separately is that sequence 6x+-1 will also include -1 when x=0.

so answer should be 33.

goyalsau wrote:

anshumishra wrote:Also, the only reason that 1 is treated separately is that sequence 6x+-1 will also include -1 when x=0.

so answer should be 33.

Yes !