Numbers Questions

1 to 300 = 300 numbers
squares btwn 1 to 300 = 1,4,9,16,25,36,49.....289 i.e, total 17
cubes = 1,8,27,64,125,216 i.e, 5
now 1 and 64 are common so total numbers that should be removed ( 17+5-2= 20 )
total 20 term removed so 300th term would be 320

Here by trial and error method, we can obseve that

404404 = 404 x 1001; 415415 = 415 x 1001, etc.

So, any number of this form is divisible by 1001.

Ans. 
4.5 = 7 x 0.5 + 1
5.5 = 4.5 x 1 + 1
12 = 5.5 x 2 + 1
49 = 12 x 4 + 1
? = 49 x 8 + 1, i.e. ? = 393

Let the original number is 82 i.e 8 + 2 = 10 and when the digits are reversed i.e 28
The difference is 82 - 28 = 54 i.e, the number is decreased by 54.

The pattern followed is *1.5 , * 2 , *2.5 , *3 , *3.5

Given numbers are 585 546 514 404 206 369
Then interchanging the 1st and 3rd digits of the given numbers, we get
585 645 415 404 602 963
Now, arranging them in ascending order
963 645 602 585 415 404
Then the last second number is 415.

In case B, odd times even will give even

1523+2323=19-423+19+423  

 The remainder on dividing by 19 will be -423+423= 0.