How many numbers can be completely divided to 240?

Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:

The difference between the sum of four consecutive odd numbers and three consecutives even numbers together is 20. Also, the largest even number is 5 more than the largest odd number. What is the sum of the smallest odd number and the smallest even number?

What will be come in place of question mark(?) in the following number series?
13 , 14 , 30 , 93, ?, 1885

What will be come in place of question mark(?) in the following number series?
8,  14, 25, 46, 82 , ?

What will be come in place of question mark(?) in the following number series?
14, 8, 7 , 11.5, 22, ?

Find the value of

Let x be the least number of 4 digit that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If x lies between 2000 and 2500, then what is the sum of the digits of x?