Are there any easy techniques available for these questions below, without getting into lengthy calculations? Please explain your approach and also recommend any resources that might be helpful in learning such techniques! Thank you.

1). If a circle, regular hexagon and a regular octagon have the same area and if the perimeter of the circle is represented by "c", that of the hexagon by "h" and that of the octagon by "o", then which of the following is true?
A) c > o > h
B) c > h > o
C) h > c > o
D) o > h > c
E) h > o > c

2). In a class comprising boys and girls, there were 45 hand shakes amongst the girls and 105 hand shakes amongst the boys. How many hand shakes took place between a boy and a girl, if each member of the class shook hands exactly once with every other student in the class?
A) 25
B) 15
C) 150
D) 300
E) 24

3). The price of a commodity increases by 25% in January. There is a subsequent 25% increase in its price in February. If a person used to get 1 unit of the commodity for $x in December, how many units of the commodity will he get for $2x in February?
A. 0.64x
B. 0.36x
C. 1.64x
D. 1.28x
E. 1.72x

4). If two positive integers are relatively prime to each other and the product of these two integers is 240, then what is the LCM of these two integers?
A. 120
B. 240
C. 80
D. 30
E. 1

5). How many times is the digit "3" written while numbering the pages of a book from 1 to 1000?
A. 243
B. 252
C. 271
D. 293
E. 300

Thanks, Walker. As requested, I'll break down the questions into individual posts. Appreciate your contributions to this forum. You have been very helpful!