Math Is Fun Forum

I recently received 100 "out of the world maths question" from somebody, I complete them but stuck with a few, so help will be great, also explanation on how you did it please.

Q1) A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all previous numbers. Determine the 12th number in the sequence.
A1) My answer is 1536, I did it bu writing it all on a piece of paper by adding them all up, there is a better way to do it right?

Q2) Adam has £2010 in his bank account. He donates £10 to charity every day. His first donation is on Monday. On what day will he donate his last £10?
A2) My answer is Monday, I did it by drawing it all up. I'm sure there is a better way to do it? Please show me how.

Q3) A circle and a square overlap such that the overlapping area is 50% of the area of the circle, and is 25% of the area of the square. Find the ratio of the area of the square outside the circle to the area of the whole figure.
A3) I have no idea about his one, please show me how you did it.

Q4) Find the number of different pairs of positive integers (a,b) for which

and

A4) I do not understand please show me how you did it.

Q5) There positive integers a,b and c are given such that

Find the value of a,b and c.
A5) I do not understand at all.

Q6) Find the number of positive integers less than 500, which is not divisible by 5 or 7.
A6) I know how to do this all on a big piece of paper, but there is a easier way? Please show me how.

Q7) Find the smallest positive integers n such that every digit of n is either 0 or 7, and n is divisible by 15.
A7) Again, I could do that on a big piece of paper, but please show me a easier way to do it.

Q8) Let n and k be two positive integers such that k is less than n. It is known that (1+2+3+4+...+n) + k = 101. Find k.
A8) I do not know how to do this.

Q9)Find the last digit of :

A9) This one got to do with mod?

That's all, thanks everyone. p.s I need help with modifying it... Like the way I do it with a few more answers, I might post it later.
EDIT*** Can someone show me the worked method?