Practice Quiz 1: The actual quiz will be open book (any book) and open notes (any notes or written material). [1] (12 points) Answer each of the following questions, and justify your answers. (a) Can 32 be written as an integer linear combination of 24 and 42? (b) Can 36 be written as an integer linear combination of 24 and 42? [2] (20 points) Suppose you have $1.45, and you want to buy some number of mints at 24 cents each and some number of chocolates at 42 cents each so that you exactly use up your $1.45. (a) Is it possible? Why or why not? (b) If instead you have 60 cents, is it possible? Why or why not? (c) Suppose you have $3. It turns out that 300 = m24 + n42 has solutions where both m and n are positive. Find at least two solutions and explain how you found them. [3] (18 points) (a) Find gcd(204, 93). Show your work. (b) Find lcm(204,93). Explain how you found your answer. (c) Use Euclid's algorithm to write gcd(204,93) as an integer linear combination of 204 and 93. Show your work.