1: Consider the following pseudocode fragment and answer corresponding questions. (For each question, you should clearly show steps about how you get the answer.) count := 0 For i = 1 to 6 For j =i+2 to 9 count: i j + count b) c) d) End-for End-for a) For the iteration of the outer loop where i = 4, how many times does the inner loop iterate? (5 Points) How many times has the variable "count" increased? (5 Points) Suppose i = 5, what is the value of "count" after the execution of inner loop? (5 Points) What is the final value of "count" after the execution of this nested loop? (5 Points) Question 2: (20 Points) Compute the value of the following questions. (For each question, you should clearly show steps about how you get the answer.) a) (-99) div 10 (5 Points) b) (-328) mod 9 (5 Points) c) Suppose n mod 5 = 3, find all possible values of n. (5 Points) d) [(45 mod 7) + (62 mod 7)] mod 7 (5 Points) Question 3: (20 Points) Question 4: Give the prime factorization for each number in non-decreasing order and find the greatest common divisor (gcd) and least common multiple (lcm). (For each question, you should clearly show steps about how you get the answer.) a) 56 (4 Points) b) 90 (4 Points) c) 470 (4 Points) d) ged(48, 84) (4 Points) e) lcm(132, 176) (4 Points) Question 4: (20 Points) Convert a text message to a number or a number to a text message using a specific scheme. The scheme associates each lowercase letter to a 2-digit number in the range 01 through 26 ("a"=01, "b"=02,..., "z"=26) and the blank character to 27. (For each question, you should clearly show steps about how you get the answer.) a) 19200118 (4 Points) b) 1618091305 (4 Points) c) 80116160914051919 (4 Points) d) real madrid (4 Points) e) never give up (4 Points)