ITPEC FE Morning April 2018 Question 8

s is the quotient and t the remainder of x ÷ y — the flowchart divides by repeated subtraction.

• •Start: s ← 0, t ← x
• •While t ≥ y: subtract y from t and add 1 to s
• •Stop when t < y

So s counts how many times y fits into x, and t is what is left, smaller than y. Example with x = 13, y = 4: t goes 13, 9, 5, 1 while s goes 0, 1, 2, 3, ending with s = 3, t = 1, and 13 = 4 × 3 + 1.

Answer (b)

Why not others:

• •(a) — swaps the roles: s counts the subtractions, so it is the quotient, and t holds the leftover
• •(d) — the dividend is x, because t starts at x, and the divisor is y, the amount subtracted; this reverses them
• •(c) — both reverses the division and swaps quotient and remainder

Key rule: In a repeated-subtraction loop, the counter is the quotient and the value left when the loop stops is the remainder.

Algorithm and Programming · AI-written, may contain errors