Question

Given the algorithm from the leap year case study with the lines numbered as follows:

1. Divide the year by 4 and if the remainder isn't 0
2. Return false (The year is not a leap year)
3. Otherwise, divide the year by 100 and if the remainder isn't 0,
4. Return true (The year is a leap year)
5. Otherwise, divide the year by 400 and if the remainder isn't 0,
6. Return false (The year is not a leap year)
7. Otherwise, Return true (the year is a leap year)

Indicate which line of the algorithm tells you whether the date is a leap year in each of the following cases:
a. 1900 Line =
b. 1945 Line =
c. 1600 Line =
d. 1492 Line =
e. 1776 Line =

Answer 1

The lines from the algorithm indicate whether each year is a leap year or not; 1900 is not a leap year (line 6); however, 1945, 1492, and 1776 are leap years (line 4), and 1600 is a leap year as well (line 7).

Step-by-step explanation:

To determine whether a given year is a leap year according to the Gregorian calendar, we can use the provided algorithm. We'll go through the steps for each year to see which line of the algorithm tells us if the year is a leap year or not.

• 1900: Divisible by 4, divisible by 100, but not divisible by 400. According to the algorithm, we stop at line 6, which returns false (The year is not a leap year).
• 1945: Divisible by 4 but not by 100. We stop at line 3, which leads us to line 4, returning true (The year is a leap year).
• 1600: Divisible by 4, divisible by 100, and divisible by 400. We proceed to the end of the algorithm and stop at line 7, which returns true (The year is a leap year).
• 1492: Divisible by 4 but not by 100. We stop at line 3, which leads us to line 4, returning true (The year is a leap year).
• 1776: Divisible by 4 but not by 100. Similar to 1492, we stop at line 3, which leads us to line 4, meaning true (The year is a leap year).

To summarize, the lines corresponding to each year are a. 1900 Line = 6, b. 1945 Line = 4, c. 1600 Line = 7, d. 1492 Line = 4, e. 1776 Line = 4.