The Following Formula Can Be Used to Find the Day

question 115

Multiple Choice

The following formula can be used to find the day of the week on which a given year begins. First calculate
$\mathrm { a } = \mathrm { y } + \llbracket ( \mathrm { y } - 1 ) / 4 \rrbracket - \llbracket ( \mathrm { y } - 1 ) / 100 \rrbracket + \llbracket ( \mathrm { y } - 1 ) / 400 \rrbracket \text {, }$
where $y$ represents the year and $\llbracket x \rrbracket$ represents the greatest integer less than or equal to $x$ . After finding $a$ , find the smallest nonnegative integer $b$ such that
$a \equiv b ( \bmod 7 )$ Then $b$ gives the day of January 1, with $b = 0$ representing Sunday, $b = 1$ Monday and so on. Find the day of the week on which January 1 would occur in the year $2030 .$

• A) Tuesday
• B) Wednesday
• C) Sunday
• D) Monday

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