Question

On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?

• A. Sunday
• B. Thursday
• C. Tuesday
• D. Friday

Hint:

Non-leap year: same date advances by \(+1\) weekday; leap year: \(+2\). When going backward, subtract accordingly.

Answer 1

The Correct Option is D

Step 1: Use year-shift rule.
2006 is a non-leap year. The same date next year shifts by \(+1\) weekday.
So \(8\) Dec \(2006 \xrightarrow{+365\ \text{days}} 8\) Dec \(2007\) is \(+1\) day.
Step 2: Work backward from 2007.
If \(8\) Dec \(2007\) is Saturday, then \(8\) Dec \(2006\) was one day earlier: \(\boxed{\text{Friday}}\).

Answer 2

Instead of applying the leap-year shift rule, count the days directly from \(8\) Dec \(2006\) to \(8\) Dec \(2007\) month by month and reduce mod \(7\).

1. Count the days: from \(8\) Dec \(2006\) to \(8\) Dec \(2007\) spans exactly \(365\) days, since neither the tail of \(2006\) nor all of \(2007\) includes a Feb \(29\) (2007 is not a leap year).
2. Reduce mod 7: \(365=52\times7+1\), so the weekday advances by exactly \(1\) day over this span.
3. Apply the shift: \(8\) Dec \(2007\) is Saturday, and Saturday is \(1\) day after Friday, so \(8\) Dec \(2006\) must have been Friday.

Checking the options, only Friday is consistent with a \(1\)-day forward shift landing on Saturday.

the correct answer is Friday.