UPSC Prelims 2008 Q10: Science & Technology – Quantitative Aptitude
March 1, 2008 was Saturday. Which day was it on March 1, 2002?
- (a) Thursday
- (b) Friday
- (c) Saturday
- (d) Sunday
Answer: (b) Friday
Explanation
Finding the day of the week six years earlier
Given March 1, 2008 was a Saturday, we need the day of the week for March 1, 2002.
| Step | Reasoning |
|---|---|
| Count days between the two dates | 6 years = 6×365 days, plus leap days falling within the span |
| Leap days within [Mar 1, 2002, Mar 1, 2008) | Feb 29, 2004 AND Feb 29, 2008 both fall within this range — 2 leap days |
| Total days | 6×365 + 2 = 2190 + 2 = 2192 |
| 2192 mod 7 | 2192 = 313×7 + 1, so remainder = 1 |
| Interpretation | 2008's weekday = 2002's weekday + 1 (mod 7) |
| Solve for 2002 | Since 2008 is Saturday, 2002's weekday = Saturday − 1 = Friday |
Why both leap days matter:
| Point | Detail |
|---|---|
| Feb 29, 2004 | Falls within the span (before Mar 2004) |
| Feb 29, 2008 | Falls within the span too (just before the Mar 1, 2008 endpoint) |
Answer: (b) Friday.
Why each option is right or wrong
- (a) Incorrect. Thursday would result from miscounting the leap days by one too many.
- (b) CORRECT. Accounting for both leap days (2004 and 2008) gives a shift of 1, making March 1, 2002 a Friday.
- (c) Incorrect. Saturday would result from forgetting to count any leap days at all.
- (d) Incorrect. Sunday doesn't match the correct leap-day-adjusted calculation.
Key point
Between March 1, 2002 and March 1, 2008, TWO leap days (Feb 29, 2004 and Feb 29, 2008) fall within the span, giving a total shift of 1 weekday — so March 1, 2002 was a Friday, one day before Saturday.
Remember
March 1, 2008 was Saturday; accounting for 2 leap days (2004, 2008) in between, March 1, 2002 was a Friday.
Common mistakes
- Forgetting that Feb 29, 2008 itself falls within the span (just before the March 1, 2008 endpoint), missing one of the two leap days.
- Assuming a simple '6 years = 6 weekday shift' without accounting for leap years at all.
- Making an arithmetic error in the mod-7 calculation.
Exam tip
When calculating weekday shifts across multiple years, carefully check EVERY leap day that falls within the exact date range — including one near either endpoint.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Calendar)
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (Calendar)