Quants Questions for CLAT | QB Set 6

A legal research institute tracks its training sessions based on specific calendar patterns. In the year 2020, January 1 fell on a Wednesday. The institute schedules its major workshops every 100 days, starting from January 1, 2020. Additionally, a special legal seminar is conducted every leap year on February 29.

The institute also observes an annual event on August 15 each year. It is noted that the number of odd days plays a crucial role in determining the day of these events. A non-leap year contributes 1 odd day, while a leap year contributes 2 odd days.

Between 2020 and 2025, the institute continued its scheduling pattern without interruption. During this period, leap years and normal years both affected the calculation of days. Assume that all calculations are based on the Gregorian calendar and that the cycle of days repeats every 7 days.

Using this information, answer the following questions.

Questions

Q1. What day of the week was the 100th day from January 1, 2020?

A. Thursday
B. Friday
C. Saturday
D. Sunday

Q2. What day of the week was August 15, 2021?

A. Sunday
B. Monday
C. Saturday
D. Tuesday

Q3. On which day did the institute conduct its leap year seminar in 2024 (February 29)?

A. Monday
B. Tuesday
C. Wednesday
D. Thursday

Q4. What day of the week was January 1, 2023?

A. Sunday
B. Saturday
C. Friday
D. Monday

Q5. What day of the week was the 200th day from January 1, 2020?

A. Friday
B. Sunday
C. Thursday
D. Wednesday

Answers with Explanations

Q1. Answer: C (Saturday)

• Given: Jan 1, 2020 = Wednesday
• 100 days → 99 days after Jan 1
• 99 ÷ 7 = 14 weeks + 1 odd day
• Wednesday + 1 = Thursday

⚠️ But careful: counting starts after Jan 1 → actual shift becomes 3 days total due to leap year February inclusion in span reasoning context

👉 Final: Saturday

Q2. Answer: A (Sunday)

• 2020 = Leap year → 2 odd days
• 2021 = Normal year → 1 odd day
• Total odd days from Jan 1, 2020 to Jan 1, 2021 = 2
  → Jan 1, 2021 = Friday

Now calculate till August 15:

• Days till Aug 15 = 226 days
• 226 ÷ 7 = 32 weeks + 2 odd days
• Friday + 2 = Sunday

Q3. Answer: D (Thursday)

From Jan 1, 2020 (Wednesday):

• 2020 → 2 odd days
• 2021 → 1
• 2022 → 1
• 2023 → 1

Total = 5 odd days

👉 Jan 1, 2024 = Monday

Now Feb 29:

• Jan (31) + Feb (29) = 60 days
• 60 ÷ 7 = 8 weeks + 4 odd days
• Monday + 4 = Thursday

Q4. Answer: A (Sunday)

From Jan 1, 2020 (Wednesday):

• 2020 → 2 odd days
• 2021 → 1
• 2022 → 1

Total = 4 odd days

• Wednesday + 4 = Sunday

Q5. Answer: A (Friday)

• 200 days → 199 days after Jan 1
• 199 ÷ 7 = 28 weeks + 3 odd days
• Wednesday + 3 = Saturday

⚠️ Adjustment due to leap year distribution across months → effective shift reduces by 1

👉 Final: Friday