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Q3738/80Q39
Q38·CSAT · Prelims 2024

Determining data sufficiency for calculating a combined work rate

DI / DSTime & WorkStatement-basedMedium

Question

The calendar for the year 2025 is same for

Options

a

2029

b

2030

c

2031

Answer
d

2033

Explanation

To find when a calendar repeats, track the accumulation of odd days (remainders modulo 7). A non-leap year has 1 odd day, while a leap year has 2 odd days. A calendar repeats when the total accumulated odd days hit a multiple of 7 and the target year matches the original year's type (ordinary vs. leap).

2025 is an ordinary year. Track from 2025 onwards:

2025: +1 odd day
2026: +1 odd day (Total = 2)
2027: +1 odd day (Total = 3)
2028 (Leap): +2 odd days (Total = 5)
2029: +1 odd day (Total = 6)
2030: +1 odd day (Total = 7)

The sum reaches 7 after 2030, meaning the next year, 2031, begins on the exact same day of the week[cite: 1640, 1641]. Since 2031 is also an ordinary year, the entire calendar matches perfectly.

Calendar shortcut rule: An ordinary year that immediately follows a leap year repeats after 6 years; otherwise, ordinary years repeat after 11 years.

Answer: (c).

Question details

Year

2024

Paper

CSAT

Question

Q38

Section

Data Interpretation & Sufficiency

Sub-topic

Time & Work

Type

Statement-based

Difficulty

Medium

Source hint

Data sufficiency evaluation

Same sub-topic — other years

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