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11 Feb 2022, 22:04
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (02:45) correct
54%
(02:42)
wrong
based on 107
sessions
History
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Time
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Not Attempted Yet
In year N, the 300th day of the year is a Tuesday. In year N+1, the 200th day is also a Tuesday. On what day of the week did the 100th day of year N-1 occur?
A. Thursday
B. Friday
C. Saturday
D. Sunday
E. Monday
Chinese GMAT guide
A. Thursday
B. Friday
C. Saturday
D. Sunday
E. Monday
Chinese GMAT guide
12 Feb 2022, 05:23
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The issue with this question is that one must account for the possibility of there being a leap year amongst the 3 years.
Because we are working with 100 day intervals (given N's 300th weekday, N+1's 200th week day and are asked to solve N-1's 100th day), knowing how many weeks there are in 100 days will be helpful in constructing a short table. \(100/7 = 14\) with a remainder of 2 days.
300th day and 200th day of two years, and are asked to work out the weekday of the 100th day of another year
Year N:
We are told that the 300th day is a Tuesday, which means that the 200th day will have been 14 weeks and 2 days ago, a Sunday. The 100th day will have been 14 weeks and 2 days ago from the 200th day, so Thursday.
300th day Tuesday
200th day Sunday
100th day Friday
Year N+1:
We are given that the 200th day is a Tuesday. The 300th day will be 14 weeks and 2 day ahead, so Thursday, and the 100th will be 14 weeks and 2 days before, making it a Sunday. A day will shift a single day in a year in a normal year, and two days if the following year is a leap year. Given that each of the 100th, 200th and 300th days occur 2 weekdays after in N+1, we know that N+1 is a leap year, which means that N-1 is not.
300th day Thursday
200th day Tuesday
100th day Sunday
Year N-1:
As we know that neither N-1 nor N are leap years, we just need to go back one weekday from N's 100th day, which means that N-1's 100th day was a Thursday.
[100th day Thursday
Answer A
Because we are working with 100 day intervals (given N's 300th weekday, N+1's 200th week day and are asked to solve N-1's 100th day), knowing how many weeks there are in 100 days will be helpful in constructing a short table. \(100/7 = 14\) with a remainder of 2 days.
300th day and 200th day of two years, and are asked to work out the weekday of the 100th day of another year
Year N:
We are told that the 300th day is a Tuesday, which means that the 200th day will have been 14 weeks and 2 days ago, a Sunday. The 100th day will have been 14 weeks and 2 days ago from the 200th day, so Thursday.
300th day Tuesday
200th day Sunday
100th day Friday
Year N+1:
We are given that the 200th day is a Tuesday. The 300th day will be 14 weeks and 2 day ahead, so Thursday, and the 100th will be 14 weeks and 2 days before, making it a Sunday. A day will shift a single day in a year in a normal year, and two days if the following year is a leap year. Given that each of the 100th, 200th and 300th days occur 2 weekdays after in N+1, we know that N+1 is a leap year, which means that N-1 is not.
300th day Thursday
200th day Tuesday
100th day Sunday
Year N-1:
As we know that neither N-1 nor N are leap years, we just need to go back one weekday from N's 100th day, which means that N-1's 100th day was a Thursday.
[100th day Thursday
Answer A
20 Jun 2025, 03:37
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1. Find the weekday of the 1st day of year N:
300th day of year N is Tuesday.
300 days = 42 weeks + 6 days
So 300th day is 6 days after the start of the year.
If 300th day = Tuesday, then start of year N = Tuesday - 6 days.
Tuesday - 6 = Wednesday
So, Jan 1 of year N was a Wednesday.
2. Find the weekday of 100th day of year N-1:
Days between Jan 1 of year N and day 100 of N-1 year is 365 - 100 = 265 days.
265 days/ 7 = 37 weeks + 6 days.
Going back 37*7=259 days from Wednesday (Jan 1 of year N) will give have same Wednesday. So to reach the 100th day we have to go back 6 days in the week. So
Wednesday - 6 days = Thursday.
Hence A.
300th day of year N is Tuesday.
300 days = 42 weeks + 6 days
So 300th day is 6 days after the start of the year.
If 300th day = Tuesday, then start of year N = Tuesday - 6 days.
Tuesday - 6 = Wednesday
So, Jan 1 of year N was a Wednesday.
2. Find the weekday of 100th day of year N-1:
Days between Jan 1 of year N and day 100 of N-1 year is 365 - 100 = 265 days.
265 days/ 7 = 37 weeks + 6 days.
Going back 37*7=259 days from Wednesday (Jan 1 of year N) will give have same Wednesday. So to reach the 100th day we have to go back 6 days in the week. So
Wednesday - 6 days = Thursday.
Hence A.
