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27 Jun 2016, 10:11
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On the 25th of November in 1990, John was trying to make a new plan for Jan 1991. However, he did not have a new calendar that included Jan 1991. Then, in order to match a new plan for Jan 1991, which of following months of 1990 should he look at?
A. March
B. April
C. May
D. June
E. July
A. March
B. April
C. May
D. June
E. July
27 Jun 2016, 22:23
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smartguy595
You need to find the month which will replicate the month of Jan 1991. This will happen when the number of days between the 1st of that month and 1st Jan are a multiple of 7.
Each month has at least 28 days which is a multiple of 7.
Start from July (option (E)) - July has 3 additional days. August has 3. Sep has 2. Oct has 3. Nov has 2. Dec has 3.
3 + 3 + 2 + 3 + 2 + 3 = 16
June has 2 additional days so 16+2 = 18
May has 3 additional days so 18+3 = 21
Starting from May 1, the number of days is a multiple of 7 till Jan 1991 so Jan calendar will mirror the May calendar.
Answer (C)
27 Jun 2016, 10:57
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Let us assume 31st of Dec, 1989 was a Sunday and 1st of Jan, 1990 was a Monday. As 1990 wasn't a leap year, so number of days in 1990 = 365.
Now 365 mod 7 = 1. That means, 365th day of the year 1990, i.e. 30/12/1990, was a Monday
(if [day of the year] mod 7 = 0 then its day will be same as 31st of Dec, 1989. ex. 7th Jan, 14th Jan and so on)
Similarly if [day of the year] mod 7 = 1 then its day will be same as 1st of Jan, 1990. ex 8th Jan, 15th Jan and so on)
As we now know 365th day of the year 1990, i.e. 30/12/1990, was a Monday, so 1st of Jan, 1991 will be a Tuesday.
Now, we have to find out which month among the options has 1st of that month as a Tuesday.
Let's start with option A:
1st of March is 31(Jan)+28(Feb)+1 day of the year = 60. So, 60 mod 7 = 4. So, 1st of March was a Thursday.
So option A is out.
Option B.
1st of April is 31(Jan)+28(Feb)+31(March)+1 day of the year = 91. So 91 mod 7 = 0. So, 1st of April was a Sunday.
Option B is out.
Option C.
1st of May is 31(Jan)+28(Feb)+31(March)+30(April)+1 day of the year = 121. So 120 mod 7 = 2. So, 1st of May was a Tuesday.
Hence, we have got our answer.
Answer C. Day of 1st of May, 1990 is same as Day of 1st of Jan, 1991.
Now 365 mod 7 = 1. That means, 365th day of the year 1990, i.e. 30/12/1990, was a Monday
(if [day of the year] mod 7 = 0 then its day will be same as 31st of Dec, 1989. ex. 7th Jan, 14th Jan and so on)
Similarly if [day of the year] mod 7 = 1 then its day will be same as 1st of Jan, 1990. ex 8th Jan, 15th Jan and so on)
As we now know 365th day of the year 1990, i.e. 30/12/1990, was a Monday, so 1st of Jan, 1991 will be a Tuesday.
Now, we have to find out which month among the options has 1st of that month as a Tuesday.
Let's start with option A:
1st of March is 31(Jan)+28(Feb)+1 day of the year = 60. So, 60 mod 7 = 4. So, 1st of March was a Thursday.
So option A is out.
Option B.
1st of April is 31(Jan)+28(Feb)+31(March)+1 day of the year = 91. So 91 mod 7 = 0. So, 1st of April was a Sunday.
Option B is out.
Option C.
1st of May is 31(Jan)+28(Feb)+31(March)+30(April)+1 day of the year = 121. So 120 mod 7 = 2. So, 1st of May was a Tuesday.
Hence, we have got our answer.
Answer C. Day of 1st of May, 1990 is same as Day of 1st of Jan, 1991.
