November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:43 am

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014 ?

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

Answer: A
Source: Official guide

The period from November 16, 2001 to November 16, 2014 is 13 years.
If we ignore the leap years, the total number of days during that period = (13)(365)
Since 3 of the years during that period had 1 extra day, the TOTAL number of days during the given period = (13)(365) + 3

Important: Although we COULD evaluate (13)(365) + 3 to get 4749, we can save ourselves a bit of time by making a few observations

Notice that 364 is a multiple of 7. In fact 364 = (7)(52)
So, (13)(365) + 3 = (13)(364 + 1) + 3
= (13)(364) + (13)(1) + 3
= (13)(364) + 16
= (13)(364) + 14 + 2
= 7[(13)(52) + 2] + 2

Since 7[(13)(52) + 2] is a multiple of 7, we know that after 7[(13)(52) + 2] days, the day will be FRIDAY
So, after 7[(13)(52) + 2] + 1 days, the day will be SATURDAY
And after 7[(13)(52) + 2] + 2 days, the day will be SUNDAY

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Thu Jun 18, 2020 5:43 am

November 16, 2001, was a Friday. If each of the years 2004, 2008, and 2012 had 366 days, and the remaining years from 2001 through 2014 had 365 days, what day of the week was November 16, 2014 ?

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

Answer: A
Source: Official guide

Solution:

We see that there is a 13-year span from November 16, 2001 to November 6, 2014. If each year were 365 days, the total number of days in this 13-year span would be 365 x 13 = 4,745 days. However, since 3 of the years during this span each has 1 extra day, the actual number of days in this span is 4,745 + 3 = 4,748 days. Since 4,748/7 = 678 R 2, we know that there were 678 weeks and 2 days from Friday, November 16, 2001 until November 16, 2014. The remainder of 2 tells us that November 16, 2014 was 2 days after Friday, so it was Sunday.

Answer: A