parkhydel wrote:
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
PS91151.02
This is essentially a remainder problem. First, there are 13 years. Think of how old you'd be on Nov 16, 2014 if you were born on Nov 16, 2001.
Three of the years have 366 days, and the other ten years have 365 days.
It helps to break the calculations down to bite-size pieces. Find the remainders for 366 and 365, then use the additive property of remainders described below, rather than calculating the total number of days and finding the remainder for that big number.
To find the remainder when 366 is divided by 7, look for an easy-to-find multiple of 7 near 366... like 350.
366 is 16 more than 350, so the remainder when 366 is divided by 7 is the same as the remainder when 16 is divided by 7... that is 2.
Likewise, 365 is 15 more than 350, so the remainder when 365 is divided by 7 is the same as the remainder when 15 is divided by 7... that is 1.
In total, here's what we've got, using abbreviated notation.
3 x 366 DIV 7 = 3 x R2 = R6
10 x 365 DIV 7 = 10 x R1 = R10
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R6 + R10 = R16 = R2
To finish it off, FRIDAY + R2 = FRIDAY + 2 DAYS = SUNDAY
Answer A
For this approach, it helps to understand the additive property of remainders. For example,
remainder when dividing 7 by 4 = 3
remainder when dividing 14 by 4 = 2
Adding these two remainders 3 + 2 = 5 and then dividing 5 by the divisor of 4 leaves a remainder of 1.
If you add 7 + 14 = 21 and then divide by 4, the remainder is also 1.
Likewise, if you add several of the same remainders together, you can multiply the remainders and then divide by the divisor to get the remainder.
For example, 7 x 3 = 21. The remainder when you divide 7 by 4 is 3. Multiply that remainder of 3 by 3 = 9 and then divide by 4 to get a remainder of 1, which is the same remainder you get when you divide 21 by 4.
So for this problem:
3 years with 366 days, so 3 x remainder of 2 = 6
10 years with 365 days, so 10 x remainder of 1 = 10
Add 6 + 10 = 16 then divide by 7 to get a remainder of 2.
It takes a lot of words to write this out, so instead I suggest using notation like 7 DIV 4 = R3 to mean "7 divided by 4 yields a remainder of 3"
Or if you're familiar with MOD notation, it's the same thing... 7 MOD 4 = 3
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