Sunday, October 3, 2010

Challenging P6 2010 SA2 Nanyang P2 Q15

The table below shows the day of the week that 1st January falls on from the year 1981 to 2000. Note that Day 1 of a week is a Monday and Day 7 is Sunday. There are 31 days in the month of January.
a) What number does the letter C represent ? (Ans : 3)
b) What number does the letter F represent ? (Ans : 7)
c) Which day of the week will 1st February 2012 fall on ? (Ans : Wednesday)

2003 - 1981 = 22 years

22/4 = 5 leap years (max)   Leap year --> 366 days

22 x 365 + 5 =8035 days    Account for leap years

8035 + 4 = 8039     Since 1 Jan 1981 is 4 (Thursday).

8039/7 = 1148 r 3

a) It was 3.


2006 - 1981 = 25 years

25/4 = 6 leap years (max)

25 x 365 + 6 + 4 = 9135

9135/7 = 1305 or 1304 r 7   Need to express with a remainder

b) It was 7.


2012 - 1981 = 31 years

31/4 = 7 leap years (max)

31 x 365 + 31 + 7 + 4 = 11357 days

11357/7 = 1622 r 3

3 --> Wednesday

c) It is Wednesday.

5 comments:

  1. sorry can you explain the additional of 4 after the calculation of days?

    8035 + 4 = 8039

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  2. + 4 because 1 Jan 1981 is 4 - Thursday.

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  3. i am sorry..but i do not understand this method...can i explain it a bit further? thanks! =D

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  4. The previous anonymousSeptember 19, 2010 at 7:44 PM

    I meant it as can you explain it a bit further..><thx!

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  5. Hi, There's a simpler way to work out this question. Just observe the pattern from 1981: 4,5,6,7,(Skip 1), 2,3,4,5, (Skip 6), 7,1,2,3,(Skip 4), 5,6,7,1, (Skip 2),3,4,5,6, (Skip 7), and so on. :) Enjoy.

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