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[YLH88]

Vanilla Cake:

YLH88:

2) Nanyang 2010 P6 Prelim Paper 2 Qn 15

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)

http://www.postimage.org/image.php?v=Pqcy_EA

Vanilla Cake:

Q2 is easy. You need to know something about leap year.OK, briefly leap year is the year where the number can be divided by 4 without any remainder. After every leap year, you jump by 2 days.

Look at Q2 again, you will find that a leap year starts from 1984 onwards:
1984
1988
1992
1996
2000
2004
2008

by understanding how leap years work, you will get:

A: 1
B: 2
3 - 2003
4
E: 6
F: 7 - 2006
G: 1
H: 2
I: 4
J: 5
2011 : 6
2012 : 7

(a) Letter C (2003) represents 3.

(b) Letter F (2006) represents 7

1st Jan 2012 -> Sunday
29 Jan 2012 -> Sunday ( add 4 weeks ie 4x7 = 28 days )
30 Jan 2012 -> Monday
31 Jan 2012 -> Tuesday
1 Feb 2012 -> Wednesday
(c) The day of the week which 1st February 2012 will fall on - Wednesday.

Hi YLH88,

I am the mum of Vanilla Cake.Pls take a look at http://psle2010a.blogspot.com/2010/09/challenging-p6-2010-sa2-nanyang-p2-q15.html which is detailed and better than Vanilla Cake's explanation.
You may wish to browse through http://psle2010a.blogspot.com/search?updated-min=2010-01-01T00%3A00%3A00%2B08%3A00&updated-max=2011-01-01T00%3A00%3A00%2B08%3A00&max-results=50 in which he had olved and posted most of the 2010 P6 Prelim Maths questions from top schools.
Thanks.

VC's mum

Hi,

From Observer's solution, I'm still abit confused on how the following steps are derived :

a) why need to add 4 to 8035 ?

2003 - 1981 = 22 years
22/4 = 5 leap years (max)
22 x 365 + 5 =8035 days
8035 + 4 = 8039 --> ??
8039/7 = 1148 r 3


ans : It was 3.


b) why need to add 4 to 25 x 365 + 6 ?

2006 - 1981 = 25 years
25/4 = 6 leap years (max)
25 x 365 + 6 + 4 = 9135 --> ??
9135/7 = 1305 or 1304 r 7

ans : It was 7.

c) why need to add 7 + 4 to 31 x 365 + 31 + 7 + 4 ?

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

ans : It is Wednesday.


Thank you very much!

[Vanilla Cake]

YLH88:

Hi,

From Observer's solution, I'm still abit confused on how the following steps are derived :

a) why need to add 4 to 8035 ?

2003 - 1981 = 22 years
22/4 = 5 leap years (max)
22 x 365 + 5 =8035 days
8035 + 4 = 8039 --> ??
8039/7 = 1148 r 3

ans : It was 3.

b) why need to add 4 to 25 x 365 + 6 ?

2006 - 1981 = 25 years
25/4 = 6 leap years (max)
25 x 365 + 6 + 4 = 9135 --> ??
9135/7 = 1305 or 1304 r 7

ans : It was 7.

c) why need to add 7 + 4 to 31 x 365 + 31 + 7 + 4 ?

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

ans : It is Wednesday.

Hi YLH88,
Why don't you voice your query in the http://psle2010a.blogspot.com/2010/09/challenging-p6-2010-sa2-nanyang-p2-q15.html#comments or post your query in the cbox of his blog while waiting for comments from KSP members?
Thanks.

VC mum

[firebird]

Dear Dharma


Good morning sir.

Many thanks for your solutions.

As mention by you, I have missed some part in Question 4 b). Iam retyping it as follows:

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.

a) Find the ratio of male speakers to male participants at the conference.

b) Halfway 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind, How many speakers were there at the conference?


Very sorry for the error

Thank you
Firebird

[firebird]

Dear VC mum


I do not know any of the answers as the questions were given by my son’s school.

There was some ommission of important word while typing. Possibily, the differences in answers due to this typo error.

Kindly refer to the one retyped. I am very sorry for the trouble.

With best regards
Firebird

[Dharma]

firebird:

Dear Dharma


Good morning sir.

Many thanks for your solutions.

As mention by you, I have missed some part in Question 4 b). Iam retyping it as follows:

At a conference made up of speakers and participants, there were 20% more men than women. The ratio of male speakers to female speakers was 8:5. There was an equal number of male and female participants.

a) Find the ratio of male speakers to male participants at the conference.

b) Halfway 40 male participants left the conference and another 60 female participants joined the conference. In the end, there were 3/4 as many male participants as female participants remaining behind, How many speakers were there at the conference?


Very sorry for the error

Thank you
Firebird

Q3)

Good morning firebird.

Male : Women = 6 : 5
Male speakers : Female speaker = 8 : 5
Male participants : Female participants = 1 : 1
8u + 1p/(5u + 1p) = 6/5
40u + 5p = 30u + 6p
10u = 1p
a) Male speakers : Male participants = 8u : 1p = 8u : 10u = 4 : 5
b)
1p – 40/(1p + 60) = ¾
4p – 160 = 3p + 180
1p = 340
10u = 340
Total number of speakers = 13u = 13 x 34 = 442

[corneyAmber]

YLH88:

Hi,

From Observer's solution, I'm still abit confused on how the following steps are derived :

a) why need to add 4 to 8035 ?
The Jan 1 in 1981 falls on day 4.

2003 - 1981 = 22 years
22/4 = 5 leap years (max)
22 x 365 + 5 =8035 days
8035 + 4 = 8039 --> ??
8039/7 = 1148 r 3


ans : It was 3.


b) why need to add 4 to 25 x 365 + 6 ?
Same as above

2006 - 1981 = 25 years
25/4 = 6 leap years (max)
25 x 365 + 6 + 4 = 9135 --> ??
9135/7 = 1305 or 1304 r 7

ans : It was 7.

c) why need to add 7 + 4 to 31 x 365 + 31 + 7 + 4 ?
+4 is same as above
+7 is the number of leap years
+31 because there are 31 days in Jan and the question asks for 1st Feb

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

ans : It is Wednesday.


Thank you very much!

[Herbie]

Hi beauty queen


$10-$3/10 = $0.70 (cost of pencil)

I dun understand the above sentence why $3/10?

Can explain???

Uncle Dharma can help??

Many thanks!

[YLH88]

ksi:

YLH88:

Hi,

From Observer's solution, I'm still abit confused on how the following steps are derived :

a) why need to add 4 to 8035 ?
The Jan 1 in 1981 falls on day 4.

2003 - 1981 = 22 years
22/4 = 5 leap years (max)
22 x 365 + 5 =8035 days
8035 + 4 = 8039 --> ??
8039/7 = 1148 r 3


ans : It was 3.


b) why need to add 4 to 25 x 365 + 6 ?
Same as above

2006 - 1981 = 25 years
25/4 = 6 leap years (max)
25 x 365 + 6 + 4 = 9135 --> ??
9135/7 = 1305 or 1304 r 7

ans : It was 7.

c) why need to add 7 + 4 to 31 x 365 + 31 + 7 + 4 ?
+4 is same as above
+7 is the number of leap years
+31 because there are 31 days in Jan and the question asks for 1st Feb

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

ans : It is Wednesday.


Thank you very much!

Hi ksi,
Thank you so much for the explanation!!

Hi VC's mum,
Thanks for the advise but ksi has kindly provided the explanation

[firebird]

Dear Dharma , Vanilla cake & VC mum


Many thanks. You have cleared my doubts.

With best regards
Firebird

[Dharma]

Herbie:

Hi beauty queen


$10-$3/10 = $0.70 (cost of pencil)

I dun understand the above sentence why $3/10?

Can explain???

Uncle Dharma can help??

Many thanks!

3B + 7P = $10
1B – 1P = $1
3B – 3P = $3
10P = ($10 - $3)
1P = ($10 - $3)/10 = $0.70
1B = $0.70 + $1 = $1.70