Tutor MathsGuru: Ask me for your burning Maths questions!
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Solutions to JA’s questions.
Q1)Find the sum of the first 100 numbers in the following number sequence.
1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,…
1 to 9 = 9 numbers
1,0,1,1,12…1,7,18,1,9 = 20 numbers
2,0,2,1,2,2…2,7,2,8,2,9 = 20 numbers
3,0,3,1,3,2…3,7,3,8,3,9 = 20 numbers
4,0,4,1,4,2…4,7,4,8,4,9 = 20 numbers
Total 89 numbers
Last 11 numbers : 5,0,5,1,5,2,5,3,5,4,5
Sum of 1st 100 numbers =
1+2+3+4+5+6+7+8+9+1+0+1+1+1+2+1+3+1+4+1+5+ …+ 5+1+5+2+5+3+5+4+5
(1+2+3+…+8+9) = 45
(1+0+1+1+1+2+…+1+8+1+9) = (1x10) + 45 = 55
(2+0+2+1+2+2+…+2+8+2+9) = (2x10) + 45 = 65
(3+0+3+1+3+2+ …+3+8+3+9) =(3x10) + 45 = 75
(4+0+4+1+4+2+…+4+8+4+9) = (4x10) + 45 = 85
(5+0+5+1+5+2+5+3+5+4+5) =(5x6) + 10 = 40
Sum = 45+55+65+75+85+40 = 365
Q2)The Sentosa High School’s telephone number is an eight digit number.The sum of the two numbers formed from the first three digits and the last five digits respectively is 66558.The sum of the two numbers formed from the first five digits and the last three digits is 65577.Find the telephone number of the The Sentosa High School.
Let the telephone number be abcdefgh
defgh + abc = 66558
(10000d + 1000e + 100f + 10g +h)+(100a + 10b + c) =60000 + 6000 + 500 + 50 + 8
d = 6
1000e + 100(f+a) + 10(g+b) + (h+c) = 6000 + 500 + 50 + 8 ………………(1)
abcde + fgh = 65577
(10000a + 1000b + 100c + 10d + e)+(100f + 10g +h) = 60000 + 5000 + 500 + 70 +7
a = 6
1000b + 100(c +f) + 10(d+g) + (e +h) = 5000 + 500 + 70 + 7 ……….(2)
From (1)
1000e + 100(f+6) +10(g+b) +(h+c) = 6000 + 500 + 50 + 8 …………….(3)
f+6 = 15; f = 9
Since f = 9; e = 5
From (2)
1000b + 100(c+9) + 10(6+g) + (4+h) = 5000 + 500 + 70 + 7 ……………(4)
C + 9 = 15; c = 6
Since c = 6; b = 4
From (3)
5000 + 1500 + 10(g+4) + (h+6) = 6000 + 500 + 50 + 8
h+6 = 8
h=2
g+4 = 5
g=1
abcdefgh = 64665912
646 + 65912 = 66558… ok
64665 + 912 = 65577…ok
The telephone number is 64665912
Q3)Placed on a table is a maths problem
89+16+69+6X+Y8+88
X and Y represents a digit.
Two students A and B sit on the opposite sides of the table facing
each other.They read the problem from
their directions and both get the same answer.What is their answer?
89 + 16 + 69 + 6X + Y8 + 88 = 88 + 8Y + X9 + 69 + 91 + 68
262 + 6X + Y8 = 316 + X9 + 8Y
(6X + Y8 ) – (X9 + 8Y) = 54
X and Y can 1, 6, 8 or 9
1 and 8 looks the same when seen from both directions
6 will look like 9 to the person opposite and vice versa.
By trial and error, using X =1 & Y = 9
(61 + 98 ) – (19 + 86) = 54 —ok
89+16+69+61+98+88 = 421 -
Hi Mathsguru,
Pls refer to http://www.orlesson.org/orp/09Ma/2009-P6-Math-SA2-PeiChun.pdf. There are no given answers for Q13 to Q18 in paper 2.
Pls kindly provide the answers for these questions. Thanks in advance.
:love: -
Leo and Tom are given some money each. If Leo and Tom spend $50 and $25 each day respectively, Leo still have $600 when Tom has spent all his money. If they spend $25 and $50 each day respectively, Leo will still have $1800 when Tom has spent all his money. How much money is given to Leo.
=
Hi,
The method to solve this type of question (and other tricky PSLE maths problem sums) can be found in the book \"Raffles Maths Tricks - Volume 1\", which is available at Popular Book store.
http://www.postimage.org/image.php?v=gxYh3kS
http://www.postimage.org/image.php?v=gxYhaPi -
Hi Mathsguru,
Need your help with the following 2 questions :
1) Tim gives 20% of his salary to his wife every month. There is an increase of 5% in his salary this month. Hence, the sum of money which he gives to his wife increases by $100.
a) How much money did he give to his wife last month ?
b) How much money does he earn each month after his pay rise ?
2) A writer writes a uniform number of words every week. He would delete 25% of his words at the end of every week. From last week onwards, the number of words he writes every week increases by 10%. As a result, the number of words he deletes at the end of the week increases by 300.
a) How many words did he write in a week originally ?
b) How many words did he delete last week ?
Thank you!
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[quote]Leo and Tom are given some money each. If Leo and Tom spend $50 and $25 each day respectively, Leo still have $600 when Tom has spent all his money. If they spend $25 and $50 each day respectively, Leo will still have $1800 when Tom has spent all his money. How much money is given to Leo.
[/quote]Hi,
For this question, how come we can't get the answer by using 2u + 600 = 1400 where 2u being the 1st part where we know the spending of Leo is $50 and Tom is $25 ?
Thank you. -
Hi mathsguru,
Need your help with the following 2 qtns:
1) In a class, 16 of the pupils are boys. Then 3/4 of girls left the classroom.
If 1/6 of the original number of pupils are now girls, find the number of
pupils in the class at first.
2) The number of apples is 5/11 of the number of pears at a fruit stall. After
Mrs Fong bought half of the pears, there were a total of 189 apples and
pears left at the stall.
a) How many apples were there at the stall?
b) How many apples and pears were at the stall at first?
Thank you! -
YLH88:
Hi Jasmine,Hi Mathsguru,
Need your help with the following 2 questions :
1) Tim gives 20% of his salary to his wife every month. There is an increase of 5% in his salary this month. Hence, the sum of money which he gives to his wife increases by $100.
a) How much money did he give to his wife last month ?
b) How much money does he earn each month after his pay rise ?
2) A writer writes a uniform number of words every week. He would delete 25% of his words at the end of every week. From last week onwards, the number of words he writes every week increases by 10%. As a result, the number of words he deletes at the end of the week increases by 300.
a) How many words did he write in a week originally ?
b) How many words did he delete last week ?
Thank you!
Here are my solutions:
http://www.postimage.org/image.php?v=PqDTXMi
http://www.postimage.org/image.php?v=PqDT_gr
Cheers,
MathsGuru -
Tiramisu Coco:
Hi Tiramisu Coco,Hi mathsguru,
Need your help with the following 2 qtns:
1) In a class, 16 of the pupils are boys. Then 3/4 of girls left the classroom.
If 1/6 of the original number of pupils are now girls, find the number of
pupils in the class at first.
2) The number of apples is 5/11 of the number of pears at a fruit stall. After
Mrs Fong bought half of the pears, there were a total of 189 apples and
pears left at the stall.
a) How many apples were there at the stall?
b) How many apples and pears were at the stall at first?
Thank you!
Here are my solutions:
http://www.postimage.org/image.php?v=Ts1fRkoS
http://www.postimage.org/image.php?v=Ts1fRmU0
Cheers,
MathsGuru -
Vanilla Cake:
Hi Vanilla Cake,Hi Mathsguru,
Pls refer to http://www.orlesson.org/orp/09Ma/2009-P6-Math-SA2-PeiChun.pdf. There are no given answers for Q13 to Q18 in paper 2.
Pls kindly provide the answers for these questions. Thanks in advance.
:love:
In case you think I've overlooked your msg, fret not! End of my lunch break, so gotta go teach tuition now...I will post my solutions to your questions as soon as I can either tonite or tmr morning.
Cheers,
MathsGuru
P/S: I would appreciate much if the questions are typed out, then I won't have to waste time typing them out. Oh, and just a thought here after reading your post (no offence though!): Sooner or later, I can \"foresee\" myself getting questions like \"Hey MathsGuru, pls provide solutions for XXX School 2009 SA2 Paper 2...\"
*keeping my fingers crossed that this won't happen...*
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Thank you mathsguru for the prompt reply. Really appreciate your help
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