Tutor MathsGuru: Ask me for your burning Maths questions!

[carebear]

MathIzzzFun:

Neat:

Hi Morning,


Please assist the following:

Ethan and Jay share a box of pens. If Ethan gives 1/4 of his share to Jay, Jay will have 14 more pens than Ethan. If Ethan gives 1/2 of his share to Jay, Jay will have 24 more pens than Ethan. What is the ratio of Ethan share to Jay share?

Thanks in advance.

Hi neat,

this question is similar to one discussed earlier at http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=27&t=6373&start=3600

cheers.

So the answer is Ethan:Jay = 5:6

[Neat]

MathIzzzFun:

Neat:

Hi Morning,


Please assist the following:

Ethan and Jay share a box of pens. If Ethan gives 1/4 of his share to Jay, Jay will have 14 more pens than Ethan. If Ethan gives 1/2 of his share to Jay, Jay will have 24 more pens than Ethan. What is the ratio of Ethan share to Jay share?[quote]

Thanks in advance.

Hi neat,[quote]Hi MathsIzzzFun
Refer to that,may I know why is it 2 units?

Tks[/quote] :yikes:

this question is similar to one discussed earlier at http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=27&t=6373&start=3600

cheers.[/quote]

[Vanilla Cake]

Pls :imdrowning: and TIA for your precious time cum effort to provide the worked solutions for the following questions (not in exact words/order as appeared in the test):


Q1
n bottles at start. Delivers equal number of bottles at 4 houses each. From start, crosses a road and number of bottles doubles. Everytime moves to the next house, number of bottles doubles. At the end of the 4th house, there are no bottles left. Find the smallest possible value of n.

Q2
Shade a 8x8 square such that all the rows have the same number of shaded squares and no two columns have the same number of shaded squares.

Q3
n+(n+1)+(n+2)+........+(n+886)+(n+887).
The sum of 888 consecutive number is a perfect square.
Find the smallest value of n.

[MathIzzzFun]

Vanilla Cake:

Pls :imdrowning: and TIA for your precious time cum effort to provide the worked solutions for the following questions (not in exact words/order as appeared in the test):


Q1
n bottles at start. Delivers equal number of bottles at 4 houses each. From start, crosses a road and number of bottles doubles. Everytime moves to the next house, number of bottles doubles. At the end of the 4th house, there are no bottles left. Find the smallest possible value of n.

Q2
Shade a 8x8 square such that all the rows have the same number of shaded squares and no two columns have the same number of shaded squares.

Q3
n+(n+1)+(n+2)+........+(n+886)+(n+887).
The sum of 888 consecutive number is a perfect square.
Find the smallest value of n.

Hi

Q1. I hope I understand the question correctly, here goes:

n = 2^m-1 where m = 4 in this case
n=15

Number of bottles, B = 2^(m-1) =8

Working backwards,

At the 4th house, number of bottles = B
At the 3rd house before delivering, number of bottles = B/2 + B = 3/2 B
At the 2nd house before delivering, number of bottles = 3/4B + B = 7/4 B
At the 1st house before delivering, number of bottles = 7/8B + B = 15/8 B

Smallest number of bottles n = 15/8 B is when B = 8

So, n = 15, B = 8

Q2.
http://i55.tinypic.com/hulyma.jpg\">


Q3.
n is an integer and n > 0
n+(n+1)+(n+2)+........+(n+886)+(n+887)
= 888n + 888 x 887/2
= 4 x 111 x (2n + 887)
= S

For S to be a perfect square, 111x(2n+887) must be a square number
Note that 2n +887 is an odd number.
Thus smallest n such that 111 x (2n + 887) is a square number is such that
2n + 887 = 9 x 111
So n = 56




cheers.

[wahwah]

Hi,

Need help in the following questions. Many thanks in advance.

Q1. One of the integers among 1,2,3,…,n is deleted. The average of the remaining (n-1) numbers is 602/17. Which number is deleted?

Q2. A student has taken examinations and 1 more examination is coming up. If he scores 100 in the upcoming examination, his overall average (of the n+1 examination) will be 90, if he scores 60 in the upcoming examination, his overall average will be 85. Find the number n.

Q3. The digits 3,4,5 and 7 can form 24 different four- digit numbers. Find the average of these 24 numbers.

[MathIzzzFun]

wahwah:

Hi,

Need help in the following questions. Many thanks in advance.

Q1. One of the integers among 1,2,3,...,n is deleted. The average of the remaining (n-1) numbers is 602/17. Which number is deleted?

Q2. A student has taken examinations and 1 more examination is coming up. If he scores 100 in the upcoming examination, his overall average (of the n+1 examination) will be 90, if he scores 60 in the upcoming examination, his overall average will be 85. Find the number n.

Q3. The digits 3,4,5 and 7 can form 24 different four- digit numbers. Find the average of these 24 numbers.

Hi

Q1. 602/17 = 35 7/17 so the number of terms is around 70

Nearest multiple of 17 = 68

602/17 = 2408/68
Number of terms = 69

Sum of 1 to 69 = 69 x 35 = 2415
2415 - 2408 = 7

Number of terms = 69
Number deleted = 7

Q2. http://i55.tinypic.com/11kifef.jpg\">

Q3. Each digit will appear 6 times in each place value, so the average = (7777 + 5555 + 4444 + 3333 ) x 6 / 24

cheers.

[Herbie]

wah! all the n question are not Primary school maths right??

[CoffeeCat]

Herbie:

wah! all the n question are not Primary school maths right??

I m not wahwah but i can tell the questions can be found in primary school maths competitions =).

[wahwah]

Hi MathIzzzFun,

Thanks for the solution. But can you explain the model for Q2, my boy can’t understand it though he has been looking at it since Saturday.

[MathIzzzFun]

wahwah:

Hi MathIzzzFun,

Thanks for the solution. But can you explain the model for Q2, my boy can't understand it though he has been looking at it since Saturday.

Hi

I have added two more arrows in the model

http://i52.tinypic.com/21cuk8z.jpg\">

The blue arrow shows how the average marks increase when a new score (100) which is higher than the original average is added, and the red one shows how the average marks decrease after a new score which is lower than the original average mark is added.

When a new score of 100 is added, the overall average is 90. So the difference of (100-90) is divided among existing students to bring up the average.

Similarly, when a new score of 60 is added and the overall average becomes 85, in this case, the \"added\" marks of (85-60) for the new student is being contributed equally from the existing students.

Another way is look at is : imagine the original average mark as water level in a container, and adding a new \"tube\" with a higher water level so that the final water level in both the container and the tube reaches the same new level.

cheers.