Tutor MathsGuru: Ask me for your burning Maths questions!

[aiong]

Thank you

[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.

[HoSayLiao]

Ali has $300. He lost 1/3 of it and ends up with $200. To have the $300 again, he needs to win $100 which is ½ of the $200. 1/3 is known as the Losing Fraction (LF) and ½ is known as the Winning Fraction (WF). ½ times 1/3 = 1/6. 1/6 is the product of the LF and WF, known as the PLW. Find the LF and the WF if the PLW is 81/400.

[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.

[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.