math problems #5

My favorite question was number 10.

10) The sum of five consecutive integers is 75. The sum of the largest and smallest of these five integers is:
a)15 b)25 c)26 d)30 e) 32

I first started with 12+13+14+15+16 but that equaled to 70.
so next i tried
13+14+15+16+17 which equaled to 75!
and than you have to add the largest and smallest integer (13+17) which equaled to 30, therefore the answer is number d!
Overall, i like questions like these. Where you have to add up different numbers, or consecutive numbers to find your answer. I think these types of questions are fun, and good for the brain. I also like this questions because it is straightforward.

Problem # 2

Number 14 was my favorite question.
14) The sum of the digits of a five-digit positive ineger is 2. (A five-digit integer cannot start with zero.) Th enumber of such integers is:
a)1 b)2 c)3 d)4 e)5

Well i thought to myself, what could be added that equals to 2? "1 and or 2 with 0's"
Than I proceeded to write down all the possibilities. (keeping in mind that the number could not start with 0):

11000
10100
10010
10001
20000

therefore there is 5! (answer is e)
I like this question because i like questions that are straightforward, and you dont' have to think outside the box for ways to solve the problem. ^^

rational expressions!

If i see this on a math test, my first reaction would be "WOAH! o.o how am i suppose to do this?!" But after breaking it down, and realizing that it is just many smaller steps mashed into one equation, i realize it isnt very hard to solve ^^

For the first equation:
1) you always want to get rid of the negative exponents first, so you first switch the numbers with the negative exponents to the top or bottom, turning it to be positive.
2)next you take the 5/2 and put it with each of the digits.
3)solve each of the mini math question that has the 5/2 now.
3) than make sure your final number is in the simplest form! voila! you're done ^^

For the 2nd equation:
1) first you want to take out the first root.
2) solve the new equations, and than take out the second root.
3) than solve the equation
4) make sure it is in simplest form! You're done! ^^

(i did not have the newest version of word so i coulnd't showed step by step with the answers)

Canadian Math Contest

Question number 16.
The odd numbers from 5 to 21 are used to build a 3 by 3 magic square. (In a magic square, the numbers in each row, in each column, and the numbers on each diagonal have the same sum.) If 5, 9 and 17 are placed as shown what is the value of x?

when i first saw this question i thought to myself, "this question is doable, but its going to take a long time to figure out! there are so many different possibilities" But after thinking about it, with a couple of trial and errors i was able to figure it out.
First i wrote down all the odd digits from 5 to 21 and crossed out the digits that were already placed. Than i thought to myself "well if you want all the same sum, than the row with the lowest digit will probably be in the same row with the highest digit! Than i just continued to place the rest of the digits and it worked! :)
It was my first time doing the math contest, and i was very nervous!
but once i started, i began to relax a little and just tried to solve the problems one at a time. Towards the end, i began to feel pressed for time, and got a little fustrated with the questions that i could not solve.
Overall, i thought that the time limit was a little too short, but it was a good experience! I may have not done that well, but it was my first time, so i believe ill get better with practice ^^

good qualities to be good in math

To be good in math, the top 3 qualities i think you need to be good in math is to be patient, hard working and to think abstractly.

I think that patience is the most important because if there is a difficult math question, you need to the patience to be able to try, try again. To try the different methods to figure out the answer. It may take a long time, but if you have the patience you can do it! :)
You also have to be hardworking. Math is a continuous learning passage, and if you slack off in one year, it'll only get harder and harder. You have to listen to the lessons, work hard on the homework and to work even harder if it is difficult for you.
Lastly, you need to be able to think abstractly. Sometimes there are many different ways to find the answer, and being able to think abstractly will let you check your answers to see if it is correct. This quality is very important for word questions. With word questions you have to be able to think of a way to solve it, whether it is with a specific formula, or that is takes more than one step.

Overall, i think i have to work harder on all three :) But the one i have the most difficulty is to think more abstractly. I need to be able to train my brain to put the information given to you, into a way to solve the question.

math contest question

My favorite math question was number 15.

In the multiplication show, P and Q ecah represent a single digit, and the product is 32951. What is the value of P + Q?

39P x Q3 = 32951

First, you know that 3 x P has to be a digit that ends in a 1, because the product ends in a 1. Therefore, 3 x 7 = 21.
Now we made an educated guess that P = 7, So than you plug in:
397 x 3 to get the first product.
397 x 3 = 1191.
Now you have to find out that, 32951 (the ending product)- 1191 (The first product) = x (The second product)
Therefore x + 1191 = 3295.
which is 31760.
Than you have to say that Q x 7 = a digit that ends in a 6.
So you make an educated guess that Q would = to 8.
than you plug in 397 x 83 which equals to 32951.
than you add Q + P = 7 + 8 = 15.
Thus, your answer would be 15.

I like this question because at first it seems really hard, but if you use logic to figure it out, it is actually a simple question. AFter I figured out the answer, I felt really smart! ^^

Math Question #10

My favorite math problem is number 10.
#10: The sum of nine sonsecutive positive integers is 99. THe largest of these integers is: (a)9 (b) 11 (c)19 (d)7 (e)15
I like this problem because there are many different ways to solve the problem. You can take the more mathematical way, or you can do the simple guess and check and still get the answer.
You can use the method of:
x + x+1 + x+2 + x+3 .... etc and find the answer.
Or you can use the formula of finding the sum of the sequence.
And you can use the method of guess and check. Even if you're not sure if the answer is right, you can always plug in the numbers to see if its right.

In the end the anser is (E) 15.

7+8+9+10+11+12+13+14+15=99

Tower of Hanoi

Mr Cheng today showed us a game called Tower of Hanoi.
At first i tried trial and error and it took me a very long time, and i did almost twice as many moves than the minnimum. After you think about it, there is a pattern and strategy. Once you figure out the pattern for the 3 and 4 rings, you do the same for the 5 rings.
Or, if you get stuck, you could cheat and look at the solution and copy it ^^.
Overall this game is hard at first, but once you think about it, it is easy to beat.