math problems

[peekaboo]

i'm having trouble solving what should be easy math.
it's supposed to be at the 9th grade level.

i solved the first one but i think i used math which is too advanced for 9th grade.

i couldn't solve the second one.

the third one is also giving me trouble. i can solve it with a little probability and some more option counting but i think there should be a non complicated way.

can you guys solve them?

http://i151.photobucket.com/albums/s...ascal_math.jpg

[blue60007]

Here's what I got:

23) 120/pi ~= 38.2°
24) no idea, but I'll think about it.
25) let's see....3 time each digit must equal a number with even digts. Numbers can't have 4's (leaves you with 3x4 = 12). I'm thinking any other even number is legal. That leaves you with 192 possibilities (3x4x4x4), if that's true. But wait , you a 6 must be followed by an 8 and can't be the last digit. I've been trying to think of a fancy way to figure out how many that leaves...but it might come down to doing a tree diagram... OK, did a semi-fancy way, and found 76 combinations to be the answer...

[Stuey]

I only tried # 2.

I got 4022. Is this really ninth grade math? I don't think I would have been able to do it then.

I used Excel to do this but only b/c I didn't have graph paper. And no, I didn't go all the way up to 2007 haha. Although... lol, nah I'm not going to go there.

So... did I win?

This is how I figured it out... the upper left and lower right hand corner numbers will always be perfect squares. What I mean is, if you have four boxes, the number 4 is at the top right corner. 9 is at the bottom right when 9 squares, 16 is at the top left when 16 squares, etc.

The closest perfect square to 2007 is 45 * 45 = 2025. The next lowest is 44 * 44 = 1946. (1946 + 2025)/ 2 < 2007, so 2007 is going to be on a horizontal edge (that's a bit weird wording, but bear with me).

I filled in a few corners and saw that on each now line downwards, the separation between the numbers increase. 9 - 2 = 7. Then 24 - 9 = 15 (7+8). Then I moved over a bit and filled in a few more corners. 119 - 80 = 39 (7 + 8 + 8 + 8 + 8). 80 - 49 = 31 (7 + 8 + 8 + 8), and so forth.

Now, we get to 2007 which is not anywhere near a corner. The number above 2007 is going to be 2007 - x. The number below 2007 is going to be 2007 + x + 8. Add these two numbers together. 2007 - x + 2007 + x + 8 = 2007 + 2007 + 8 = 4014+8 = 4022.

To check this, I took the top-down sequence 119, 80, 49. 119 + 49 = 168. 80 + 80 + 8 = 168.

So... the answer is definitely 4022. *takes a bow*

I still stand by that this is not normal 9th grade stuff. This might be something on the SATs that <1% of students are expected to know or something, or possibly on the GREs.

[Brad the best]

i didn't see such things till at least grade 11 math which i dropped out of to go to university and now have to go back to do next year *groans . stupid high school

[blue60007]

Got 4022 as well. I wasn't going to get any sleep until I figured it out (yes, I'm a nerd). I used scratch paper and a pda calculator while laying in bed. lol. I found the same thing with perfect squares on the "corners" and subtractring backwards. I should check my work on the first one since Idid it on sticky notes.

What I did is take the closest perfect square which was 45 and subtracted 2007 from it and got 18. odd squares are on the bottom right, so the corners diagonal to 45 are 43 and 47. 43^2 is one block closer to 2007 so I took 43^2-17 to be the number above and 47^2-19 to be number below, added and got 4022.

[peekaboo]

i do not know what the correct answers are yet but i can see the 5 available answers for each question.

4022 is answer E so you might be right.
even your answer was too complicated for me to follow without doing it myself.
i'll try in a little bit.

the minimum answer to question 25 is higher than 76.

the answers to 23 are all higher than 38.2 degrees.
here's what i did:
area of the small circle = Pi*(1)^2= Pi
area of the small circle's shaded area =( Pi - ADC/2)*(1)^2= Pi - ADC/2
area of the large circle's shaded area = 0.5ADC*(2)^2 -0.5ADC*(1)^2
total shaded area= Pi + ADC
and then:
Pi+ADC = (5/12)*Pi*(2)^2
Pi+ADC = (5*Pi)/3
3*Pi+3*ADC = 5*Pi
3*ADC = 2*Pi
ADC = (2/3)*Pi = 120 degrees

[LeftyAce]

# 23: I agree with 120 degrees (slightly diff method, but worked out ok).

#24 hurts my brain :-)

#25: I get 54;

the only single digit even numbers you can multiply by 3 and get only even digits are 0, 2 and 8 (Yielding 0, 6 and 24). All others yield an even digit and an odd digit (3*4=12, 3*6=18, etc).

So we've got ourselves a 4 digit number consisting of the digits 0,2 and 8. Now, it can't start with 0, or it would be a 3 digit number :-) So, for the first digit we have two choices:
2

For the next three digits, we have 3 options for each one, so the number of choices for them is 3*3*3. Multiply this by the 2 options for the first digit, and you get 54 possible numbers.

Do we have a winner?

[peekaboo]

here are the questions with the answers not blurred:

http://i151.photobucket.com/albums/s...ong/pascal.jpg

this was part of a competition test, but he's in grade 9 and there should be some simple way to solve these problems.

[blue60007]

Originally Posted by LeftyAce # 23: I agree with 120 degrees (slightly diff method, but worked out ok). #24 hurts my brain :-) #25: I get 54; the only single digit even numbers you can multiply by 3 and get only even digits are 0, 2 and 8 (Yielding 0, 6 and 24). All others yield an even digit and an odd digit (3*4=12, 3*6=18, etc). So we've got ourselves a 4 digit number consisting of the digits 0,2 and 8. Now, it can't start with 0, or it would be a 3 digit number :-) So, for the first digit we have two choices: 2 For the next three digits, we have 3 options for each one, so the number of choices for them is 3*3*3. Multiply this by the 2 options for the first digit, and you get 54 possible numbers. Do we have a winner?

As I said above...6 followed by an 8 works. 2682 x 3 = 8046. 3 x 6 gets 18, yes, but carry the 2 over from 8 x 3 and you get 20.

My answer for the first one is probably wrong.

OK, here's what I think the answers are:
1) 120° (I worked backwards to verify this)
2) 4022
3) 82 - wrote a quick program that checks possible answers