For the math geniuses...

[chiwawa626]

For the math geniuses, if your into this sort of thing, help me do these problems:
http://bwsvi.com/math.jpg

This is a sample sheet from a previous contest, im taking it soon so i was trying to do these...if you could do you think you can post the steps and the answer on how you solved it? Thanks

 

[rayma2]

1) a=1 b=2..

that is as much as I wanted to think......

edit:
-------
sqrt(3^2 +4^2) = 5
1^2+2^2 = 5

 

[mastaki11a]

#2 is 10
n/7=5
(n/7)7=5(7)
n=35

so
2n/7=x
2(35)/7=x
70/7=x
10=x

 

[SOSTrooper]

#3 is 12 apprentices. Amateur and apprentice both work twice as slow as a professional.


#5 is (99,80) I think.

 

[RaynorWolfcastle]

Originally posted by: mastaki11a
#2 is 10
n/7=5
(n/7)7=5(7)
n=35

so
2n/7=x
2(35)/7=x
70/7=x
10=x

the question is what is the REMAINDER...
take a number n, say 12... divide it by 7, you get a remainder of 5
now 2n%7 = 24%7 = 3;

try with n = 19... 19%7 = 5
2n%7 = 38%7 = 3... etc


*edit* replaced the erroneous division operators with the correct remainder ones

 

[hamburglar]

answer for #2 is 3.

say we have n=12. The remainder is 5. 2n=24. When divided by 7, the remainder is 3.

 

[JW310]

Originally posted by: mastaki11a
#2 is 10
n/7=5
(n/7)7=5(7)
n=35

so
2n/7=x
2(35)/7=x
70/7=x
10=x

Um, no, but you're close... you can't have a remainder greater than what you're dividing by. let's assume that n = 12. Then 12/7 = 1 remainder 5. 2n = 24, so then 24/7 = 3 remainder 3.

so #2 is 3, not 10.


Another way that seems to work is that if you have a number and get a remainder of 5 when you divide by 7, twice that number should give you twice the remainder. So that would give you a remainder of 10. Since 10 is greater than 7, the number being divided by, the answer would be 10mod7, or 3.

[edit] Damn, I gotta type faster[/edit]

JW

 

[da loser]

#2 should be 3, since n/7=x+5/7, 2n/7=2x+5*2/7=2x+1+3/7
#4 -1, multiply out, a(b+1)+b(a+1)=ab, cancel out ab, ab+a+b=0, a+b=-ab, 1/a+1/b=a+b/b*a =-1

 

[kuk]

#1: a=1 b=2
#2: 3
#3: Is this some sort of trick question? 12 apprentices ...
#4: -1
#5: (118,80)
#6: 9989898989


Sorry for not explaining, but I did these on the run, and consequently, I can't confirm these results.

 

[chiwawa626]

Heh can anyone explain 3, 5, 6? I got 1 and 2 myself

 

[chiwawa626]

#3 seems a little too easy:

A= Time of Amature, P= Time of Professional, X= Time of Apprentice
P=.5A
X=2P=2(.5A)=A
Thus: X=A

So it takes 12 for both Apprentices and Amatures.

 

[SWirth86]

Originally posted by: chiwawa626
Heh can anyone explain 3, 5, 6? I got 1 and 2 myself

3 Apprentice and Amateur are the same...

 

[chiwawa626]

hmm attempting 4 now, i looked at what da loser wrote, but i still cant get it, can someone help?

 

[Moonbeam]

For #6 I got 99999785960 but I'm not sure it's right.

There are 9 single digit numbers, 1----9 and 51 two digit two numbers for a total of a 111 digit number. That means we need an 11 digit number to find. Preserving the 9 from 9, 19 29 39 and 49 that leaves 50,51,52,53,54,55,56,57,58,59,60 to find the biggest 6didget number and the biggest one I can see is 7,8, 5, 9, 6, 0.

 

[chiwawa626]

Originally posted by: Moonbeam
For #6 I got 99999785960 but I'm not sure it's right.

There are 9 single digit numbers, 1----9 and 51 two digit two numbers for a total of a 111 digit number. That means we need an 11 digit number to find. Preserving the 9 from 9, 19 29 39 and 49 that leaves 50,51,52,53,54,55,56,57,58,59,60 to find the biggest 6didget number and the biggest one I can see is 7,8, 5, 9, 6, 0.

hmm that looks very rite to me, i can follow the logic...hmm...anyone confirm?

 

[chiwawa626]

They do say math is a universal language....http://www.kultunderground.org/w200002/brainfitness.htm
This spanish site confirms Moonbeam's answer.

 

[AvesPKS]

Heh... I used to be in Math League!

 

[Krakerjak]

chiwawa626

#4 - multiply both sides by (a+1)(b+1)

u get [ (b+1)/b ] + [ (a+1)/a ] = 1

separate - [b/b] + [1/b] + [a/a] +[1/a] = 1

so you get - [1/a] + [1/b] = 1 - 1 - 1 = -1

 

[chiwawa626]

Originally posted by: Krakerjak
chiwawa626

#4 - multiply both sides by (a+1)(b+1)

u get [ (b+1)/b ] + [ (a+1)/a ] = 1

separate - [b/b] + [1/b] + [a/a] +[1/a] = 1

so you get - [1/a] + [1/b] = 1 - 1 - 1 = -1

Yay i get it! thanks dude...

Anyone explain #5?

 

[ArmenK]

Originally posted by: chiwawa626

Originally posted by: Krakerjak
chiwawa626

#4 - multiply both sides by (a+1)(b+1)

u get [ (b+1)/b ] + [ (a+1)/a ] = 1

separate - [b/b] + [1/b] + [a/a] +[1/a] = 1

so you get - [1/a] + [1/b] = 1 - 1 - 1 = -1

Yay i get it! thanks dude...

Anyone explain #5?

Heres a hint

 

[chiwawa626]

Originally posted by: ArmenK

Originally posted by: chiwawa626

Originally posted by: Krakerjak
chiwawa626

#4 - multiply both sides by (a+1)(b+1)

u get [ (b+1)/b ] + [ (a+1)/a ] = 1

separate - [b/b] + [1/b] + [a/a] +[1/a] = 1

so you get - [1/a] + [1/b] = 1 - 1 - 1 = -1

Yay i get it! thanks dude...

Anyone explain #5?

Heres a hint

thanks dude! i get it now

YAY!

 

[silverpig]

#5.

Look at the triangles formed between the squares and the axes. The smallest side of the triangle is of length 19 (you can tell by the x coordinate of the given point). From the y coordinate, you can see that 99 = length of smallest leg + length of other leg. From this you can determine that the length of the other leg is 80.

The x coordinate of the point in question is a distance of the small leg + the large leg away from the origin in the x direction or 80 + 19 = 99.

The y coordinate of the point is a distance of a large leg away from the origin in the y direction or 80. Thus:

(99, 80) is the correct answer.