Calling all Math Wizards ...?

Question

HELP ! My math IQ test is to be submitted tomorrow I have no one who can work out the following questions. Can you Help ?
1. What are the co-ordinates of a point of trisection of the line segment joining the points (-4, 3) and (2, -1) ?
2. If 7 odd whole numbers are multiplied together, then the what is the chance that the last digit of their product is 1, 3, 7, 9, 5 ?
3. What is the next number of the series :
17, 19, 15, 23, 7, 39, ?
(also state the rule applied)

Answer 1

1. Trisection means a point where the segment is cut into three pieces. You can find the trisection by adding the x coordinates and dividing by 3. Do the same with the y coordinates. Answer is (-2/3, 2/3). The second trisection point can be found by adding the x coordinates and multiplying by 2/3 and repeating the same with y coordinates. The answer will be (-4/3, 4/3)

2. The probability or chance is 1 because when odd number of odd integers are multiplied the answer is always odd which means the answer will end in either 1, 3, 5, 7, or 9.

3. It seems like the series progresses by adding and then subtracting the increments of power of 2.
17 + 2^1 = 17 + 2 = 19
19 - 2^2 = 19 - 4 = 15
15 + 2^3 = 15 + 8 = 23
23 - 2^4 = 23 - 16 = 7
7 + 2^5 = 7 + 32 = 39
The next number will be 39 - 2^6 = 39 -64 = -25
The number after that will be -25 + 2^7 = 103

Answer 2

ok, for the second question... read me very carefully
First, a "simple" result:
when I'm writing for example "1*5=5", I mean "if you multiply a number that ends with a 1 with a number that ends with a 5, the result is a number that ends with a 5", ok? So:
1*1=1, 1*3=3, 1*5=5, 1*7=7, 1*9=9;
3*1=3, 3*3=9, 3*5=5, 3*7=1, 3*9=7;
5*1=5, 5*3=5, 5*5=5, 5*7=5, 5*9=5;
7*1=7, 7*3=1, 7*5=5, 7*7=9, 7*9=3;
9*1=9, 9*3=7, 9*5=5, 9*7=3, 9*9=1.

I hope you'll agree with that. So what does that stuff implies?
First, you choose your first random odd number. You have 1/5 chance to get a 1, 1/5 to get a 3, 1/5 chance to get a 5, etc...
Then you choose your second random number. You have the same probability.(1/5 each). Then you multiply them.
all the multiplication beneath have the same probability to be computed (1/5*1/5=1/25). You get a number ending with a "1" 4 times out of 25, with an "3" 4 times out of 25, with a"5" 9/25, with a "7" 4/25, a "9" 4/25.
Now you choose your third number. (with a probability of 1/5 for each number). We have to multiply this new number with the previous result. Because of the result of the first multiplication, each multiplication in the list do not have the same probability to be computed. The ones in the 1st, 2nd, 4th and 5th lines have each a probability 4/25 to be computed, and the ones in the 3rd line a probability 9/25.
The probability to get the odd number "n" out of the second multiplication will be: 1/5(sum other all the multiplication whose result is n) (proba to get this multiplication).
then the chance to get a 5 will be :
1/5*(5*9/25+4*4/25)=61/125
the chance to get a 1,3,7or9 will be :
1/5*(4*4/25)=16/125.

etc, etc...
If you multiply 7 odd number, the probability to get a 1,3,7,9 will be: 4^6/5^7=~0.0524%

and the probability to get a 5 will be: 1-4^6/5^7~0.946%


MORE SIMPLE EXPLANATION
when you multiply an odd number by 1,3,7 or 9, if you look at the list of multiplication, you have a probability 4/5 to get a 1,3,7 or 9, if you do two multiplication, it will be (4/5)*(4/5), three multiplication: (4/5)^3, etc... seven mult: (4/5)^7 . Each of the number 1,3,7,9 appears with the same probability. So the individual proba will be 1/4*global-proba. ie 4^6/5^7.
And as the total of the proba must be one, the proba to get a 5 is 1-4^6/5^7.

I hope I've been clear enough... at list, you have the correct result and some kind of explanation. The best is still to try to figure it out with your own way of thinking!
Good luck!

Answer 3

3) 17+2 = 19
19- 4=15
15+8=23
23-16=7
7+32=39
So first add 2^1 then subtract 2^2, add 2^3, substract 2^4 and finaly add 2^5.
Next number is 39-2^6 = -25
1) (0.3,0.4) (I could be wrong)
2) I have no clue so I'm not a wizard, just a little magician :)

Answer 4

1.
One point cannot trisect a segment. It can only bisect the segment.

2.
I don't know that. Try probablity.

3.
(-25)
Series = +2 -4 +8 -16 +32 -64.......

Answer 5

this isn't a complicated project. look at it as 2 fractions. 149/31 = x/100 in case you multiply each and every aspect by utilizing 100, you'll cancel the 100 on the right aspect and be left with (149/31) x 100 = x this comes out to 480 and 20/31.

Answer 6

For question 2:
If you multiply any number of odd numbers, the result will be odd, and therefore end in 1,3,5,7, or 9.

Answer 7

Well if we answered those questions it wouldn't be your IQ test now would it?

Answer 8

if it's an iq test, doesn't that mean you should do it yourself?? if someone else helps you, then that could overstate your iq.

Answer 9

It's YOUR IQ test... not OUR IQ test.