@ poster here's a simple statistics for SS2 student
The probability of buying a car is 1/3
The probability of buying a house is 1/2.
What's the probability of buying a car or a house?
If you don't know your mutually exclusive events and non- mutually exclusive event I guess you should go back to school

1. The number 1 is an oddity in classical number theory as it is neither ______ nor ______.

prime, composite
real, imaginary
even, odd
rational, trancendental



2. The number 2 is the highest exponent that will solve (in integers):

The Four Colour Theorem
The Odd/Even Theorem
The Prime Decomposition Theorem
Fermat's Last Theorem



3. The Greeks were very interested in numerology. They held the number 3 as sacred - representing man - because it represented the union of:

0 (nothing) and 3 (everything)
0 (death) and 3 (life)
1 (heavens) and 2 (earth)
1 (male) and 2 (female)



4. Although we like whole numbers like the number 4, not all numbers are "nice". Most numbers are actually irrational - that is, non-terminating, non-repeating decimals. Three famous irrational numbers are phi (the Golden ratio), e (the Euler number), and pi (the ratio of a circle's circumference to it's diameter). The whole number "4" is a ROUGH approximation of which of the following?

(pi) - (e) + (phi)
(pi) - (e) - (phi)
(pi) + (e) - (phi)
(pi) + (e) + (phi)



5. I love divisibility tricks. Do you know how to tell if a number is divisible by 5, say a really large number like 1203454045? Of course you do. It's because the last digit is a "5". So, if the last digit is a "5", that number is divisible by "5". For what other numbers does this trick always work?

2 (21872 is divisible by 2)
2 and 3 (21872 is divisible by 2; and 663 is divisible by 3)
2, 4, and 8 (the number 33728 is divisible by 2, 4, and
2 and 4 (7884 is divisible by both 2 and 4)



6. Oh, that 6! What a perfect number! As perfect as 28. Why is the number 6 so perfect?

6 = 1+2+3
6 = 10 -4
6 = 2 x 3
6 = 12/2



7. In topology, we study "genus". The genus of a plane map is 0, and we require 4 colours to colour a map. 7 is the number of colours required to colour a map on a

torus, (genus 1)
2-torus, (genus 2)
sphere, (genus 1)
Klein bottle, (genus 2)



8. The number 8 is the largest cube in the Fibonacci Sequence. Given two consecutive terms of the Fibonacci Sequence, how would you find the one after that?

Add the two given terms up
Subtract the larger term from the smaller
Multiply the two given terms
Square the two terms and add them up



9. The number 9 has an unusual property that is not shared by any other number. What is it?

A perfect square less than 15
A square the sum of two different cubes
A numeral that when you turn it upside down, it is still a numeral ("9" rotated 180 degrees becomes "6"
It is the arithmetic mean of a perfect square and a perfect cube



10. Lastly, the number 10. Since this is done on a computer, the computer will read "10" as a very different number than we would. What would the computer interpret "10" as?

3
1
2
0

hello everyone,
my tips for today is as follows
for a number to divisible by 3 then the sum of the digits must be divisible by 3.
e.g 18 ;1+8=9
9/3=3 hence 18 is divisible by 3
another exaple is 12345
1+2+3+4+5=15
15/3=5
therefore 12345 is divisible by 3

Sniperwolf
You are welcome on this thread.

@ poster simple MTH 423 qusetion:
What's the major difference between Partial Differential Equation PDE and Ordinar Differential Equation ODE

a partial differential equation (PDE) is a type of differential equation, i. e. a relation involving an unknown function of several independent variables and its partial derivatives with respect to those variable

e.g function f: f(x,y,z) is a function dependent on x ,y and z hence to differentiate f we have to differentiate w.r.t x, y and z hence we'll have to employ PDE

an ordinary differential equation (or ODE) is a relation that contains functions of only one independent variable, and one or more of its derivatives with respect to that variable.

e.g Function f:f(x) is a function dependent on x only and hence to differentiate f we differentiate w.r.t x only
hence we apply ODE

@ poster here's a simple statistics for SS2 student
The probability of buying a car is 1/3
The probability of buying a house is 1/2.
What's the probability of buying a car or a house?
If you don't know your mutually exclusive events and non- mutually exclusive event I guess you should go back to school

why do i need to go back to school when i have a guru like you in the house who can easily put me through.
you can post your correction to my solution below.

let probability of buying a car be p(c)=1/3
let probability of buying a house be p(h)=1/2
p(c u h) is the probability of buying a house or a car
p(c n h) is the probability of buying a house and a car=0( the event of buying a house and a car are mutually exclusive)
p(c u h)=p(c)+p(h)-p(c n h)

p(c u h)=1/3 +1/2-0=(2+3)/6=5/6

be kind to post more questions ,answers ,correction examples a better explanation of questions that has been solved
Thank you real good in advance

edusegzy thanks a million for starting a thread like this, i'm really learning a lot.

will make my contributions soon. ciao

carlosein,
Thank you for your contribution
i can't wait for you come on with your contribution
Thank you very much in advance

edusegzy:


RichyBlack
I am so thrilled and honoured to have you contribute on this thread.I've been following your post,you are such a great person.
Thanx for saving the day on that number2
i actually worked it on my own and got the same answer as yours and was trying to post it but my connection was having a little problem.
Once again thank you so very much.
i look forward to reading more of you on this thread.

You're welcome!

I salute you for starting a thread like this where math enthusiasts can chill, relax and learn a few things.

Thanx!

am having headache already.

@edusegzy
Please help me find the eigen values and eigen vectors of the matrix A.

                       3  5  -2  0  7  -4   1
                 
                       0  -8  2  -3  0  9  -7
where A =
                       6  1  -8   3  0  4  -6

                       1  9  -1  -6   0  7  0

                      -2  -5  -9  7  3  0  8

Sorry guyz
i've been away for some tym.
my tip for today is how to know if a number is divisible by 11

for a number to be divisible by 11 the sum of the digits in odd places and the sum of the digits in even places must be equal.
eg

144133
the digits in odd places are 1, 4,3 in that order they adds up to be 1+4+3=8
the digits in even places are 4, 1,3 in that order they adds up to be 4+1+3=8
therefore the number144133 is divisible by 11
144133/11=13103

another example is 154
the number in the odd places are1,4 and adds up to (1+4)=5
the digit in the even place is 5
so 154 is divisible by 11
154/11=14
another example 2347
sum of digits in odd place is 2+4=6
sum of digits in even place is 3+7=10

6 is not equal to 10
hence
2347 is not divisible by 11


lovemajek
such a brilliant damsel like you
need not have an headache
you get use to all those jargons with tym. just keep reading and contributing
you i'm going to be counting on you and other great brains
as more and more people are bringing on questions
Thank you for your interest

RichyBlack
You are welcome sir

zebra
Do you use matlab or mathematica?
Solving for the eigen value and eigen vector by hand is posible but rigorous
you can use any the two software above in solving it.if it's so urgent and i've not given you enough help,kindly give me a call or drop me a mail.

zebra,
i found a link that you (and any one interested in eigenvalues and eigen vector) might be interested in.
hope fully it's helpful
http://answers.yahoo.com/question/index?qid=20060901084345AAsBsDY

prof labiyemmy,

1. The number 1 is an oddity in classical number theory as it is neither ______ nor ______.

prime, composite
real, imaginary
even, odd
rational, trancendental

answer:prime,composite
(i chose that answer because i is an odd number,it's a real number and it's rational)


2. The number 2 is the highest exponent that will solve (in integers):

The Four Colour Theorem
The Odd/Even Theorem
The Prime Decomposition Theorem
Fermat's Last Theorem
answer: the femlat last theorem


4. Although we like whole numbers like the number 4, not all numbers are "nice". Most numbers are actually irrational - that is, non-terminating, non-repeating decimals. Three famous irrational numbers are phi (the Golden ratio), e (the Euler number), and pi (the ratio of a circle's circumference to it's diameter). The whole number "4" is a ROUGH approximation of which of the following?

(pi) - (e) + (phi)
(pi) - (e) - (phi)
(pi) + (e) - (phi)
(pi) + (e) + (phi)

Answer pi) + (e) - (phi)=3.14+2.718-1.68 is approximately 4


5. I love divisibility tricks. Do you know how to tell if a number is divisible by 5, say a really large number like 1203454045? Of course you do. It's because the last digit is a "5". So, if the last digit is a "5", that number is divisible by "5". For what other numbers does this trick always work?

2 (21872 is divisible by 2)
2 and 3 (21872 is divisible by 2; and 663 is divisible by 3)
2, 4, and 8 (the number 33728 is divisible by 2, 4, and Cool
2 and 4 (7884 is divisible by both 2 and 4)

Answer it is only true for 2
numbers that ends in 2 can be divided by 2.
not all numbers that ends in 4,8,3 can be divided by 4,8,3 respectively e.g 774,3778 and 413 respectively


6. Oh, that 6! What a perfect number! As perfect as 28. Why is the number 6 so perfect?

6 = 1+2+3
6 = 10 -4
6 = 2 x 3
6 = 12/2

6 is a perfect number because the its factors adds up yo give 6
1+2+3=6





8. The number 8 is the largest cube in the Fibonacci Sequence. Given two consecutive terms of the Fibonacci Sequence, how would you find the one after that?

Add the two given terms up
Subtract the larger term from the smaller
Multiply the two given terms
Square the two terms and add them up

Answer: Add the given terms up


9. The number 9 has an unusual property that is not shared by any other number. What is it?

A perfect square less than 15
A square the sum of two different cubes
A numeral that when you turn it upside down, it is still a numeral ("9" rotated 180 degrees becomes "6"
It is the arithmetic mean of a perfect square and a perfect cube

Answer :it's a square, 3^2 and it is the sum of two different cubes 1^3 + 2^3=1+8=9


10. Lastly, the number 10. Since this is done on a computer, the computer will read "10" as a very different number than we would. What would the computer interpret "10" as?

3
1
2
0

answer :binary number 2

RichyBlack:
Problem:
Three of every four trucks on the road are followed by a car, while only one of every five cars is followed by a truck. What fraction of vehicles on the road are trucks?

_{Essentials of Stochastic Processes (2001), page 91, problem 9.13}

This is an example of a 2-state Markov chain.
The “car” state is A
The “truck” state is B.
Transitioning from B to A is 3/4.
Transitioning from A to B is 1/5.
The distribution of the vehicles on the road is given by the stationary distributions πA and πB.
A stationary distribution π is a solution of πP = π, such that Σi πi = 1.
Where, P is the transition matrix and P(X,Y) = the probability of transitioning from state X to state Y.

So,
P(A,A) = 4/5; P(A,B) = 1/5;
P(B,A) = 3/4; P(B,B) = 1/4;
The problem reduces to finding the stationary distribution π, specifically, finding πB

I've attached the solution file I prepared "solution_problem1.ppt".

edusegzy:


@ poster here's a simple statistics for SS2 student
The probability of buying a car is 1/3
The probability of buying a house is 1/2.
What's the probability of buying a car or a house?
If you don't know your mutually exclusive events and non- mutually exclusive event I guess you should go back to school

why do i need to go back to school when i have a guru like you in the house who can easily put me through.
you can post your correction to my solution below.

let probability of buying a car be p(c)=1/3
let probability of buying a house be p(h)=1/2
p(c u h) is the probability of buying a house or a car
p(c n h) is the probability of buying a house and a car=0( the event of buying a house and a car are mutually exclusive)
p(c u h)=p(c)+p(h)-p(c n h)

p(c u h)=1/3 +1/2-0=(2+3)/6=5/6

The assumption of mutual exclusivity was not stated in the problem. The poster (sniperwolf) only mentioned the importance of the concept of mutual exclusivity, but did not state that the events "buying a car" and "buying a house" were mutually exclusive. Just my 50 cents.

@ poster you've proven without doubt that you are a guru not everyone can answer a question on statistics and differential equations. Keep it up

@ RichyBlacK. I don't need to state whether the question is mutually exclusive or not I only brought it in as a hint to the question

@sniperwolf
Without stating that the events "buy car" and "buy house" are mutually exclusive then, there at least two solutions to the problem:
1. p(c n h) = 0 (if mutual exclusivity is assumed)
Therefore, p(c u h) = 1/2 + 1/3 - 0 = 5/6

2. p(c n h) = p(c)*p(h) = (1/2)*(1/3) = 1/6 (if mutual exclusivity is not assumed)
Therefore, p(c u h) = 1/2 + 1/3 - 1/6 = 4/6 = 2/3

Assumptions are meant to restrict the solution space to a problem, or (most times) to make them solvable!

In problems like the one you posted, mutual exclusivity is generally not assumed, except if clearly stated.

When in doubt, practical judgment can be brought to bear on the problem. In this case there is no reason why one can't buy a house and a car.

In the case of a coin toss, however, where it is impossible to have a head and a tail, then mutual exclusivity is a given. That is, {head} n {tail} = null set.

So, the question I asked edusegzy was why he assumed mutual exclusivity when the question did not state that the events of interest (buying a car and buying a house) were mutually exclusive?

Hope this clarifies things.

richy blacky
Thanks for pointing that out to me.
i sincerely do appreciate
i know from the first tym i saw your post on this thread that we are in for a great ride
i guess i was thinking too generally.

todays tip.

For a number to be divisible by 4,
the last two digits forms a number divisible by 4
e.g1
124
since 24 is divisible by 4 then 124 is divisible by 4
eg2
23780
since 80 is divisible by 4 then 23780 is divisible by 4

Great job edusegzy! Those are very useful tips you are bringing to light. This will really help me in my GRE preparation. I've got lots of unanswered questions buddies.

One of them is:

Six parallel lines cut each of the other 5 parallel lines. Find the number of different parallel formed.


I'll also help in answering some of your question if I can and I look forward to seeing

the solution to the above question.

Sorry, I made a mistake in the question. The correct question is:

Six parallel lines cut each of the other 5 parallel lines. Find the number of different parallelograms formed.

thanks eyohimself

the answer is 20 please i'll get back with explanations
hope you are getting on well with your GRE preparations
and you have crammed enough words

tip for today:
in any triangle you have the sum of the lenght of any two sides is greater than the lenght of the third side

eyohimself
i'm sorry the answer cannot be 20
get back later

The answer is far more than 20. The number of parallelograms is much. I hope I'll get a candid explanation.

I tried solving it using combinatorics but my reasoning seems specious.

Well, for the GRE, been grappling with words for some time now. The quant if not for some technicalities,

I'll say it's ok.

Men, edusegzy, this is a great Job u r doing. Let's keep it rocking!

edusegzy:

richy blacky
Thanks for pointing that out to me.
i sincerely do appreciate
i know from the first time i saw your post on this thread that we are in for a great ride
i guess i was thinking too generally.

edusegzy, you're welcome.

Eyohimself:

Sorry, I made a mistake in the question. The correct question is:

Six parallel lines cut each of the other 5 parallel lines. Find the number of different parallelograms formed.

Eyohimself, this is interesting. Thanks for posting.

edusegzy:

thanks eyohimself

the answer is 20 please i'll get back with explanations

The above is the correct answer if the solution is restricted to unit-sized //ograms.

However, it is incorrect if no restrictions are placed on the size of the //ograms.


Solution:
======
Assuming //ograms of any size within the 5*4 = 20 unit-sized //ograms, then the number of //ograms (of any size) formed = 150.

Explanation:
=========
This is a two-dimensional grid problem. Of course you can imagine the 3-D version!
Let K = total number of unit-sized //ograms formed.
Let SetK = the set of unit-sized //ograms formed (|SetK| = K).
Let G = total number of different //ograms formed.
Let SetG = the set of different //ograms formed (|SetG| = G).

It is clear that G > K (as edusegzy pointed out)
It is also obvious that G is less than power set of SetK, i.e., G < 2^K (because all //ograms must be formed using a contiguous set of unit-sized //ograms)
So, K < G < 2^K

Imagine a set of unit-sized //ograms lined up contiguously to form a row. Let's see how many //ograms (of any size) are formed as the number of unit-sized //ograms is increased:
1 gives 1
2 gives 3
3 gives 6
4 gives 10
.
.
.
X gives X(X+1)/2

So, the above is a 1-D version of the problem. For the 2-D version, the version posted by Eyohimself, we simple multiply. The justification for multiplication is not hard to figure out.

The intersecting parallel lines (two sets, each set in different directions but assuredly intersecting) form a 5 by 4 grid of unit-sized //ograms.

How many //ograms are formed from a row of 5 unit-sized //ograms?
=5(5+1)/2 = 15.

How many //ograms are formed from a row of 4 unit-sized //ograms?
=4(4+1)/2 = 10.

Multiply.

Answer = 15*10 = 150.

richyblacky

day in day out ,you sweep me off my feet with your ingenuity.
thanks for saving the day.

eyohimself.
i like to solve the question the lazy way.
since the question is a GRE question then it should be an objective question.
would you be kind to post the options? then i'll use what i call elimination method to knock out which cannot be the answer. .
On a very serious note i think you should learn (if you have not been doing it) to use the elimination method when solving the GRE questions.
i hope you'll be kind also to give your input on this thread

Hello all,
today's tip
a number is divisible by 5 if it ends in 5 or 0
eg1 30

eg23000000787675

a number is divisible by 8 if the last three digits forms a number divisible by 8

eg1 1008

008 are the last three digits
008/8=1

eg2
765876565657278320

the last three digits are 3,2,0

it forms the number 320

320/8=40

hence

765876565657278320 is divisible by 8

@ RichyBlack,

Men, your ingenuity baffles me. I've been grappling with this problem for about 3 days. Just arrived at a definitive solution while I was sleeping .I woke up immediately to come post the solution I reasoned only to see some detailed and vivid logical explanation to the problem by you.

That implies this form is visited by people with ready wits. Kudos RichyBlack [/b]for that great explanation. Thats an indelible impression you've created on me.
Hopefully, we'll get more of such from this forum.

Well, I used combinatorics to arrive at my final answer.

The number of //ograms formed would be:

[b]6C2 * 5C2 = 150.

Explanation

There are 6 // lines crossing 5 // lines.

A //ogram is formed by 2 opposite // lines and by 2 other opposite // lines.

The 6 // lines would form 2 of the opposite sides of each //ogram while the other 5 // lines would
form the other two opposite sides.

2 opposite sides of the //ogram can be chosen from 6 // lines in 6C2 ways.

The other 2 sides can be chosen from the 5// lines in 5C2 ways.

In all, the total number of //ograms that will be formed would be:

6C2 * 5C2 = 15 * 10= 150.

@ edusegzy

Well, the question is an actual GRE question.A friend got it as one of his question while he was writing the GRE. He couldn't remember the options.

Yeah, I will sure make my own inputs on this thread. This is a nice thread you started.

More is on the way. Shall be posting questions for people to solve.

I've got a databank of actual GRE questions from friends who wrote it over the past 2 yrs.

Hope it'll be of help to future GRE writers and me too as I prepare for the exams coming up in about 34 days time.

Edusegzy, you seem to know some stuff about the GRE? Have you written it in the past?

Any preparation tips for Verbal and the Quant section?

RichyBlack, Your suggestion on the GRE would be winsomely welcomed. I'm sure

they are going to be really sagaciously enrapturing.

Nairalanders, please show yourself and let the thread keep prodding on vehemently.

Divisibility criteria for 6 and 9

A number is divisible by 6 if that number is divible by 2 and 3.

Since we know the divisibility criteria for 2 and 3, then it'll always be

a facile task to discern if 6 divides a number or not.

As an example,

395 384 706 is divisible by 2 since the unit digit of the number is 2.

The number is also divisible by 3 since the sum of its digits ( 3 + 9 + 5 + 3 + 8 + 4 + 7 + 0 + 6 = 45 ) is divisible by 3.

=> 395 384 706 is divible by 6.

395 384 706 / 6 = 65 897 451

A number is divisible by 9 if the sum of its digits

is divisible by 9.

As an example,

The sum of the digits of the number 63 is:

6 + 3 = 9.

9 is divisible by 9.

Hence 63 is divisible by 9 or you can say,

9 divides 63.

These shortcuts are really vital in time-constraining exams like the GRE, GMAT and job-recruiting aptitude test.

They can save you valuable amount of time and you can eschew clumsy calculations if you endear them dotingly.

This is another GRE question:

A vending machine dispenses gumballs in a regularly repeating cycle
of ten different colors. If a quarter buys 3 gumballs, what is the
minimum amount of money that must be spent before three gumballs of the
same color are dispensed?

(A) $1.00
(B) $1.75
(C) $2.00
(D) $2.25
(E) $2.50


Please explanations are needed on how to get the correct answer.


SPOILER: B

eyohimself
you sound to me like you are really ready for GRE with all the vocabs that kept popping up in your writings .i wrote my GRE on july 27th i scored 780 quant , 610 verbal not too good though.
eyohimself i really want to hear that you score lot more that this.i have a friend who scored 1520 (790 quant,730 verbal)and i'm seriously looking towards breaking that record. so i'm registering again very soon.be kind to let me know which school you are choosing because apart from a high GRE score and your undergrad grade you need to choose a school that you have a high chance of being admitted.If you schooled in Nigeria my brother it is not a plus for you because the guyz from asia are dominating the admitted list.They score so high as in 1600/1600.(get the picture)so the advice go for a low ranking school and walk your way up from there

solution:
21/3=7*.25=$1.75