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**krassi_holmz****Real Member**- Registered: 2005-12-02
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28.

IPBLE: Increasing Performance By Lowering Expectations.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Excellent, krassi_holmz! Keep up the good work!**

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***29. Out of 40 students, 25 are boys, 16 are married, 10 are married boys. What is the probability that a chosen student would be an unmarried girl?

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***30. If x,y, and z be respectively the sums of p, q, and r terms of an Arithmetic Progression, prove that

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***31. Two numbers are selected at random from 1,2,3,4,....100 and are multiplied. Find the probability of the product being a multiple of 3.

***32. A and B are two independent events. The probability that both A and B occur is 1/6 and that of neither of them occuring is 1/3. Find the probability of occurence of A.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Ninja 101****Member**- Registered: 2006-02-20
- Posts: 936

Annoyed statement:

I can never read that writing like in ***30

and what's more I told you.

Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

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**lightning****Real Member**- Registered: 2007-02-26
- Posts: 2,060

they are 10 boy marred too each other?

Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Firstly, don't post in a 9-month-old thread unless you have something to contribute...I think even *you* know that 10 boys are not married to each other.

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**lightning****Real Member**- Registered: 2007-02-26
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this is 9 months old? i no that but it's a puzzle it's sopost to be tricky!

Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:

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**Eeyore****Member**- Registered: 2007-04-16
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ganesh wrote:

***32. A and B are two independent events. The probability that both A and B occur is 1/6 and that of neither of them occuring is 1/3. Find the probability of occurence of A.

Sorry, not enough information to find a unique solution.

I found that P(A) is not equal to P(B). And, since A and B are interchanged "without loss of generality," a.k.a. WOLOG,

then it seems there are two possibilities for P(A).

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**Stanley_Marsh****Member**- Registered: 2006-12-13
- Posts: 345

To 31

there are 33 numbers which are the multiple of 3 , then the probability of chosing one from 1-100 will be 33/100 , if u chose two number which are not the multiple of 3 , then the probability is (67/100)^2 , then the probability we want is 1- (67/100)^2

To 32 ,

P(A)=x , P(B)=y

xy= 1/6 , (1-x)(1-y)=1/3

y=5/7 ,x= 7/30

*Last edited by Stanley_Marsh (2007-04-27 05:42:58)*

Numbers are the essence of the Universe

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**mathsyperson****Moderator**- Registered: 2005-06-22
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Or perhaps x=5/7, y=7/30. We don't know, and that's the point Eeyore was making.

Wologs are cute.

Why did the vector cross the road?

It wanted to be normal.

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**Stanley_Marsh****Member**- Registered: 2006-12-13
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I check that

P(A on , B off) + P(B on , A off ) + P(A on ,B on ) +P(A off ,B off ) =1

Numbers are the essence of the Universe

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***33. A Pythagorean triple is a set of three numbers such that the sum of squares of the first two numbers is equal to the square of the third. For example, (3,4,5) is a Pythagorean triple. These formthe lengths of the three sides of a right angled triangle.

Prove that there are an infinite number of primitve Pythagorean triples ( The set (6,8,10) is a Pythagorean triple but not a primitve Pythagorean triple because it is of the form(3n,4n,5n) where n=2 and (3,4,5) is a Pythagorean triple. For example,another primitve Pythagorean triple is(5,12,13)).

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***34. Prove that a rhombus is a cyclic quadrilateral if and only if it is a square.

***35. Prove that a parallelogram is a cyclic quadrilateral if and only if it is rectangle.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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***36. In a get-together, every person present shakes hand with every other person once. If there are 91 handshakes in all, how many persons attended the party?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**pi man****Member**- Registered: 2006-07-06
- Posts: 251

*Last edited by pi man (2007-10-14 11:47:56)*

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**JaneFairfax****Member**- Registered: 2007-02-23
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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Outstanding, pi man and Jane Fairfax!!!**

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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37. A vendor has a pair of weighing scales and four weights, the total of all the four weights being 40 kilograms. With the help of any or multiple of these four weights alone and only one wighing on the scale, he can weigh any integral value of weight from 1 to 40 kilograms, both inclusive. How many do these four weights measure?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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38. Can you give a list of 1,000 consecutive non-primes?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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39. How many prime numbers approximately lie between 1 and 1000?

40. What do 1296 and 625 have in common?

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**mathsyperson****Moderator**- Registered: 2005-06-22
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Why did the vector cross the road?

It wanted to be normal.

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**JaneFairfax****Member**- Registered: 2007-02-23
- Posts: 6,868

ganesh wrote:

Non primes are natural numbers that are not prime, also known as composite numbers.

No, not all natural numbers that are not prime are composite numbers!

A composite number is a number that is a product of two or more prime numbers. The number 1 is not a composite number. However, the number 1 is a natural number that is not prime!

So, do you want composite numbers (which will exclude 1), or do you want non-prime natural numbers (which will include 1)?

*Last edited by JaneFairfax (2007-10-31 05:34:07)*

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