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## #126 2007-12-18 01:34:25

ganesh
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Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

47. I have four marked weights. The sum of the four weights is 40 kilograms. With a pair of scales and these four weights, I can distribute any quantity from 1 kilogram to 40 kilograms (whole numbers). What are the four weights?

48. A pole stands at the mid-point of side AB of a triangular plot ABC. Find the height of the pole if the angles of elevation of the top of the pole at A, B, and C are 45°, 45°, and 30° respectively and BC=AC=150 meters.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #127 2007-12-24 21:52:55

ganesh
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Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

ganesh wrote:

#41. Create a 4X4 Magic Square using the numbers 1-16 without referring. If you can do it in less than five minutes, thats a very good performance.

Here's the solution to the problem!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #128 2008-01-05 01:20:22

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: *** Problems

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #129 2008-01-05 02:25:54

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

Thank you for answering to activate the topic.
However, your answer isn't correct, JohnnyReinB!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #130 2008-01-05 15:55:25

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: *** Problems

But tell me, does scales create a possibility of the weights canceling out?

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #131 2008-01-05 18:39:44

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

You may use both the pans. You may also put some wights on the left and some on the right to get the required weight.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #132 2008-01-06 02:35:11

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

49. The Greatest Common Divisor of

is ______________.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #133 2008-01-07 19:59:24

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

50. What is the value of

?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #134 2008-01-12 18:27:19

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: *** Problems

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #135 2008-01-12 19:00:39

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

No, not (x+y), JohnnyReinB!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #136 2008-01-12 19:09:51

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: *** Problems

x-y?

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #137 2008-01-12 19:20:11

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

Yes, you are correct!!!
Well done, JohnnyReinB!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #138 2008-01-12 19:27:29

JohnnyReinB
Member
Registered: 2007-10-08
Posts: 453

### Re: *** Problems

Hehe, there were only two choices, anyway, Ganesh.

"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted"

Nisi Quam Primum, Nequequam

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## #139 2008-01-18 09:13:31

lester_day
Member
Registered: 2007-11-19
Posts: 4

### Re: *** Problems

ganesh wrote:

***1

Two numbers x and y are chosen at random from the set [1,2,3,4,..........,3n]. What is the probability that x² -y² is divisible by 3?

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## #140 2008-01-18 09:16:32

lester_day
Member
Registered: 2007-11-19
Posts: 4

I make it 1/6

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## #141 2008-01-18 09:18:33

lester_day
Member
Registered: 2007-11-19
Posts: 4

### Re: *** Problems

ganesh wrote:

50. What is the value of

?

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## #142 2008-01-18 09:19:07

lester_day
Member
Registered: 2007-11-19
Posts: 4

I make it 2

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## #143 2008-01-18 09:27:31

lester_day
Member
Registered: 2007-11-19
Posts: 4

### Re: *** Problems

ganesh wrote:

***2

Solve for x.

(x-1)³+(x-2)³+(x-3)³+(x-4)³+(x-5)³=0

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## #144 2008-01-18 09:29:58

lester_day
Member
Registered: 2007-11-19
Posts: 4

### Re: *** Problems

I make it 3. The middle term is zero and the other terms cancels out.

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## #145 2008-01-19 18:19:09

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

Very well done, lester_day! Your answers are correct!!!
Outstanding!!!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #146 2008-08-13 04:25:58

Sudeep
Member
Registered: 2008-07-21
Posts: 20

### Re: *** Problems

Let the quadratic ax^2 + bx + c be such that a, b, c are distinct and each of a, b, c belong to {1, 2, 3, ..., n} such that x+1 divides ax^2 + bx + c.
If the number of such quadratic polynomials are < 99, then max (n) is ??

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## #147 2008-08-13 05:34:59

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: *** Problems

max(n) = 15

Why did the vector cross the road?
It wanted to be normal.

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## #148 2008-08-13 05:58:10

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

I get 10.

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## #149 2008-11-17 02:07:03

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

#51. Complete the  next two numbers in the series of Perfect Numbers:-

6, 28, ____, _______.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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## #150 2008-11-18 16:56:56

ganesh
Administrator
Registered: 2005-06-28
Posts: 29,760

### Re: *** Problems

#52. Factorize:-

x³ - 23x² + 142x - 120.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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