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**ganesh****Moderator**- Registered: 2005-06-28
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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.

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**ganesh****Moderator**- Registered: 2005-06-28
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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!

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**JohnnyReinB****Member**- Registered: 2007-10-08
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*"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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**ganesh****Moderator**- Registered: 2005-06-28
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Thank you for answering to activate the topic.

However, your answer isn't correct, JohnnyReinB!!!

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**JohnnyReinB****Member**- Registered: 2007-10-08
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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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**ganesh****Moderator**- Registered: 2005-06-28
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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.

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**ganesh****Moderator**- Registered: 2005-06-28
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49. The Greatest Common Divisor of

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**ganesh****Moderator**- Registered: 2005-06-28
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50. What is the value of

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**JohnnyReinB****Member**- Registered: 2007-10-08
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*"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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**ganesh****Moderator**- Registered: 2005-06-28
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No, not (x+y), JohnnyReinB!

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**JohnnyReinB****Member**- Registered: 2007-10-08
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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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**ganesh****Moderator**- Registered: 2005-06-28
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Yes, you are correct!!!**Well done, JohnnyReinB!!!**

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**JohnnyReinB****Member**- Registered: 2007-10-08
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Hehe, there were only two choices, anyway, Ganesh.

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**lester_day****Member**- Registered: 2007-11-19
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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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**lester_day****Member**- Registered: 2007-11-19
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I make it 1/6

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**lester_day****Member**- Registered: 2007-11-19
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ganesh wrote:

50. What is the value of

?

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**lester_day****Member**- Registered: 2007-11-19
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I make it 2

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**lester_day****Member**- Registered: 2007-11-19
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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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**lester_day****Member**- Registered: 2007-11-19
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I make it 3. The middle term is zero and the other terms cancels out.

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**ganesh****Moderator**- Registered: 2005-06-28
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Very well done, lester_day! Your answers are correct!!!**Outstanding!!!**

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**Sudeep****Member**- Registered: 2008-07-21
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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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**mathsyperson****Moderator**- Registered: 2005-06-22
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max(n) = 15

Why did the vector cross the road?

It wanted to be normal.

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**JaneFairfax****Member**- Registered: 2007-02-23
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I get 10.

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**ganesh****Moderator**- Registered: 2005-06-28
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#51. Complete the next two numbers in the series of Perfect Numbers:-

6, 28, ____, _______.

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**ganesh****Moderator**- Registered: 2005-06-28
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#52. Factorize:-

x³ - 23x² + 142x - 120.

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