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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,102

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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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,102

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

*"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****Administrator**- Registered: 2005-06-28
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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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**JohnnyReinB****Member**- Registered: 2007-10-08
- Posts: 453

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****Administrator**- Registered: 2005-06-28
- Posts: 26,102

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.

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

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

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

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

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

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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****Administrator**- Registered: 2005-06-28
- Posts: 26,102

No, not (x+y), JohnnyReinB!

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

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

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****Administrator**- Registered: 2005-06-28
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Yes, you are correct!!!**Well done, JohnnyReinB!!!**

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

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**JohnnyReinB****Member**- Registered: 2007-10-08
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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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**lester_day****Member**- Registered: 2007-11-19
- Posts: 4

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
- Posts: 4

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
- Posts: 4

I make it 2

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

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
- Posts: 4

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

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

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

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

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
- Posts: 4,900

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
- Posts: 6,868

I get 10.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 26,102

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

6, 28, ____, _______.

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

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

x³ - 23x² + 142x - 120.

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

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