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**ganesh****Moderator**- Registered: 2005-06-28
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These are to be answered within five minutes, with or without paper and pencil/pen, but without a calculator.

#1. There are atleast 200 numbers between 1 and 1000 which end in 3 and are prime numbers. True or False? Give reasons.

#2. A number n, either a single digit number or a number containing 2, 3, or 4 digits ending in 5 is repeatedly doubled. At some stage, the resultant number is divisible by 1,000,000. True of False. Give reasons.

#3. A number of the form

is more often a prime number than a non-prime. true or False. Give reasons.

#4. The probability of not getting atleast one 6 when a dice is cast 4 times is less than that of getting it. true of False? Explain.

#5. The numerical value of the (Cusrved) Surface Area of a rectangular sheet folded to form a right circular cylinder is greater than its volume. true of False? Give reasons.

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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**JaneFairfax****Member**- Registered: 2007-02-23
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*Last edited by JaneFairfax (2007-03-07 16:42:05)*

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**ganesh****Moderator**- Registered: 2005-06-28
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Excellent, JaneFairfax!

Your answer to #4 and #5 are aboslutely correct!

Great work!!!

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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**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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**ganesh****Moderator**- Registered: 2005-06-28
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Excellent, mathsyperson!!!

Your answers and reasoning are very close to perfect, I'd say perfect, but for the doubt you expressed in the solution to the last problem.

All the same, all your answers are correct, and I can prove the result where you had expressed some doubt, if you think it is necessary, and post here.

#6. Prove that for a Pythogorean triple a,b, and c, a², b² and c² cannot be a Pythogorean triad. Counter-proof or counter-exampmles are most welcome.

#7. Given below are the trignometric and Inverse trignometric ratios grouped in three pairs. Tell me, what is the basis of grouping them.

(Cosθ, Sinθ), (Tanθ, Cotθ), (Secθ, Cosecθ).

Please do give a mathematically acceptable and elegant reply and as I say always, use the hide tag.

(

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****Moderator**- Registered: 2005-06-28
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#8. Inside a square of side 'a', another square is constructed with side a/2. Inside the smaller square, another square of side a/4 is constructed. This process in continued indefinitely. What is the area of all the squares so formed put together, including the parent square?

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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**ganesh****Moderator**- Registered: 2005-06-28
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Very well done, JaneFairfax and mathsyperson! JaneFairfax, wouldn't it be better if you explained how you got the solution? Good reasoning, mathsyperson!

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#9. How many numbers ending in 3 between 1 and 1,000 are non-primes?

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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Well, if I have counted correctly looking at this list, there should be 42 primes ending in 3 between 1 and 1000. Therefore the number of non-primes ending in 3 between 1 and 1000 should be 100 − 42 = 58.

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**ganesh****Moderator**- Registered: 2005-06-28
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JaneFairfax, you looked at the right list. Well done!

10. If the sum of 3 numbers in a Geometric Progression is 3.5, what is the first number?

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

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

the first number is 2 ? I think it has many answers ..

*Last edited by Stanley_Marsh (2007-05-19 16:15:50)*

Numbers are the essence of the Universe

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**pi man****Member**- Registered: 2006-07-06
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**mathsyperson****Moderator**- Registered: 2005-06-22
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I agree with Stanley. You can craft a sequence to make any answer you want be right.

Edit: As long as that answer is in (0,14/3].

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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*Last edited by JaneFairfax (2007-05-19 22:43:42)*

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**JaneFairfax****Member**- Registered: 2007-02-23
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*Last edited by JaneFairfax (2007-05-19 23:06:02)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
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That's the answer I got as well, except that the left inequality should be strict.

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 22,042

You are all right, I mjust wanted any of the possible solutions to be posted!

Well done, Stanley_marsh, pi man, Jane Fairfax and mathsyperson!!!

11. When would the probability of getting a 6 be more than not getting one when a dice is thrown? (that is, after how many throws?)

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

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**ganesh****Moderator**- Registered: 2005-06-28
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12. A box without a lid is made of wood whixh is 3 cm thick, its external dimensions are length : 86 cm, breadth: 60 cm and height : 45 cm. Find the capacity of the box in cubic centimetres.

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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For #11, do you mean **at least one** 6?

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**ganesh****Moderator**- Registered: 2005-06-28
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Both your ansers are correct,

Excellent work, Jane Fairfax!

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

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**ganesh****Moderator**- Registered: 2005-06-28
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13. A baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?

14. M men agree to purchase a gift for Rs. D. If three men drop out how much more will each have to contribute towards the purchase of the gift?

A. D/(M-3)

B. MD/3

C. M/(D-3)

D. 3D/(M²-3M)

15. There are 5 red caps, and 4 green caps. If one draws randomly a cap, what is the probability of getting a red cap?

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

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**ganesh****Moderator**- Registered: 2005-06-28
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16. A man bought a horse and a cart. If he sold the horse at 10 % loss and the cart at 20 % gain, he would not lose anything; but if he sold the horse at 5% loss and the cart at 5% gain, he would lose $10 in the bargain. The amount paid by him was $_______ for the horse and $________ for the cart.

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

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**ganesh****Moderator**- Registered: 2005-06-28
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#17. The parallel sides of a trapezium are 60 cm and 46 cm. The non-parallel sides are 13 cm and 15 cm. Find the area of the trapezium.

#18. Find the area of a regular hexagon inscribed in a circle of radius 5 cm.

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

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