# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2007-03-07 16:18:15

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### 5 Star Questions

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 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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## #2 2007-03-07 16:40:49

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

### Re: 5 Star Questions

Last edited by JaneFairfax (2007-03-07 16:42:05)

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## #3 2007-03-07 20:23:55

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

Excellent, JaneFairfax!
Great 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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## #4 2007-03-07 23:01:47

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

### Re: 5 Star Questions

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

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## #5 2007-03-08 16:27:51

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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 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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## #6 2007-04-27 18:07:44

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

#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?

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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## #7 2007-04-27 19:20:30

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

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## #8 2007-04-28 00:03:06

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

### Re: 5 Star Questions

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

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## #9 2007-04-28 16:30:52

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

Very well done, JaneFairfax and mathsyperson! JaneFairfax, wouldn't it be better if you explained how you got the solution? Good reasoning, mathsyperson!

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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## #10 2007-04-28 16:31:31

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

#9. How many numbers ending in 3 between 1 and 1,000 are non-primes?

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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## #11 2007-04-28 18:36:37

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

### Re: 5 Star Questions

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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## #12 2007-05-19 15:53:14

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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?

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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## #13 2007-05-19 16:11:10

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

### Re: 5 Star Questions

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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## #14 2007-05-19 16:21:46

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

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## #15 2007-05-19 21:43:56

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

### Re: 5 Star Questions

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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## #16 2007-05-19 22:43:25

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

### Re: 5 Star Questions

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

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## #17 2007-05-19 23:00:05

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

### Re: 5 Star Questions

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

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## #18 2007-05-19 23:04:11

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

### Re: 5 Star Questions

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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## #19 2007-05-23 20:19:25

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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?)

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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## #20 2007-06-02 03:03:47

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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.

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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## #21 2007-06-02 05:57:23

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

### Re: 5 Star Questions

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

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## #22 2007-06-02 17:38:32

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

Excellent work, Jane Fairfax!

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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## #23 2007-12-13 18:54:03

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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?

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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## #24 2007-12-17 20:38:10

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

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.

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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## #25 2007-12-27 20:34:18

Jai Ganesh
Registered: 2005-06-28
Posts: 47,414

### Re: 5 Star Questions

#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.

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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