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**ganesh****Moderator**- Registered: 2005-06-28
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**These questions are to be answered orally, within a minute, without the use of paper, pen/pencil and calculator.**

1. There is a number whose double is greater than its half by 45. Find the number.

2. In a fraction, the denominator is greater than the numerator by 6. When 8 is added to the denominator, the value of the fraction becomes 1/3. Find the fraction.

3. Find the number which is greater than the aggregate of its third, tenth, and twelfth parts by 58.

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**ganesh****Moderator**- Registered: 2005-06-28
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4. The difference between two numbers is 3 and the difference between their squares is 51. Find the numbers.

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**ganesh****Moderator**- Registered: 2005-06-28
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5. Which are the three integers, in Arithmetic Progression, whose produce is a prime number?

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**ganesh****Moderator**- Registered: 2005-06-28
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6. $434$0 is a number divisible by 36 where $ represent a single digit 0,1,2,3,4,5,6,7,8, or 9. What number does $ represent?

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**ganesh****Moderator**- Registered: 2005-06-28
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7. Driving through the country leisurely, I travelled 7 miles on the first day, and increased my travel each day by 4 miles, travelling 51 miles on the last day. How many days did I travel and what was the total distance I covered?

8. A train is one miles long. It travels at the rate of one mile a minute through a tunnel which is also one mile long. How much time will it take for the trian to completely pass through the tunnel?

9. When the product of three consecutive numbers is divided by each one of them in turn, the quotients add up to 74. What are the numbers?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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3, 5, 6 and 7 remain.

I have no idea what aggregates are, I can't think of any solution for 5, I got 6 but in more than a minute and I'd never be able to do 7 in a minute either.

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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mathsyperson,

3. aggregate = total

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**ganesh****Moderator**- Registered: 2005-06-28
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10. Can you tell the biggest number that can be formed using four 1s?

11. What number does MDCLXVI in Roman numerals represent?

12. The time is 2.15 PM. What is the angle between the hands of the clock?

13. I have a box two of whose dimensions are 4" and 3". Compute the third dimension of the box such that the space diagonal of the box is an integer.

14. A farmer built a fence around his cows, in a square shaped region. He used 27 fence poles on each side of the square. How many poles did he need altogether?

15. The digits of 12 reversed is 21. The square of 12 is 144 and the digits reversed gices 441, the square of 21. Can you think of another pair of such two digit numbers?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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10. Urm, 1111? I have a feeling that's too simple though.

11. 1666

12. Got an answer, not in time.

13. 12"

14. 104

15. Er, 22 and 22?

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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Answers to 11, 13, 14 are correct, mathsyperson!

Good job!

(The answer to (10) is 11^11 and (15) is 13, 31)

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**ganesh****Moderator**- Registered: 2005-06-28
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16. If 6 men can pack 6 packets of candy in 6 minutes, how many men are required to pack 60 packets in 60 minutes?

17, Find the next two terms in the sequence:-

17, 15, 26, 22, 35, 29, ___, ___.

18. In a get-together, where every person shook hands with every other person present once, there were 28 handshakes altogether. How many people attended the get-together?

19. Is 50986128 a perfect square?

20. How many digits would 2^50 contain?

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

16. Answered, but not in time. I'm kicking myself about it now though.

17. 44, 36

18. 8 people

19. No, because it ends in 8. Squares don't.

20. The only way I can think of to do this is with logs, and I don't see how you could use that without a calculator in 1 minute. So I'm missing something here.

Why did the vector cross the road?

It wanted to be normal.

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**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

mathsy, 2 easy ways of getting approximate answers to 20 without a calculator:-

a) every power of 10 requires just over 3 powers of 2. Therefore 50 powers of 2 suggests between 15 and 16 powers of 10.

b) If you know that log 2 = 0.3010 (which you should!), then log 2^50 = 15.05. Again, about 15 powers of 10

By both methods, this gives me 16 digits in the answer.

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**ganesh****Moderator**- Registered: 2005-06-28
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**Excellent, mathsyperson, and ashwil!Yes, ashwil is right, both the methods are correct. I thought anyone who has known logarithms should remember log[sub]10[/sub]2≈ 0.3010.**

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**ganesh****Moderator**- Registered: 2005-06-28
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21. Which of these is the greatest fraction?

7/11, 13/21, 4/7, 12/19

22. The Greatest Common Divisor of two numbers is 16 and their Least Common Multiple is 336. If one of these numbers is 112, the other one is ______.

23. The value of log (3/5) + log (5/36) + log 12 is equal to ________.

24. A class has 20 boys and 30 girls. The average age of the boys is 11 years and that of the girls is 12 years. What is the average of the whole class?

25. Successive discounts of 15% and 20% on an article amounts to total discount of _____%.

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**ganesh****Moderator**- Registered: 2005-06-28
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26. A father is 4 times his son's age. In 30 years, the son's age will be half of his father's age. What are the father's and son's ages at present?

27. Can you get 31 using the digit 3 fives times and any of the mathematical symbols?

28. The difference between the ages of two persons is 30 years and the produce of their ages is 1624. What are the ages of the two persons?

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**ganesh****Moderator**- Registered: 2005-06-28
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(29) A mule and a donkey were going to the market laden with wheat. The mule said, "if you give me one measure, Iwould be carrying twice as much as you, but if I give you one, we would be having equal measures." What were their burdens?

(30) Amanda has 12 pairs of white socks and ten pairs of red socks. She keeps them all in the same drawer. If she picks out three socks at random, what is the probability that she would get a matching pair?

(31) I drove the first 60 kilometers at 30 km/hour and the next 60 kilometers at 50 km/hour. What was my avergae speed for the trip?

(32) The sum of two numbers is ten. Their product is twenty. Can you find the sum of the reciprocals of the two numbers?

(33) Which of the following is the greatest?

log(20+40), log20+log40, Log(60-30), log60 - log30

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**RauLiTo****Member**- From: Bahrain
- Registered: 2006-01-11
- Posts: 142

26 - the son : 15 and the father : 60

27 - 3 ^ 3 + 3 + 3/3

28 - what do u mean by produce ?

i will try with the rest time later

ImPo$$!BLe = NoTH!nG

Go DowN DeeP iNTo aNyTHinG U WiLL FinD MaTHeMaTiCs ...

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,466

RauLiTo,

28 - produce was a typographical error. read as 'product'.

Answers to 26 and 27are correct.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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34. If the product of two numbers is 320 and their ratio is 1:5, what is the difference between the squares of these two numbers?

35. In a single throw of a pair of dice, what is the probability of getting a sum of 8?

36. A father is now three times as old as his son. Five years ago, he was five times as old as his son. What is the square of the sum of their ages?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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37. What is the value of tan1° tan2° tan3° .......tan88° tan89°?

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

Nice puzzle, ganesh. I liked this one very much.

Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 16,466

**Very good, mathsyperson!**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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38. Two persons start walking at a steady pace of 3 km/hour from a road intersection along two roads that make an angle of 60° with each other. What will be the shortest distance separating them at the end of 20 minutes?

39. In the sequence 462, 420, 380, X, 306 what does X stand for?

40. The surface area of a cube is 216 sq.m. What is its volume?

41. A thief running at 8 km/hour is chased by a policeman whose speed is 10 km/hour. If the thief is 100 metres ahead of the policeman, what time would the policeman require to catch the thief?

42. How many metres is 100 metres more than 100 yards?

43. Which one of the following figures would generatea cone when rotated about one of its straight sides?

(a) An equilateral triangle

(b) A sector of a circle

(c) A segment of a circle

(d) A right angled triangle.

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**ganesh****Moderator**- Registered: 2005-06-28
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44. A rectangle has perimeter of 50 metres. If its length is 13 metres more than its breadth, what is its area?

45. In an accurate clock, what is the angle which the minute hand moves in 2 hours and 20 minutes?

46. A pack of 52 cards are shuffled and two cards are drawn at random one after the other. What is the probability that both of them are jacks?

47. A man starts walking in the North Easterly direction from a point. After walking a distance of 500 metres, he turns Southward and walks a distance of 400 metres. What is his distance and direction with reference to the starting point?

48. If the price of a television set is increased by 25%, by what percentage should the new price be decreased to bring the price back to the original?

Character is who you are when no one is looking.

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