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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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49. A rectangular area of lawn of dimesnions x and y is surrounded by a pathway of width 2 meters. What is the toal area of the pathway?

50. The length, breadth, and height of a room are l, b, and h units respectively. What is the perimter of the ceiling expressed as a percentage of the total area of the four walls?

51. When three coins are tossed together, what is the probability of getting all coins of the same face up?

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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**Ninja 101****Member**- Registered: 2006-02-20
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the answer to 48 is a trick and people were supposed to say 25. well that's silly because the price would be 125 percent. then if that number was the new 100 percent and the number was 100 and is now 125 it will have to decrease by 20%. this is because 25 goes into 125 5 times and 100 devided by 5 = 20.

i think that's it but i'm not sure. i think i've just outsmarted myself.

Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

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**Ninja 101****Member**- Registered: 2006-02-20
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29:

I think the mule has 2 and the donkey has 3.

Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

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**Ninja 101****Member**- Registered: 2006-02-20
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erk. i think they get harder as you go along.

Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Ninja 101, your answer to #48 is correct!

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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**Ninja 101****Member**- Registered: 2006-02-20
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yay! finally! something right!

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

**#39**

x is 342.

Can someone please help me out here btw. I have a hard time expressing what really going on in a particular sequence. I know what's happening, it's just putting it into words in a *correct* manner.

**#40 **

First off, let's get the area of 1 side:

Now, let's get the length of the sides:

Therefore, the answer is:

**#49 **

Let's start with the area of the path just next to the sides with lengths of

This leaves the area of the corners. If I understand the puzzle correctly, the width of the path is measured from the edge of the lawn, to the outer edge of the path. Therefore, these 'edges' must be evenly curved, forming a of a circle with a radius of 2. And since there are 4 of these corners, the total area of the corners is:

Adding these two areas, gives us the total area of the path.

Let A be the area of the path:

**#51**

The number of different outcomes of a throw is:

which can also be written as (t: tales, h: heads)

t - t - t

t - t - h

t - h - h

t - h - t

h - h - h

h - h - t

h - t - t

h - t - h

(obviously I wouldn't do this normally, just showing it to the ones who might not be familiar with this)

This gives us 2 out of 8 posibilities where all the coins have the same face up, and they are ofc t - t - t, and h - h - h.

So the answer is

edit: There's actually a reason for why I'm not just writing the answer. I'm showing what I'm actually doing, which might help me explain things to other people(practice makes perfect), and at the same time, people can understand how to solve the problem, if they couldn't do it themselves.(My teacher would hate me for that sentence :P grammer is prolly messed up, and it's a bit long^^)

*Last edited by Patrick (2006-04-03 06:14:20)*

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Well done, Patrick! All your answers other than #49 are correct! **

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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52. Out of three examinations with a total of 500 marks each, a student scored 45% and 55% in the first and second examinations. To have an average of 60% in all the three, how many marks should the student score in the third examination?

53. Two trains were procedding in the same direction on parallel tracks at 29 km/hour and 65 km/hour respectively. The driver of the first train noticed that it took exactly 16 seconds for the faster train to pass by him. What is the length of the faster train?

54. Fill in the blank.

4/9, 9/20, ___, 39/86

55. What is the value of X in the series:

5, 8, 13, X, 34, 55, 89.

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

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**Patrick****Real Member**- Registered: 2006-02-24
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52.

since

55.

you just add the two numbers before the one you want.. A classic example of series

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Well done, Patrick! **

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

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**rm****Member**- Registered: 2006-03-14
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**rm****Member**- Registered: 2006-03-14
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***49. Area of pathway = (x+4)*(y+4) - xy = 4x + 4y + 16

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Well done, rm! All your answers are correct!**

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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56. The monthly income of Arthur and Richard are in the ratio 4:3 and their monthly expenses are in the ratio 3:2. If both of them save $600 a month, whats the total of their income?

57. What is the maximum number of pieces 5cm x 5 cm x 10cm that can be cut from a bigger piece 5cm x 30 cm x 30cm size?

58. If x=-2, what is the value of x³-x²-x-1?

59. A person start from a point A and travels 3 km eastwards to B and then turns left and travels thrice that distance to reach C. He again turns left and travels five times the distance he covered between A and B and reaches his destination D. What is the distance he travelled from his starting point A to his destination D?

60. A club has 108 members. Two-thirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?

61. A bag contains 20 balls, 8 of them green, 7 white and 5 red. What is the minimum number of balls that must be picked up from the bag blindfolded without replacing any of it to be assured of picking atleast one ball of each color?

62. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% too Mathematics. If the total number of candidates was 2000, how many candidates took both Physics and Mathematics?

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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63. In a class, there are 18 boys who are over 160 cm tall. If these boys constitute three-fourths of the boys and the total number of boys is two-third of the number of students in the class, what is the number of girls in the class?

64. A rectangular piece of metal sheet measuring 50 cm by 100 cm is rolled into a cylinder of height 50 cm. If the cost of painting te cylinder is $50 per square meter, what would be the cost of painting the outer surface of the cylinder?

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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65. From the given equations, find the possible value of x+y.

66. A city has a population of 300,000 out of which 180,000 are males. 50% of the population is literate. If 70%of the males are literate, what is the number of literate females?

67. In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned botha car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both?

68. Water is filled in a container in such a manner that its volume doubles every five minutes. If it takes 30 minutes for the container to be full, in how much time would it be one-fourth full?

69. In 1930, a person's age was 8 times that of his son. In 1938, the father's age became 10 times that of his son's age at 1930. What would be the age of the father and the son in 1940?

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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70. A complete cycle of a traffic signal takes 60 seconds. During each cycle, the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, what is the probability that the light will not be green?

71. A trader fixed the price of an article in such a way that by giving a discount of 10% on the price fixed, he made a profit of 15%. If the cost of the article is $72, what is the price fixed on it?

72. What is the time taken by a train of length 150 metres, travelling at a speed of 90 km/hour to cross a 200 metre bridge?

73. Two ladies simultaneously leave cities A and B connected by a straight road and travel towards each other. The first lady travels at a speed 2 km/hour faster than the second and reaches B one hour before the second lady. If the two cities A and B are 24 kilometres apart, what is the speed of each lady?

74. X started a business by investing $ 30,000. Y joined the business after some time and invested $ 20,000. At the end of the year, profit was divided in the ratio 2:1 proportional to the investment made. After how many months did Y join the business?

75. When the time is 3.25, what is the acute angle made by the hour hand and minute hand of the clock?

76. In a company, 60% of the employees are men. Of these 40% draw more than $ 50,000 per annum. If 36% of the total employees of the company draw more than $ 50,000 per annum, what is the percentage of women drqwing less than $ 50,000 per annum?

77. The age of a man is three times the sum of the ages of his two sons. Five years later, his age would be double the sum of the ages of his sons. What is his present age?

78. What is the length of the longest pole that can be placed in a room 12m long, 9m wide and 8m high?

79. A bus is moving at a speed of 30 km/hour ahead of a car travelling with a speed of 50 km/hour. How many kilometres are they apart if it takes 15 minutes for the car to catch up with the bus?

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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80. A car travels the first one-third of a certain distance at a speed of 10 km/hour, the next one-third at 20 km/hour and the third one-third at 60 km/hour. What is the average speed of the car for the whole journey?

81. A walks around a circular field making one round per hour while B runs around it making six rounds in an hour. If both of them start from the same point in the same direction at 7.30 AM, when will B cross A the first time?

82. Four different candles which can last for 5 hours, 4 hours, 3 hours, and 2 hours of burning are lit in a room at the same instant and are allowed to burn till three candles in the room get extinguished. If the cost of burning each candle is 75 cents per hour, what is the total cost involved?

83. A two member committee comprising of one male and one female member is to be formed out of five males and three females. Amongst the females, Ms.A refuses to be a member of the committee in which Mr.B is taken as a member. In how many different ways can the committee be constituted?

84. Three flags, each of different color, are available for a military exercise. Using these flags different codes can be generated by waving

(i) a single flag of different colors, or

(ii) any two flags in a different sequence of colors, or

(iii) three flags in a different sequence of colors.

What is the maximum number of codes that can be generated?

85. Three bells toll at intervals of 9, 12, and 15 minutes respectively. All the three toll together at 8 AM. At what time would they first toll together again?

86. The total time taken by a person in going to a place by walking and returning on bicycle is 5 hours and 45 minutes. He would have gained 2 hours by riding the bicycle both ways. What would be the time taken by him to walk both ways?

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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87. What is the value of

88. What is the value of

89. In an election, a total of 500,000 voters participated. A candidate got 255,000 votes which was 60% of the valid votes. What was the percentage of invalid votes?

90. 12 workers working 10 hours a day complete a work in 15 days. How many days would 15 workers working for 8 hours a day require to complete the same work?

91. A machine is sold at a profit of 10%. Had the machine be sold for $40 less, a loss of 10% would have been incurred. What is the cost price of the machine?

91. A sum of money deposited at compund interest becomes three times itself in 5 years. In how many years would the sum of money amount to nine times itself?

92. What is the least number by which 3675 should be multiplied so that the resultant is a perfect square?

93. What are the values of A and B if

94. A 40 litre mixture contains wine and water in the ratio 3:1. In order to make the ratio of wine and water 5:2, how many litres of water is to be added?

95. The length of a rectangle is 10% more than a square and its width is 10% less than the square. What is the ratio of area of the rectangle to that of the square?

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**rm****Member**- Registered: 2006-03-14
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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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**Excellent, rm! All your answers other than the annswer to question 91 are correct! **

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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96. Two cars X and Y start from two places A and B respectively which are 700 kilometers apart, at 9.00 AM. Both the cars run at a speed of 60 kilometers/hour. Car X stops at 10.00 AM and starts again at 11.00 AM. At what time do the cars cross each other?

97. A and B start from the same point and in the same direction at 7.00 AM to walk around a rectangular field 400 metres by 300 metres. A and B walk at the rate of 3 km/hour and 2.5 km/hour respectively. How many times would they cross each other if they continue to walk until 12.30 PM?

98. Nine different letters are to be dropped in three different letter boxes. In how many different ways can this be done?

99. How many three-digit even numbers are there such that 9 comes as a succeeding digit in any number only when 7 is the preceeding digit and 7 is the preceeding digit only when 9 is the succeeding digit?

100. In how many different ways can six players be arranged in a line in such a way that two of them, David and Ian, are never together?

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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101. The speed of a car increaes by 2 kilometers per hour after every hour. If the distance travelled in the first hour was 40 kilometers, what would be the total distance travelled by the car in 12 hours?

102. What should replace '?' in the following equation?

103. If A and B are positive integers such that

,

then what is the value of 5A+7B?

104. Twenty times a positive integer is less than its square by 96. What is the integer?

105. Two numbers are in the ratio 4:5. When the cube of the first, square of the second and both the first and second numbers are added, the total is 630. What is the product of the two numbers?

106. The average age of the students is 23 years in a class of 75 students. The average age of the male students is 24 years and the average age of the female students is 20 years. What is the ratio of the number of male students to female students?

107. What is the value of x if

108. A shopkeeper gives three successive discounts of 15%, 35% and 20% respectively. What is the total resultant discount given to the customers?

109. When two dices are thrown, what is the probability that the numbers shown by both are equal?

110. A solid sphere of radius 3 cm is melted and converted into a long wire of diameter 0.2 cm. Find the length of the wire.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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111. A train started from a station with a certain number of passengers. At the first halt, half of the passengers alighted and 120 new passengers got into the train. At the second halt, half of the passengers alighted and then the train left for its destination with 360 passengers. How many passengers were in the train when it started from the first station?

112. What is the LCM of

113. A number when divided by 765 leaves a remainder 42. What would be the remainder if the number is divided by 17?

114. If an angle of a triangle remains unchanged but each of its two including sides is doubled, by what factor would the area get multiplied?

115. If m and n are natural numbers such that

what is the value of m?

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