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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 44,425

#61. Two crystal spheres of diameter

are being packed in a cubic box of side length x. If the crystal spheres are placed in the box and the rest of the box is completely filled with packing powder, approximately what portion of the box is filled with packing powder?#62. What is the sum of the first 100 terms common to the series

17, 21, 25, 29, 33, 37, ...... and 16, 21, 26, 31, 36, .........?

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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#63.Consecutive odd numbers are arranged in rows as shown below. If the rows are continued in the same pattern, what is the middle number of row 51?

1

3 5

7 9 11

13 15 17 19

21 23 25 27 29

.......................................

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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**Muggleton****Member**- Registered: 2009-01-15
- Posts: 65

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 44,425

Answer to #63:-

Correct, Muggleton!

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
- Posts: 44,425

#64. What is the coefficient of

in the product?

#65. If the

terms of an Arithmetic Progression are in Geometric progression, what is the common ratio of the Gemoetric progression?#66. If a, b, and C are in Arithmetic Progression, then

(1) Arithmetic Progression

(2) Geometric Progression

(3) Harmonic Progression

(4) None of these

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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#67. If the common ratio of a Geometric progression a, b, c, d, e........ is r, is

also a Geometric Progession? If so, what is the common ratio?

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

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

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Answers to #64, #65, #66, and #67.

#65, #66, and #67 : Correct.

#64. Please give me some time to simplify your answer check the correctness. Iam rnning out of time now!

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
- Posts: 44,425

#68.The numbers 34041 and 32506 when divided by a certain number of three digits, leave the same remainder. What is the number?

#69. My wrist watch is slow by 5 minutes at 3 pm, on Wednesday. It was 8 minutes fast at 9.00 am on Friday. At what time did the watch show the correct time?

#70. A cistern has a leak which empties it in 8 hours. A tap is turned on which fills the cistern at the rate of 6 liters a minute, as a result, the cistern is now emptied in 12 hours. How many liters can the cistern hold?

#71. A certain basket-ball team has played

of its games and has 17 wins and 3 losses. What is the maximum number of games that the team can lose and still win at least of the total games played?#72. A log 7 feet long is cut into three pieces, the length of the longest piece being equal to the sum of the length of the other two pieces. What is the length of each piece?

#73. Simplify:-

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Answers to #68, #69, #70, #71, #72:-

Answers to #68, #69, #70 :- All correct!

Answer to #71: I get a different answer. I think it is you who have to correct your answer Please check.

#72 :

Okay, #72 stands corrected, as desired by JaneFairfax!

#72. A log 7 meters long is cut into three pieces, the length of the longest piece being equal to the sum of the length of the other two pieces. What is the length of each piece?

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

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

should be a 10sec question...with process of elimination.:D

*Last edited by careless25 (2009-01-21 16:49:37)*

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

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

for 72 Jane it is in Kilometers per hour.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 44,425

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
- Posts: 44,425

careless25,

Answer to #72:**Perfect! Well done!!!**

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

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 560

ganesh wrote:

Wow, i should have known this. I still get confused when using feet, yards, miles, acres, etc. Base of 10 makes it much more easier i guess.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 44,425

#74. What is the value of x if

#75. Jerome invested $400 at the beginning of every month in a bank paying 8% interest per annum on recurring deposits. How much would he get at the end of 3 years?

#76. From the top of a hill 400 meters high, the angle of depression of the top and the bottom of a tower are 30° and 45°. What is the height of the tower?

#77. In an examination, the average makrs scored by the student was 50 marks. After detecting certain errors in correction and awarding marks, the marks scored by 100 students had to be reduced from 90 to 60. As a result, the average marks scored by the students came down to 45. What is the total number of students who appeared for the examination?

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Answers to #74, #76, and #77:

JaneFairfax,

Answers to #74, and #77 are correct.**Very Good!**

Regarding answer to #76, please check your answer.

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
- Posts: 44,425

#78. What is the value of

to 20 terms?

#79. What is the value of the sum of the series

#80. The Hamonic Mean of two numbers is 4, their Arithmetic Mean A and Geometric Mean G satisfy the relation

What are the two numbers?

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

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

Persnickety!

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**JaneFairfax****Member**- Registered: 2007-02-23
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**Jai Ganesh****Administrator**- Registered: 2005-06-28
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Answer to #76:

Correct. Very Good.

Answer to #78.

The '.' represents 'product' not the decimal!

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

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

If you want to represent multiplication with a dot, it should be a centre dot (\cdot), not a baseline dot!

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