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

MathIsFun has a similar puzzle: One and a Half Hens

http://www.mathsisfun.com/puzzles/one-a … ution.html

*Last edited by JaneFairfax (2008-05-27 04:49:49)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

I am really sorry, JaneFairfax!

I thought you had answered #69 when you had actually answered #68. I sincerely apologize for that hasty post. I tend to make mistakes when I try to be quick. **You are perfectly right!**

Speed and accuracy don't go hand in hand, when thinking is involved.

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
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Answer to #69:**Excellent, JaneFairfax!**

Character is who you are when no one is looking.

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

#45 is similar to #68.

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**ganesh****Moderator**- Registered: 2005-06-28
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Yes, it is, JaneFairfax! I didn't notice that!

#70. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

The vertices of the square are A, B, C, and D. The vertices of the equilateral triangle are B, P, and C. Hence, one of the sides of the equilateral triangle is BC. The square also has BC as one of its sides.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

#71. Consider the set S = {1, 2, 3, ...., 1000}. How many Arithmetic Progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

Character is who you are when no one is looking.

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**JohnnyReinB****Member**- Registered: 2007-10-08
- Posts: 453

*"There is not a difference between an in-law and an outlaw, except maybe that an outlaw is wanted" *

Nisi Quam Primum, Nequequam

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**JaneFairfax****Member**- Registered: 2007-02-23
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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

Answers to #70, and #71:

**Excellent, JaneFairfax! Keep it up!**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

#72. Eric wrote down all the possible three digit numbers with distinct digits on a blackboard. Brian erased all the numbers on the blackboard whose first and last digits were either both odd or both even. How many numbers are left on the blackboard?

Character is who you are when no one is looking.

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**JaneFairfax****Member**- Registered: 2007-02-23
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Can the three-digit numbers start with 0?

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**ganesh****Moderator**- Registered: 2005-06-28
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No, they wouldn't be three digit numbers then!

Character is who you are when no one is looking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
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This smilie is expressing the answer by interpretive dance.

Why did the vector cross the road?

It wanted to be normal.

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

ganesh wrote:

No, they wouldn't be three digit numbers then!

I wasnt sure if you meant numbers as in integers or numbers as in numeric expressions. For example, 012 may be a two-digit *integer*, but as a *numeric expression*, it has three digits. (It could be the combination to a lock, say.) I just want to be sure which one (integers or numeric expressions) you meant.

Anyway

*Last edited by JaneFairfax (2008-05-29 11:52:51)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
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Jane, you've worked out the amount of numbers that got erased.

Why did the vector cross the road?

It wanted to be normal.

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

*Last edited by JaneFairfax (2008-05-29 21:43:03)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

Answer to #72:**Brilliant, JaneFairfax!**

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#73. If the persons A and B have incomes in the ratio 7 : 5 and

expenditures in the ratio 3 : 2 and each one of them saves $ R, then,

what is the income of A?

#74. At 7 : 55 a.m. a police jeep started chasing a stolen car

running at 85 km/hr ahead of it by 5 km. At what time will the police jeep

overtake the stolen car, if its speed is 100 km/hr?

#75. It takes the same time to go 20 km downstream as it takes

to go 12 km upstream. If the speed of the boat used is 8 km/hr in still

water, the speed of the stream (in km/hr) is____________.

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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#76. 3 men and 5 boys can do nineteen-twentieth of a piece of work in 3 days. 4 men and 8 boys can do fourteen-fifteenth of the same work in 2 days. In what time can a boy do the whole work?

#77. A tap P can fill a tank in 10 hours Another tap can empty the tank in 11 hours. The taps P and Q are opened alternately for one hour each. If P is opened first, after how many hours will the empty cistern get filled?

#78. A boy running up a staircase finds that when he goes two steps at a time, there is one step leftover. When he goes up three at a time, two steps are leftover and when he goes up four at a time, there are three left over. What is the minimum number of total stairs?

Character is who you are when no one is looking.

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**careless25****Real Member**- Registered: 2008-07-24
- Posts: 555

*Last edited by careless25 (2008-12-24 06:10:16)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

careless25,

Your edited answer is correct!**W E L L D O N E!!!**

You also deserve this award for saying you edited the answer

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

#79. A side of a cube is √3. What is the maximum length of a stick it can contain?

#80. What is the value of xyz if

#81. A gives half his salary to his wife, half of the remaining salary to his son and one-third of what remains to his daughter. He is left with $500. What is his salary?

Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,801

Complete the series/Fill in the blank:-

#82. 1, 16, 81, 256, ___.

#83. 720, 360, ___, 30, 6, 1.

#84. 5, 8, 16, 19, 38, 41, 82, ____.

#85. 11, 13, 17, 19, ____, 25, 29.

Character is who you are when no one is looking.

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