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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,313

411. The average of 11 numbers is 10.9. If the average of

the first six numbers is 10.5 and that of the last six numbers

is 11.4, then what is the middle (6th) number?

412. The perimeter of one face of a cube is 20 cm. What is its volume?

413. What is the number of revolutions made by a wheel of

diameter 56 cm in covering a distance of 1.1 km (use pi= 22/7)?

414. What is the curved surface of a right circular cone of height

15 cm and base diameter 16 cm?

415. A circular well of diameter 2 metres is dug to a depth of 14 metres. What is the volume of the earth dug out? (use pi= 22/7)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,313

416. A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?

417. A student appeared for five papers in an examination, where the maximum marks were the same for each paper. His score in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. In how many papers did he got more than 50% marks?

418. A certain city has a circular wall around it, and the wall has four

gates pointing north, south, east and west. A house stands outside the city, three kms north of the north gate, and it can just be seen from a point nine kms east of the South Gate. What is the diameter of the wall that surrounds the city?

419. A square, whose side is 2 meters, has its corners cut away so as to form an octagon with all sides equal. What is the length of each side of the octagon, in meters?

420. Consider a triangle. Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the length of its third side?

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,313

421. The probability of getting a prime number from a number chosen at randon from 1 to 20 is __________.

422. What is the slope of the line 3x+4y+2=0?

423. If sinx=cos 48°, what is x?

424. If cos θ =12/13, find (cosecθ tanθ + sinθ cosecθ).

425. a ladder makes an angle 60° with the floor and its lower end is 4 m from the wall. Find the length of the ladder.

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

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

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

421) 8 out of 20 or two-fifths or 40%. ( 1 is not prime according to one source I read)

422) -3/4 slope

423) 90 - 48 degrees or 42

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

John E. Franklin wrote:

( 1 is not prime according to one source I read)

A prime number is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself.

The key word here is 'distinct', meaning non-identical. So 1, with only one divisor(1), is not a prime number.

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

424. If cos θ =12/13, find (cosecθ tanθ + sinθ cosecθ).

425. a ladder makes an angle 60° with the floor and its lower end is 4 m from the wall. Find the length of the ladder.

x.cos60 = 4, cos60 = 0.5, x = 4/0.5 = 8

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

Woah. Octadecuple posting. It'd look a lot nicer if you just edited your existing latest post whenever you thought of a new answer, instead of just making a new post for it. Chains of 2 or 3 posts of answers are alright, but 18 is a bit much.

Also, I'd say that 49! can only be divided by 14 eight times.

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

OK. Editing and deleting now...

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

117. 49! can be divided by 14 62 times before becoming a decimal.

237. No - 4 more men should be employed to get this work done.

241. Raymond was in fifth position.

243. Saturday

246. 4

247. 58,968

248. 5

249. 0.1 cubic millilitres? I kinda rushed this one, so it may not be correct.

250. 40

252. 60

253. 10%

263. $680

271. 8

294. 640,000

295. 10:21 P.m.

304. 0.5

311. 15

398. 2475

412. 125cm³

423. x = 42

*Last edited by Devanté to put answers in numerical order, and:*

*Last edited by Devanté (2006-10-09 03:39:35)*

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

I'm going to change my answer for 117, and say 48 instead of 64.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

187) 16

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**holla****Member**- Registered: 2006-10-12
- Posts: 73

why change your answer? after all, with the way your brain works, your first instinct/inclination is normally correct unless you are revising an error...

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

That simply is not true. And I can change my answers whenever I wish, thank you.

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**holla****Member**- Registered: 2006-10-12
- Posts: 73

dude, chill! maybe if you spent more time with real people that aren't online, then you would be able to see that being rude and a total egomaniac aren't going to get you anywhere socially...and btwe, you're welcome!

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

Holla, what is it about Devanté that makes you feel the need to flame everything he says?

You're perfectly courteous to everyone except him, so what is it about him that makes your attitude so different? Please try to work things out, or I'll have no choice but to ban you. And I don't want to, because you've been helping out in a few of the Help Me topics.

Why did the vector cross the road?

It wanted to be normal.

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**holla****Member**- Registered: 2006-10-12
- Posts: 73

fifty words? really?

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

#117

49! can be evenly divided by 14 only 8 times. To be divisible by 14, it must also be divisible by 7. When calculating N = 49!, the only time a 7 is factored in is when multiply by 7, 14, 21, 28, 35, 42, and 49 (two 7's in that one).

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

Me and pi man are both awesome at answering that question.

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

And I fail. >_>

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**NP****Member**- Registered: 2007-02-25
- Posts: 2

ganesh wrote:

(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? Don't know the answer

(33) Which of the following is the greatest?

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

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,313

Sum of reciprocals:-

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

*Last edited by JaneFairfax (2007-02-26 16:21:26)*

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,313

That one is remarkably simpler!

Great work, JaneFairfax!

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

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

Yes, I fell into that trap as well. I diligently worked out what the two numbers needed to be, and it was only when I got to adding their reciprocals that I realised that I needn't have. Very nice, sneaky puzzle.

Why did the vector cross the road?

It wanted to be normal.

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**koller****Member**- Registered: 2007-11-23
- Posts: 1

By selling 8 dozen pencils, a shopkeeper gains the selling price of 1 dozen pencils. What is his profit percentage?

where can i get the answer?????

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