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**ganesh****Moderator**- Registered: 2005-06-28
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316. In a mixture of 60 liters, the ratio of milk and water is 2:1. If the ratio of the milk and water is to be 1:2, what is the amount of water to be added?

317. An amount of $41 is divided amongst 50 children. Each boy gets 90 cents and each girl gets 65 cents. How many boys are there in the group?

318. A jar of whisky contains 40% alcohol. A part of this is replaced by another liquid containing 19% alcohol. The percentage of alcohol in the new misture is 26. What part of the original liquid had been replaced?

319. 15 liters of a misture contains 20% alcohol and the rest water. If 3 liters of water is added to it, what is the percentage of alcohol in the new mixture?

320. 729 ml of a mixture contains milk and water in the ratio 7:2. How much wate is to be added to get a mixture containing milk and water in the ratio 7:3?

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**ganesh****Moderator**- Registered: 2005-06-28
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321. If loga+logb=log(a+b), express b in terms of a.

322. If log(x+1)+log(x-1)=log3, what is x equal to?

323. If log8/log2=x, what is x equal to?

324. What is the value of x if

325. If

then what is the value of

?

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**John E. Franklin****Member**- Registered: 2005-08-29
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My guesses:

325. Add three. Logs are interesting.

324. 2^(5+3)/10, wait calculator says I'm wrong, uh not common log, so (much thinking for minutes) 0.8 +0.2 = 1 so that might be a clue because .2 is 1/5 and 2^5 is 32, I think I'm on the right track! To be continued later.

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**ganesh****Moderator**- Registered: 2005-06-28
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John,

Your answer to question no.325 is correct. Well done!

For 324, rewrite the equation as

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
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324 revisited:

32^1 = 32 and 32^(1/5) = 2, so 32/2 is answer. What's that rule called, I'll check the formula section.

Yep! I checked the formulas, and found x^m ÷ x^n = x^(m-n). Super-duper!!

*Last edited by John E. Franklin (2006-05-24 04:12:59)*

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**John E. Franklin****Member**- Registered: 2005-08-29
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#323 guess: log of 8 is about .9 if I remember right and log of 2 is .31 maybe so .9/.3 = 3 for an estimate.

Let's see log 1000/log 100 = 3/2 =1.5 but log 100000/log 10000 = 5/4, hmmmm...

This is hard. I'll cheat with a calculator... Cool!! Logs are weird, 2^3 is 8 so 3 is answer, but why?

And same for natural log. So log base 2 of 8 is 3. log 8/log 2 = log base 2 of 8.

Hmmm, I'll have to check the formula section for this one... Hmm, can't find it.

*Last edited by John E. Franklin (2006-05-24 04:27:17)*

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**ganesh****Moderator**- Registered: 2005-06-28
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326. What is the area of an equilateral triangle whose side is 8 cms?

327. What is The length of each side of an equilateral triangle whose area is 4√3 cm²?

328. In ΔPQR, side QR=10 cm, height PM=4.4 cm and side PR = 11 cm. What is the length of altitude QN?

329. The area of a square with side x is equal to the area of a triangle with base x. What is the altitude of the triangle?

330. What is the altitude of an equilateral triangle of side 2√3 cm?

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**ganesh****Moderator**- Registered: 2005-06-28
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331. How many diagonals are there in a decagon?

332. A polygon has 27 diagonals. How many sides does it have?

333. The ratio of interior angle of a regular polygon to its exterior angle is 7:2. How many sides does the polygon have?

334. The sum of the interior angles of a regular polygon is twice the sum of its exterior angles. How many sides does the polygon have?

335. The difference between the interior and exterior angles of a regular polygon is 60°. How many sides does the polygon have?

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**luca-deltodesco****Member**- Registered: 2006-05-05
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328. In ΔPQR, side QR=10 cm, height PM=4.4 cm and side PR = 11 cm. What is the length of altitude QN?

whats M ?

329. The area of a square with side x is equal to the area of a triangle with base x. What is the altitude of the triangle?

divide by xWhat is the altitude of an equilateral triangle of side 2√3 cm?

*Last edited by luca-deltodesco (2006-05-26 04:50:07)*

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**luca-deltodesco****Member**- Registered: 2006-05-05
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321. If loga+logb=log(a+b), express b in terms of a

322. If log(x+1)+log(x-1)=log3, what is x equal to?

(but for the sake of real numbers, x = 2)

323. If log8/log2=x, what is x equal to?

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**ganesh****Moderator**- Registered: 2005-06-28
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luca-deltodesco wrote:

328. In ΔPQR, side QR=10 cm, height PM=4.4 cm and side PR = 11 cm. What is the length of altitude QN?

whats M ?

Given PM is the height.

**All the answers are correct. Very well done, luca-deltodesco!**

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**ganesh****Moderator**- Registered: 2005-06-28
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336. By selling 36 apples, a vendor loses the selling price of 4 apples. What is his loss percentage?

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

338. If the Cost price of 15 tables is equal to the Selling price of 20 tables, what is the loss percentage?

339. A merchant purchased goods worth $ 400. He sold 3/4th at a loss of 10% and the remaining at a gain of 10%. What is his gain or loss percentage on the whole?

340. A trader sells an article at a gain of 15%. Had he bought it at 10% less and sold it at $4 less, he would have gained 25%. What is the Cost Price of the article?

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**ganesh****Moderator**- Registered: 2005-06-28
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341. The average age of a board of 10 advisors of a company is the same as it was 3 years back on account of the replacement of one of the older advisors by a younger man. How much younger was the new man than the director whom he replaced?

342. A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?

343. The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?

344. The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?

345. The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

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**John E. Franklin****Member**- Registered: 2005-08-29
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320. (729/9) ml

319. 100% * 3/(3+12+3)

318. I can't do without paper. These are oral puzzles, no paper right?

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**ganesh****Moderator**- Registered: 2005-06-28
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John, your replies to 319 and 320 are correct. Well done.

Yes, these are oral puzzles, no paper-pencil. And the puzzle is to be solved in a minute.

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**ganesh****Moderator**- Registered: 2005-06-28
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346. The total weight of a container of flour is 19 kilograms. After using one third of the flour, the container and the remaining flour weigh 14 kilograms. What is the weight of the container?

347. The number 33 is a multiple of 11 and leaves a remainder 3 when divided by 4. Find the next integer which is a multiple of 11 and which leaves a remainder of 1 when divided by 4.

348. Two wrist watches (twelve hour watches) are set correctly at 8'o clock. One gains two minutes per hour, the other loses one minute per hour. After how many hours would both the watches show the correct time?

349. A multiple-choice examination paper consists of twenty questions. A student get 5 marks for a correct answer, loses 2 marks for a wrong answer. No marks are given or reduced for a question omitted. If John's score in the examination is 48, what is the maximum number of questions he could have answered correctly?

350. What is the smallest sum of the two largest angles of a scalene triangle in which all the angles are in whole numbers in degrees?

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**ganesh****Moderator**- Registered: 2005-06-28
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351. A metallic sphere of radius 10.5 centimeters is melted and then recast into small cones, each of radius 3.5 centimeters and height 3 centimeters. How many such cones can be made?

352. A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. What would be the radius of the base of the cone?

353. A hollow spherical shell is made of a metal of density 3 grams per cubic centimeter. If its external and internal radii are 9 cm and 6 cm respectively, what would be the weight of the shell in kilograms?

354. What is the volume of a pyramid of base area 16 square centimeters and height 9 centimeters?

355. The dimaeter of a sphere is 6 cm. It is melted and drawn into a wire of diameter2 mm. What would be the length of the wire?

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**ganesh****Moderator**- Registered: 2005-06-28
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356. If sinθ=-12/13 and

what is secθ?

357. If

what is cosec(x)?

358. If sinx=-1/2 and x lies in the fourth quadrant, what is cosx?

359. If sinθ=5/13, what is the value of secθ?

360. If

what is the value of the given expression?

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**Nigel****Member**- Registered: 2006-05-25
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327. 16cm

349. 12 questions

350. 121 degrees?

355. Is it 30 cm?

I'm still intermediate so I don't know many of the questions...

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**ganesh****Moderator**- Registered: 2005-06-28
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Nigel,

327. What is The length of each side of an equilateral triangle whose area is 4√3 cm²?

The Area of any triangle is given by

Since a,b,c are equal and s is the semi-perimter which is 3a/2,

the area of an equilateral triangle is √3a²/2 where a is a side.

Given √3a²/4=4√3, a=4cm

349. Well done. The correct answer is 12 questions, since if he gets 13 correct, he scores 65 marks, and even assuming he answers all the other questions wrongly, it would only cause a deduction of 14 marks, thereby his score would be 51.

350. Well done. When the angles are 59, 60 and 61 degrees, that would give the smallest sum of the two largest angles, that is 121 degrees.

355. The dimaeter of a sphere is 6 cm. It is melted and drawn into a wire of diameter2 mm. What would be the length of the wire?

by converting the unit to millimeters.

We get the length as 36,000 mm or 36 meters.

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**ganesh****Moderator**- Registered: 2005-06-28
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361. What is the value of sin 150°?

362. What is the value of cos 780°?

363. What is the value of tan (-585°)?

364. What is the value of sin76°cos16°-cos76°sin16°?

365. What is the value of cos²75°+cos²15°?

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**Nigel****Member**- Registered: 2006-05-25
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Ganesh I have a question:

327. I used the 1/2absinc formula for this question. Why can't it work?

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**Nigel****Member**- Registered: 2006-05-25
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361. 0.5

362. 1

I would like to know the answers for 363, 364, 365

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**ganesh****Moderator**- Registered: 2005-06-28
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Nigel,

1/2absinc would be 1/2 x a² x √3/2 or √3a²/4.

This is because each angle of an equilateral triangle is 60 degrees and

sin 60 = √3/2

Therefore, √3a²/4=4√3, a=4.

I stand corrected.

361, your answer is correct.

However, for 362, the answer would be 1/2. Remember, sin and cos functions have a period of 360 degrees, the same as cos60.

363. Since tan(-θ) = -tanθ

tan(-585)=-tan(585).= -(tan225)= -1.

364. The formula sin(A-B)=snAcosB-cosAsinB would have to be used.

A=76, B=16, therefore, the given expression is sin(76-16)=sin60=√3/2

365. cos15=sin75, therefore, the expression is cos²75°+sin²75=1.

Are you from Norway?

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**Nigel****Member**- Registered: 2006-05-25
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Nope. You would not guess where I would be from. Serious.

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