1st REGIONAL MATH WIZARDCMU, August 1999

EASY ROUND

1. (30 sec) A chemist has 2 alcohol solutions containing 30% alcohol and 45% alcohol. How much 30% solution should be used to obtain exactly 30 cm3 of 39% solution? (12 cm3)

2. (15 sec) A man and his wife invited 8 pairs of couple for a dinner. They are to sit around a table. In how many ways can they be seated so that each man and his wife are to sit side by side? (80 640 ways)

3. (30 sec) The sum of the squares of 2 consecutive positive integers is 481. Determine the two integers. (15 and 16)

4. (30 sec) For the eight consecutive integers, the sum of the first 4 numbers is 178. What is the sum of the next 4 numbers? (194)

5. (15 sec) What is the next number in the series 1, 3, 5, 7, ___? (9)6. (15 sec) In differential calculus, it states that for indeterminate functions/forms,

the limit of that form equals the limit of its derivatives. (L'Hopital's Rule)7. (45 sec) Leila Barros, on the way for her practice, drove a car at an acceleration

of 4 m/s2. How far does she travel 5 seconds later from rest? (50m)8. (45 sec) An 8 gram bullet is fired horizontally and strike a 9-kg block of wood

at rest, after which moves 0.4 m/s with the embedded bullet. Calculate the muzzle velocity of the bullet. (450.4 m/s)

9. (20 sec) A kite of shape of a rhombus has diagonals 8 inches and 12 inches. What is its area? (48 in2)

10. (30 sec) Determine the values of x, y, and z in the following equations: xy = -8; yz = -2; and zx = 4. If x is to be positive. (4, -2, 1)

DIFFICULT ROUND

1. (30 sec) Find the diameter of the circle shown. (14)

2. (30 sec) What is the area of a triangle with sides 8, 14, 5? (no solution)3. (15 sec) What do you call the value of x for which the second derivative of a

function y with respect to x when equated to zero. (point of inflection)4. (20 sec) What is the sum of the first 100 even numbers? (10 100)5. (15 sec) What is the next number in the sequence 1, 8, 27, 64, ___? (125)6. (25 sec) If 10 chickens can lay 10 eggs in 10 days. How many more chickens

will be added to lay 100 eggs in 100 days. (zero)7. (30 sec) Water is entering a tank at 4.83 gpm. A 5-liter pail is placed under a

leaking faucet of the tank. If it was observed that it took 20 minutes to fill the pail, how much water in the tank will there be after 20 minutes? (360 liters)

8. (60 sec) A man wants to grow a tree very quickly. He buys a special kind of tree that double in height everyday. On the 21st day, the tree is 20 ft tall. On what day was it 5ft tall? (19th day)

9. (30 sec) Pipe A can fill a tank in 4 hours and pipe B can fill it in 3 hours. In how many hours can the tank be filled if both pipes are open? (1.714 hours)

10. (15 sec) A petroleum oil is sold at $19.5 per barrel. If there are 159 liters in a barrel and a dollar is equivalent to P50, how much is the oil sold in peso per liter? (P6.13/liter)

2

3

8D-2

2nd REGIONAL MATH WIZARDLiceo de Cagayan, August 31, 2000

EASY ROUND

1. (20 sec) What is the greatest prime number less than 700? (691)2. (20 sec) Is 56 a perfect, deficient, or abundant number? (abundant)3. (30 sec) Express the repeating decimal 0.1405 as a fraction? (26/185)4. (45 sec) Population of a certain country increases 50% every 50 years. If population in

1950 is 810,000, what year was the population equal to 160,000? (1750) 5. (30 sec) If the median of a set of numbers is not one of the numbers in the set, what do

you know about the set of numbers? (even number of terms)6. (30 sec) Mario prepared soup of 5 different vegetables and 3 different herbs. If he has

12 vegetables and 6 herbs to choose from, how many different soups can he make? (15840)

7. (30 sec) A bag contains 10 balls, each labeled with different integers from 1 to 10. If two balls are drawn from the bag, which is more likely to be drawn, 10 or 13? (equally likely)

8. (45 sec) Find three whole numbers in arithmetic progression whose product is a prime number? (-3,-1, 1)

9. (60 sec) A bag contains 10 balls labeled 1 to 10. If 2 balls are drawn at random, what is the probability that the sum of the integer on the balls drawn will be greater than 6? (13/15)

10. (60 sec) Express 37 +37 +37 as a power of 9. (94)

DIFFICULT ROUND1. (15 sec) In a playing card, what is the probability that a red card or a picture card is

drawn? (8/13)2. (60 sec) Village A: Population is 6800 and decreases at 120 persons/year. Village B:

population is 4200 and increases at 80 persons/year. In how many years will the population of the 2 villages be equal? (13 years)

3. (15 sec) Systems of linear equations are ____ if it has at least one solution. (consistent)

4. (45 sec) What is t and u in the equations: 8u = 7 - 2t ; 3t + 7u = 5 - 5u? (no solution)5. (45 sec) The largest angle of the triangle is 10° more than the middle size angle, and

twice the smallest angle. What is the measure of the largest angle? (76°)6. (60 sec) The radius of the sphere is initially zero. It increases at the rate 6 ft/s. Find

how fast the volume is increasing? (54 π ft3/s)7. (30 sec) How many permutations are there in the word engineering? (277 200)8. (30 sec) After Charles gave x dollars to Carla, he still has y dollars more than she does.

How much dollars does Charles have before giving money to Carla? (y + 2x)9. (30 sec) The sum of two positive integers is 36. What is x and y if their product is to be

the largest possible? (18 and 18)10. (10 sec) What do you call the arrangement of raw numerical data in ascending or

descending order? (array)

TIE BREAKER

1. (30 sec) 40 grams of alloy with 36% gold is melted with a 20-gram alloy of 20% gold. What is the percentage of gold after mixing? (40%)

2. (30 sec) A store has 10 different sizes of shoes, hi-cut and low-cut, rubber or leather, black or white. How many different kind of shoes can a person choose from? (80)

3. (30 sec) In how many ways can 3 men and 2 women be seated in a bench if the women sit together? (576)

4. (30 sec) In a class of 40 students in Algebra and Trigonometry, 30 students passed in Algebra, 36 passed Trigonometry, and 2 failed in both subjects. How many students passed both subjects? (28)

5. (30 sec) A bag contains 3 white and 5 red balls. Find the probability that two balls are drawn are both white? (3/28)

___

3rd REGIONAL MATH WIZARDSt. Peter College, August 30, 2001

EASY ROUND

1. (20 sec) A parallelogram has sides 20 ft and 30 ft. Its included angle is 30°. What is its area? (300

ft2)

2. (60 sec) An automobile moving at 32.4 kph is made to stop to 4.5 meters. If it is moving at 72

kph, what will be the distance covered if it is to be stopped with the same deceleration? (22.22

m)

3. (30 sec) Haretown is 96 miles from Tortuiseville. A hare is moving 9 mph towards Tortuiseville

and a turtle walks at 3 mph towards Haretown. At what distance will the hare travel just before

meeting the turtle? (72 mi)

4. (30 sec) The distance covered by a car is proportional to the square of its speed. If s = 0.092v2,

how fast is the distance changing wrt its speed when the speed of the car is 15 mph? (2.76 hr)

5. (60 sec) Al can paint a wall in x hours. If Bert will help him, they can finish it two hours faster

than Al can do alone. Express the time for Bert to finish the job in terms of x?

[(x2 - 2x)/2 ]

6. (10 sec) What is 270 mod 4? (2)

7. (30 sec) A man wishes to fence his lot with 100 m of wire. If one side coincides with a concrete

wall, what is the maximum area of the lot? (1250 m2)

8. (60 sec) In 11 years, Kate will be 5 times as she was 9 years ago. How old is she now? (14)

9. (60 sec) A round table is to be fit in a corner of two perpendicular walls. If at one point at the

edge of the table, the distance from one wall is 5 cm and on the other side is 10 cm, find the

diameter of the table. (50 cm)

10. (15 sec) An explorer from a certain point walks towards the south 10 miles. He then face east and

walked for another 10 miles, and then faces west and walked 10 miles and finally walked 5 miles

north. How far is he from the starting point and its location?

(5 miles towards south)

DIFFICULT ROUND

1. (120 sec) Tom's dad has a miniature pyramid of Egypt that has a height of 4 in. His dad wanted it

to be displayed but realized that it was too small. So, he made a similar pyramid whose density is

one half that of the miniature pyramid. If the mass of the miniature pyramid is the same as that of

the pyramid to be made, what is its height? (4.65 ft)

2. (30 sec) An initial colony of 32 microorganisms reproduces through simple cell division under

ideal conditions of unlimited food supply. If it is observed that the population doubles every 2

hours, what is its population if it continues to reproduce for 12 hrs? (2048)

3. (30 sec) In how many ways can six vacant seats be occupied by 9 men and 7 women if 3 or 4

seats are to be occupied by men? (5586)

4. (10 sec) A pillar 8 feet tall cast a shadow of 2 feet. If it is 28 feet tall, it will cast a shadow of how

many feet? (7 feet)

5. (10 sec) A car is moving at constant speed at 1/100 kps. How far will it travel for 1 hour?

(36 km)

6. (30 sec) Oakland and Pinewood are 70 miles apart. An automobile from Oakland moves at 28

mph to Pinewood at uniform speed. Going to Oakland from Pinewood is downhill, so the

automobile travels at 70 mph. What is the average speed of the automobile for the round trip? (40

mph)

7. (30 sec) A snail is climbing out a well that is 22 ft deep. Every day the snail climbs up 6 ft and

every night he slips back 2 ft. How many days will it take him to get out of the well? (5 days)

8. (60 sec) The demand Q of children's book depends on the price P. If Q = 360/P3/2 and each book

cost P8, how much will each be sold to maximize profit? (P24)

9. (30 sec) In how many ways can 3 2000-ohm resistors be connected, if a man has a choice of what

ever connection to be made? (7 ways)

10. (30 sec) [91/x][641/3x] = 12. Solve for x (1.44)