Instruction: Submit your answer sheet

(provided) together with this questionnaire to the office for checking.

Time Element: 4 hours 1. What is the remainder when

20x9x10x 24−−− is divided by (x – 4)?

A. 38 B. 40 C. 42 D. 44

2. Evaluate xlog

yxlogyxlog 332−

.

A. x

B. 2

x

C. 3

2

D. xy

3. It is between 3 and 4 o’clock. In ten minutes, the minute hand will be as much after the hour hand as it is now behind it. What is the time?

A. 3:13.05 B. 3:12.67 C. 3:11.36 D. 3:10.45

4. How many terms of the progression 3, 5,

7, … must be taken in order that their sum will be 2703?

A. 50 B. 51 C. 52 D. 53

5. An airplane traveled 360 miles in 2 hours

with the wind and flying back the same route, took 3 hours and 36 minutes against the wind. What was the speed of the airplane in still air?

A. 150 mph B. 145 mph C. 140 mph D. 135 mph

6. Find the sum of the odd integers from 1 to

3001 inclusive.

A. 2,253,000 B. 2,253,001 C. 2,253,101 D. 2,253,100

7. What is the sum of three geometric means

between 2 and 162?

A. 64 B. 78 C. 68 D. 72

8. A tank is fitted with two pipes. The first pipe can fill the tank in 10 hours. After it has been opened for 3 hours, the second pipe is opened and the tank is filled up in 4 hours more. How long would it take the second pipe alone to fill the tank?

A. 13.67 hours B. 13.33 hours C. 13.00 hours D. 14.00 hours

9. Hooke’s law states that the force F

required to stretch a spring x units beyond its natural length is directly proportional to x. If a weight of 6 kg stretches a spring 2 cm, then how much weight will stretch it 1.5 cm?

A. 5.2 kg B. 4.5 kg C. 5.6 kg D. 4.8 kg

10. What is the coefficient of the 5th term of the

expansion of ( )133 yx + .

A. 715 B. 751 C. 571 D. 517

11. In how many ways can 10 people be

seated around a circular table?

A. 338,820 B. 354,280 C. 317,280 D. 362,880

12. The sum of the squares of two consecutive

odd numbers is 130. What is the sum of these numbers?

A. 12 B. 16 C. 24 D. 20

13. A car 15 ft long overtakes a truck 30 ft long

which is traveling at 45 mph. How fast must the car travel to pass the truck in 3 seconds?

A. 81 fps B. 80 fps C. 79 fps D. 78 fps

14. How many triangles are formed by 20 points no three of which are on the same straight line?

A. 1,140 B. 1,274 C. 1,180 D. 1,230

15. A gallon of alcogas of high concentration is

75% alcohol and 25% gasoline. However, it has been found out that even a 50% - 50% mixture is still comparable to a regular gasoline combustibility. How much more gasoline then should be added to the high concentrate alcogas to yield a 50% - 50% concentration?

A. 0.75 gallon B. 0.50 gallon C. 0.25 gallon D. 1.00 gallon

16. The gasoline tank of a car contains 50

liters of gasoline and alcohol, with alcohol comprising 25%. How much of the mixture must be drawn off and replaced by alcohol so that the tank contains a mixture of which 50% is alcohol?

A. 12.25 liters B. 13.50 liters C. 14.75 liters D. 16.67 liters

17. When the numerator and denominator of a

certain fraction is increased by 2 and 1, respectively, the fraction becomes ½. However if 1 is added to the numerator and 2 is subtracted from the denominator, the fraction becomes 3/5. Find the original fraction?

A. 2/7 B. 3/7 C. 4/7 D. 5/7

18. Two horns A and B sound every 34

minutes and 38 minutes, respectively. They sound together at 7:00 in the morning. At what time will the two horns next sound together?

A. 4:30 PM B. 4:53 PM C. 5:08 PM D. 5:46 PM

19. What is the sum of 5 arithmetic means

between 4 and 19?

A. 57.5 B. 53.5 C. 55.5 D. 51.5

ASSIGNMENT 1 - MATHEMATICS

20. Given the following equations: 2x + y – z = 5 4x – 2y + z = - 5 6x + 4y – 2z = 17

Find the value of y.

A. 1 B. 3 C. – 1 D. 2

21. A man started his car at a certain time from a certain place. On arrive at his destination at the precise appointed time, he said “If I had averaged 6 miles per hour faster, I would have been 5 minutes early. But if I had averaged 5 miles per hour slower, I would have been 6 minutes late”. How far he had driven?

A. 30 miles B. 35 miles C. 40 miles D. 45 miles

22. ( )− =2

5x 2

A. − +225x 20x 4

B. +25x 4

C. +225x 4

D. −225x 4

23. The difference of two positive numbers is

12. Their product is 405. What is the smaller number?

A. 13 B. 16 C. 15 D. 17

24. A businessman has a choice of two rental

cars. One costs $40 per day with unlimited mileage. The other costs $25 per day plus 30 cents per mile. For what mileage is the $40 plan no more expensive than the other plan?

A. At least 50 miles per day B. No more than 50 miles per day C. At least 133 miles per day D. No more than 133 miles per day

25. A salesman drove 200 miles to visit a

client then returned home. He averaged 10 mph faster on his trip to the client than on his way home. The total trip took 7 hours 20 minutes. How long did he spend driving on his way home?

A. 3 hours 20 minutes B. 4 hours C. 5 hours D. Cannot be determined

26. Two cars pass each other at 4:00 at an overpass. One car is headed north at an average speed of 60 mph and the other is headed east at an average speed of 50 mph. At what time will the cars be 104 miles apart?

A. 5:25 B. 5:00 C. 5:10 D. 5:20

27. Together two pipes can fill a small

reservoir in two hours. Working alone Pipe A can fill the reservoir in one hour forty minutes less time than Pipe B can. How long would Pipe A need to fill the reservoir by itself?

A. 5 hours B. 4 hours and 20 minutes C. 3 hours and 20 minutes D. 5 hours and 20 minutes

28. How much 10% alcohol solution should be

mixed with 14 ounces of 18% solution to get a 12% solution?

A. 14/15 of an ounce B. 42 ounces C. 4.2 ounces D. 14 ounces

29. A piggybank contains $3.20. There are

twice as many nickels as quarters and half as many dimes as quarters. How many dimes are in the piggybank?

A. 16 B. 8 C. 4 D. 6

30. 16 is what percent of 80?

A. 5 B. 25 C. 20 D. 15

31. A book report counts toward one-fifth of a

student’s course grade. The remaining four-fifths of the courses’ average is determined by the average of six quizzes. One student’s book report grade is 90 and has quiz grades of 72, 66, 69, 80 and 85. What does she need to earn on her sixth quiz to raise her average to 80?

A. 90 B. 91 C. 92 D. 93

32. Factor: + −4 2x 5x 36

A. ( )( )( )+ − +2x 9 x 2 x 2

B. ( )( )+ −x 4 x 9

C. ( )( )− +x 4 x 9

D. ( )( )( )( )− + − +x 2 x 2 x 3 x 3

33. A piece of work can be done by Melody,

Shirley and Phen working together in 4 days. The job can also be done if Melody works for 2 days, Shirley for 7 days and Phen for 4 days, or if Melody and Shirley work together for 1 ½ days, Shirley and Phen work together for 5 days. How long would it take Melody to do the work alone?

A. 10 B. 12 C. 13 D. 11

34. In how many different ways or

arrangements can you put 3 balls, colored red, white and blue in 20 empty boxes?

A. 112 B. 120 C. 130 D. 148

35. A deer is 70 leaps of its own ahead of a

hound. Three leaps of the dear are as long as 2 leaps of the hound, but the deer makes 5 leaps while the hound is making 4 leaps. How many leaps must the hound make to overtake the deer?

A. 292 B. 286 C. 280 D. 278

36. A man and his wife decide to entertain 24

friends by giving 4 dinners with 6 guests each. In how many ways can the first group be chosen?

A. 132,780 B. 128,580 C. 134,596 D. 136,780

37. Twenty five stones are placed in a straight

line on the ground at intervals of 3 feet. Fifteen feet from the first stone a basket is placed from which a runner starts. The runner picks the stones one at a time and carries them back to the basket. How far does he ran in all?

A. 2,500 ft B. 2,450 ft C. 2,550 ft D. 2,600 ft

38. A child in a swing moved on an arc 15 feet

in length, then back three-fourths of this distance and so on until the swing “stopped”. Find the distance traveled.

A. 60 feet B. 68 feet C. 64 feet D. 72 feet

39. The safe load of a beam with a rectangular section that is supported at each end varies jointly as the width and square of the depth and inversely as the length of the beam between supports. If the safe load of the beam 3 inches wide, 6 inches deep with supports 8 feet apart is 2700 pounds, find the safe load of a beam of the same material that is 4 inches wide, 10 inches deep with the supports 12 ft. apart.

A. 6,333 lbs B. 6,500 lbs C. 6,667 lbs D. 7,000 lbs

40. An urn contains 4 red balls and 5 blue

balls. If two balls are drawn, what is the probability that one ball is red and one ball is blue?

A. 1

9

B. 4

9

C. 5

9

D. 7

9

41. A group of Koreans chartered a bus for

$300. Two of the group were unable to join and as a consequence, each of the others remaining in the group had to pay $12.50 more. How many were there in the original group?

A. 6 B. 7 C. 8 D. 9

42. A two digit number is equal to 8 times the

sum of its digits. If 45 is subtracted from the number, its digits are reversed. What is the number?

A. More than 90 B. More than 55 but less than 86 C. More than 86 but less than 90 D. Less than 55

43. A carpenter constructed a unique ladder

with 9 rungs whose length decreases uniformly from 24 cm at the base to 18 cm at the top. What is the length of the 7th rung?

A. 18.75 cm B. 19.50 cm C. 20.25 cm D. 21.00 cm

44. Find the value of x in the following

equation: ( ) ( ) xln23x2ln2xln =−+−

A. 6 B. 2 C. 3 D. 4

45. A man bought 20 chickens for P 200. The cocks cost P 30 each, the hens P 15 each and the chicks at P 5 each. How many chicks did he buy?

A. 11 B. 12 C. 13 D. 10

46. How many 5-card hands will have 3 aces

and 2 kings?

A. 16 B. 24 C. 12 D. 36

47. Find the sum of all odd numbers between

7 and 433, inclusive.

A. 46,160 B. 44,740 C. 42,640 D. 47,080

48. Find the probability of getting at least 1

head if three coins are tossed.

A. 6/8 B. 7/8 C. 5/8 D. 4/8

49. Nicole paid P 15.00 for a box of tomatoes.

She discarded 12% of the total weight as damage and sold the remainder at P 0.25 per pound. Her profit was P 7.00. How many pounds of tomatoes did she purchase?

A. 100 B. 120 C. 130 D. 140

50. The ECE graduating class of a certain school has been questioned on which of the major board subjects they liked best and the results when tabulated are as follows:

48 liked Mathematics 62 liked Electronics Engineering 55 liked Communications Engineering 16 said they liked both Mathematics and Electronics Engineering, 20 liked both Electronics Engineering and Communications Engineering and 7 said, they liked both Mathematics and Communications Engineering. Only 3 said they liked all the three subjects. If 10 said that they like General Engineering and Applied Subject (GEAS), how many were there in the graduating class?

A. 125 B. 135 C. 145 D. 115