01. Basic Engineering Correlation (Algebra) v2

Basic Engineering Correlation (Algebra Reviewer) 1. Three transformers are directly proportional to the KVA cost P30,000. The cost of each transformer is directly proportional to the KVA rating and each has a constant of proportionally of 0.9, 0.8 and 0.6, respectively. Find the cost of the KVA transformer. a. P7,500 b. P13,500 c. P15,500 d. P9,000 2. What is the sum of the following sequence of terms 18, 25, 32, 39, . . . ,67? a. 280 b. 380 c. 320 d. 340 3. A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at 3/5 of its former rate and arrives three hour after the time; but had the accident happened 50 miles farther on yhe line, it would have arrived one and one-half hour sooner. Find the length of the journey. a. 850/9 miles b. 800/9 miles c. 920/9 miles d. 910/9 miles 4. Ten less than four times a certain number is 14. Determine the number. a. 5 b. 7 c. 4 d. 6 5. The roots of a quadratic equation are 1/3 and 1/4. What is the equation? a. 12x2 + 7x + 1=0 b. 12x2 - 7x - 1=0 c. 12x2 - 7x + 1=0 d. 12x2 + 7x - 1=0 6. The geometric mean of 4 and 64: a. 30 b. 34 c. 24 d. 16 7. A certain company manufactures two products, X and Y, and each of these products must be processed on two different machines. Product X requires 1 minute of work time per unit on machine 1 and 4 minutes of work time on machine 2. Product Y requires two minutes of work time per unit on machine 1 and 3 minutes of work time per unit on machine 2. Each day, 100 minutes are available on machine 1 and 200 minutes are available on machine 2. To satisfy certain customers, the company must produce at least 6 units per day of product X and at least 12 units of product Y. If the profit of each unit of product X is P50 and the profit of each unit of product Y is P60, how many of each product should be produced in order to maximize the company's profit? a. X = 20 units, Y = 40 units b. X = 30 units, Y = 40 units c. X = 20 units, Y = 50 units d. X = 40 units, Y = 60 units 8. If 4y3 + 18y2 + 8y - 4 is divided by 2y + 3, the remainder is: a. 10 b. 12 c. 11 d. 9 9. The square of a number increased by 16 is the same as 10 times the number. Find the number. a. 8, 2 b. 6, 2 c. 4, 2 d. 2, 2 10. The seating section in a coliseum has 30 seats in the first row, 32 in the second row, 34 seats in the third row and so on, until the tenth row is reached, after which there are ten rows each containing 50 seats. Find the total number of seats in the section.

a. 1290 b. 1080 c. 890 d. 980 11. If the roots of an equation is zero, then they are classified as a. hypergolic solutions b. trivial solutions c. conditional solutions d. extraneous solutions 12. An airplane went 360 miles in 2 hours with the wind and, flying back the same route, it took 3 3/5 hours against the wind. What was its speed in still air? a. 120 mph b. 150 mph c. 140 mph d. 130 mph 13. Find the fourth proportion to 3, 5 and 21. a. 27 b. 65 c. 56 d. 35 14. Two jet planes travelling towards each other take off at the same time from two airports located 3000 miles apart. If they passed each other after two hours, determine the speed of each plane if one plane is flying at a speed 100 mph faster than the other. a. 700 and 800 mph b. 600 and 700 mph c. 700 and 900 mph d. 800 and 500 mph 15. Round off 0.003086 to three significant figures. a. 0.0031 b. 0.00308 c. 0.003 d. 0.00309 16. It is sequence of numbers that successive terms differ by a constant. a. geometric progression b. arithmetic progression c. harmonic progression d. finite progression 17. At 2:00 pm, an airplane takes off at 340 mph on an aircraft carrier. The aircraft carrier moves due south at 25 kph in the same direction as the plane. At 4:05 pm, the communication between the plane and aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier. a. 785 miles b. 557 miles c. 412 miles d. 656 miles 18. A manufacturing firm maintains one product assembly line to produce signal generators. Weekly demand for the generators is 25 units. The line operates for 7 hours per day, 5 days per week. What is the maximum production time per unit in hours required for the line to meet the demand? a. 3 hours b. 1 hour c. 2.25 hours d. 0.75 hour 19. Ana is 5 years older than Beth. In5 years, the product of their age is 1.5 times the product of their product ages. How old is Beth now? a. 20 b. 25 c. 18 d. 27

20. A chemist of a distillery experimented on two alcohol solutions of different strengths, 30% alcohol and 60% alcohol, respectively. How many cubic meters of each strength must be used in order to produce a mixture of 50 cubic meters that contain 40% alcohol? a. 20, 30 m3 b. 33 1/3, 16 2/3 m3 c. 21 1/3, 28 2/3 m3 d. 10, 40 m3 21. Subtracting 2.6 x 103 from8.26 x 104 is: a. 8.0 x 104 b. 10.86 x 104 c. 8.0 x 103 d. 10.86 x 103 22. The time requires by an evaluator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for 10 hp motor to lift 100 lbs through 50 feet, what size of motor is required to lift 800 lbs in 40 seconds through a distance of 40 feet? a. 56 hp b. 50 hp c. 58 hp d. 48 hp

23. Find the 30th term of the arithmetic progression 4, 7, 10, . . . a. 94 b. 941 c. 81 d. 104 24. Convergent series is a sequence of decreasing numbers or when the succeeding term is _______ than the preceding term. a. equal b. slightly more c. greater d. lesser 25. In the equation x2 + x = 0, one root is x equal to: a. 1 b. ¼ c. 5 d. none of these. 26. How many liters of water must be added to 35 liters of 89% hydrochloric acid solution to reduce its strength to 75%? a. 4.83 liters b. 6.53 liters c. 7.33 liters d. 5.34 liters 27. Round off 34.2814 to four significant figures. a. 34.8214 b. 34 c. 34.28 d. 34.281 28. Solve algebraiclly: 11y2 - 3x2 = 41 4x2 + 7y2 = 32. a. (-2, 2) and (2, -2) b. (± 1, ± 2) c. (± 1, ± 4) d. (2, 3)and ( -2, -3) 29. Determine the sum of the progression if there are 7 arithmetic means between 3 and 35. a. 98 b. 304 c. 214 d. 171

30. Crew No. 1 can finish installation of an antenna tower in 200 man-hour while Crew No. 2 can finish the same job in 300 man-hour. How long will it take both crews to finish the same job, working together? a. 120 man-hour b. 140 man-hour c. 100 man-hour d. 160 man-hour 31. In how many minutes after 3:00 P.M will the minute hand of a clock coincide with the hour hand? a. 15.455 b. 17.273 c. 16.364 d. 18.182 32. In a class of 40 students, 27 students like Calculus and 25 like Geometry. How many students liked both Calculus and Geometry? a. 12 b. 13 c. 11 d. 10 33. The electric power which a transmission line can transmit is proportional to the product of its design voltage and current capacity, and inversely to the transmission distance. A 115 - kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 km. How much power, in megawatts can a 230 kilovolt line rated at 150 amperes transmit over 100 km? a. 595 b. 675 c. 485 d. 785 34. The electrical resistance of a wire varies as its length and inversely as the square of its diameter. If a 100 m long and 1.25 mm in diameter has a resistance of 30 ohms, find the length of the wire of the same material whose resistance and diameter are 25 ohms and 0.74 mm respectively. a. 25 m b. 35 m c. 30 m d. 40 m 35. What time after 3 o'clock will the hands of the clock be together for the first time? a. 3:02.30 b. 3:17.37 c. 3:16.36 d. 3:14.32 36. A pump can pump out water from a tank in 11 hours. Another pump can pump out water from the same tank in 20 hours. How long will it take both pumps to pump out water in the tank? a. 6 hours b. 6 1/2 hours c. 7 1/2 hours d. 7 hours 37. If the sum is 220 and the first term is 10, find the common difference if the last term is 30. a. 3 b. 4 c. 5 d. 2 38. Equal volumes of two different liquids evaporated at different but constant rates. If the first is totally evaporated in 6 weeks and the second in 5 weeks, when will the second be one-half the volume of the first? a. 3.5 weeks b. 3 weeks c. 4 weeks d. 4 2/7 weeks 39. MCMXCIV is a Roman numeral equivalent to: a. 1994 b. 2174 c. 3974 d. 2974

40. Find the 100th term of the sequence 1.01, 1.00, 0.99, . . a. 0.01 b. 0.02 c. 0.03 d. 0.04 41. At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of 120o? a. 12:21.818 b. 12:22.818 c. 12:18.818 d. 12:24.818 42. Solve the simultaneous equations: 3x - y = 6 9x - y = 12. a. ( -1, 3 ) b. ( 1, -3 ) c. ( 1, 3 ) d. ( -1, -3 ) 43. A merchant has three items on sale: namely, a radio for P50, a clock fo P30, and a flashlight for P1. At the end of the day, she has sold a total of 100 of the three items and has taken exacly P1000 on the total sales. How many radios did he sale? a. 4 b. 80 c. 20 d. 16 44. What is the sum of the first 10 terms of the geometric progression 2, 4, 8, 16, . . . ? a. 1696 b. 2046 c. 1024 d. 1846 45. In a commercial survey involving 1000 persons on brand preferences, 120 were found to prefer brand x only, 200 persons prefer brand y only, 150 persons prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 370 prefer either brand z or x but not y, and none prefer all the three brands at a time. How many persons have no brand preference with any of the three brands? a. 200 b. 100 c. 280 d. 70 46. Which number has four significant figures? a. 1.414 b. 0.0014 c. 0.141 d. 0.01414 47. A club of 40 executives, 33 likes to smoke Marlboro and 20 likes to smoke Philip Morris. How many like both? a. 12 b. 13 c. 14 d. 11 48. The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed, what is the arithmetic mean of the remaining numbers? a. 41.25 b. 42.31 c. 44.25 d. 40.21 49. There are 9 arithmetic means between 11 and 51. The sum of the progreesion is: a. 374 b. 341 c. 320 d. 337

50. If a two digit number has X for its unit digit and Y for its tenth digit, represent the number. a. 10Y + X b. X + Y c. XY d. 10Y + Y 51. In the series 1, 1, 1/2, 1/6, 1/24, . . . , determine the 6th term. a. 1/60 b. 1/120 c. 1/150 d. 1/90 52. Round off 149.691 to the nearest integer. a. 149 b. 149.7 c. 149.69 d. 150 53. The sum of two numbers is 21, and one number twice the other. Find the numbers. a. 9 & 12 b. 7 & 14 c. 8 & 13 d. 65 & 70 54. The probability for the ECE board examinees from a certain school to pass the Mathematics subject is 3/7 and that for the Communication subject is 5/7. If none of the examinees failed in both subjects, how many examinees from the school took the examination? a. 30 b. 27 c. 29 d. 28 55. Solve for x that satisfies the equation 6x2 - 7x - 5 = 0. a. 3/5 or ¾ b. 3/2 or 3/8 c. 5/3 or -1/2 d. 7/5 or -7/15 56. Three transformers are rated 5 KVA, 10 KVA and 25 KVA, respectively. The total cost of the three transformers is P15, 000.00. If the cost of each transformer is proportional to its KVA rating multiplied by the factor 1, 0.8 and 0.6 respectively, find the cost of the 10 KVA transformer. a. P4,286 b. P4,075 c. P4,101 d. P4,393 57. Solve the simultaneous equations: 2x2 - 3y2 = 6 3x2 + 2y2 = 35. a. x-3 or 3; y2 or -1 b. x3 or -3; y2 or -2 c. x3 or -3; y-2 or 1 d. x3 or -3; y-2 or 3 58. The sum of the progression 5, 8, 11, 14, . . . Is 1025. How many terms are there? a. 25 b. 24 c. 28 d. 29 59. If x varies directly as y and inversely as z, and x = 14 when y = 7 and z = 2, find the value of x when y = 16 and z = 4. a. 4 b. 8 c. 16 d. 14

60. The arithmetic means of 6 numbers is 17. If two numbers are added to the progression, the new set of the numbers will have an arithmetic mean of 19. What are the two numbers if their difference is 4? a. 18, 22 b. 23, 27 c. 10, 14 d. 31, 35 61. The sum of Kim's and Kevin's ages is 18. In 3 years, Kim will be twice as old as Kevin. What are their ages now? a. 5, 13 b. 7, 11 c. 6, 12 d. 4, 14 62. The intensity of sound varies directly as the strength of the source and inversely as the square of the distance from the source. Write the equation to the describe relation. a. I = 1/d2 + k b. I=k/d2 c. I = kd2 d. I = d2/k 63. Determine the sum of the infinite series 1/3 + 1/9 + 1/27 +. . . a. 1 b. ¾ c. ½ d. 2/3 64. For a particular experiment, you need 5 liters of 10% solution. You find 7% and 12% solutions on the shelf. How much of the 7% solution you mix with the appropriate amount of the 12% solution to get 5 liters of 10% solution? a. 2.5 b. 2 c. 1.5 d. 3 65. Find the sum of the roots of 5x2 - 10x + 2 = 0 a. -2 b. ½ c. -1/2 d. 2 66. Maria is 36 years old. Maria was twice as old as Anna was when Maria was as old as Anna is now. Jow old is Anna now? a. 26 b. 31 c. 29 d. 24 67. Find the ratio of an infinite geometric progression if the sum is 2 and the first term is 1/2. a. 2/3 b. 1/6 c. ¾ d. ¼ 68. A tank is fitted with two pipes. The first pipe can fill the tank in 10 hours. But after it has been open 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 tha tank? a. 12.67 hr b. 10.55 hr c. 14.89 hr d. 13.33 hr

69. How many kg of cream containing 25% butter fat should be added to 50 kg of milk containing one percent butter fat to produce milk containing 2% butter fat? a. 4.17 b. 2.174 c. 5.221 d. 3.318

70. The electrical resistance offered by an electric wire varies directly as the length and inversely as the square of the diameter of the wire. Compare the electrical resistance offered by two pieces of wire of the same material, one being 100 m long and 8 mm in diameter, and the other 50 m long and 3 mm in diameter. a. R1 = 0.28 R2 b. R1 = 0.84 R2 c. R1 = 0.57 R2 d. R1 = 0.95 R2 71. A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there all together? a. 458 b. 639 c. 724 d. 538 72. A 100 g of water are mixed with 150 g of alcohol (p = 790 kg/cu.m.). What is the specific volume of the resulting mixtures? Assuming that the two fluids mix completely. a. 0.63 cu cm/g b. 0.88 cu. cm/g c. 0.82 cu cm/g d. 1.20 cu cm/g 73. One number is 5 less than another. If the sum is 135, what are the numbers? a. 65, 70 b. 60, 65 c. 75, 80 d. 70, 75 74. The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction. a. 8/5 b. 13/5 c. 5/13 d. 3/5 75. An inexperienced statistical clerk submitted the following statistics to his manager on the average rate of production of transistorized radios in an assenbly line: "1.5 workers produced 3 radios in 2 hour." How many workers are employed in the assembly line working 40 hours per week if weekly production is 480 radios? a. 12 b. 10 c. 13 d. 14 76. Find the mean proportion of 4 and 36. a. 12 b. 8 c. 16 d. 9 77. An automobile is travelling at a velocity of 10 mph. If the automobile mileage meter already reads 20 miles, find the mileage meter reading after 3 hours. a. 60 miles b. 30 miles c. 50 miles d. 40 miles 78. Find the sum of 1, -1/5, 1/25, . . . a. 6/7 b. 7/8 c. 5/6 d. 8/9 79. A man is 41 years old and his son is 9. In how many years will the father be three times as old as his son? a. 7 b. 8 c. 6

d. 5 80. A tank is fitted with an intake pipe that will fill it in 4 hours, and an outlet pipe that will empty it in 9 hours. If both pipes are left open, how long will it take to fill the empty tank? a. 7.2 hr b. 6.8 hr c. 6.2 hr d. 7.4 hr 81. Find the 1987th digit in the decimal equivalent to 1785/9999 starting from the decimal point. a. 1 b. 5 c. 7 d. 8 82. A mechanical engineer who was awarded a P450,000.00 contract to install the machineries of an oil mill failed to finish the work on time. As provided for in the contract, he has to pay a daily penalty equivalent to one-fourth of one percent of the contract price for the first ten days of the delay, one-half percent per day for the next ten days and one percent per day for every day thereafter. If the total penalty paid was P60,750.00, how many days was the completion of the contract delayed? a. 30 days b. 26 days c. 24 days d. 28 days 83. A man started driving his car at a certain time froma certain place. On arrival 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 mph slower, I would have been 6 minutes late." Find how far he had driven. a. 20 miles b. 10 miles c. 25 miles d. 15 miles 84. Pedro started running at a speed of 10kph. Five minutes later, Mario started running in the same direction and catches up with Pedro in 20 minutes. What is the speed of Mario? a. 12.5 kph b. 17.5 kph c. 20.5 kph d. 15.0 kph 85. The equation whose roots are the reciprocal of the solutions of 2x2 - 3x - 5 = 0. a. 3x2 - 5x - 2=0 b. 5x2 - 2x - 3=0 c. 5x2 + 3x - 2=0 d. 2x2 + 5x - 3=0 86. In certain Board Examination, 119 examinees too the Shop Machinery subjected, 104 examinees took thye Power Plant Machinery subject and 115 examinees took the Industrial Plant Machinery subject. Seventy-eight (78) conditioned examinees took only Shop Machinery and Power Machinery subjects. Seventy-one (71) conditioned examinees took only the POwer Plant Machinery and Industrial Plant Machinery subjects. Eighty-five (85) conditioned examinees took only Industrial Plant Machinery and Shop Machinery subjects. Fifty-four took all the three subjects. How many examinees took the Certified Plant Mechanic board examination? a. 153 b. 165 c. 158 d. 176 87. If a train passes as many telegraph poles in one minute as it goes miles per hour, how far apart are the poles? a. 78 ft. b. 98 ft. c. 68 ft. d. 88 ft. 88. A man 38 years old has a son of ten years old. In how many years will the father be three times as old as his son? a. 2 b. 3 c. 4 d. 5

89. In Algebra, the operation of root extraction is called as _____. a. revolution b. resolution c. involution d. evolution 90. Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Pedro to paint the same fence if he had to work alone? a. 15 b. 13 c. 10 d. 11 91. There are 9 arithmetic means between 11 and 51. The sum of the progression is: a. 374 b. 341 c. 320 d. 337 92. The number 1.123123123. . . Is a. surd b. transcendental c. rational d. irrational 93. Which of the following numbers should be changed to make all the numbers from an arithmetic progression when properly arranged? a. 27/14 b. 45/28 c. 20/14 d. 3/28 94. How many significant digits do 10.097 have? a. 4 b. 5 c. 2 d. 3 95. Find the sum of the infinite geometric progression 6, -2, 2/3, . . . a. 9/2 b. 7/2 c. 3/2 d. 11/2 96. The time required for two examinees to solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long will it take for the slower problem solver to solve the problem? a. 3 minutes b. 5 minutes c. 2 minutes d. 4 minutes 97. An equipment installation job in the completion stage can be completed in 50 days of 8 hours day work, with 50 men working. With the contract expiring in 40 days, the mechanical engineer contractor decided to add 15 men on the job, overtime not being permitted. If the liquidated damages is P5,000 per day of delay, and they are paid P150 per day, will the engineer be able to complete the job on time? Would he save money with the addition of workers? a. No, P20,500 losses b. Yes, P44,750 savings c. Yes, P24,500 savings d. No, P15,750 losses 98. An airplane flying with the wind, took 2 hours to travel 1000 km and 2.5 hours in flying back. What was the wind velocity in kph? a. 40 b. 70 c. 60 d. 50

99. If a = b, then b = a. This illustrates which axiom in Algebra? a. Transitive Axiom b. Reflexive Axiom c. Symmetric Axiom d. Replacement Axiom 100. The ten's digit of a certain two digit number exceeds the unit's digit by four and is one less than twice the unit's digit. Find the number. a. 59 b. 95 c. 65 d. 85 101. One pipe can fill a tank in 6 hours and another pipe can fill the same in tank in 3 hours. A drain pipe can empty the tank in 24 hours. With all three pipes open, how lomg will it take to fill in the tank? a. 2.18 hrs b. 2.23 hrs c. 2.81 hrs d. 2.32 hrs 102. An equipment installation job in the completion stage can be completed in 40 days of 8 hours day work with 40 men working. With the contract expiring in 30 days, the mechanical engineer contractor decided to add 10 men on the job, overtime not being permitted. If the liquidated damages is P2,000 per day of delay, and the men are paid P80 per day, will the engineer be able to complete the job on time? a. No, there would be no savings b. No, P16,000 would be lost c. Yes, there would just be break even d. Yes, P16,000 would be saved 103. It takes Butch twice as it takes Dan to do a certain piece of work. Working together they can do the work in 6 days. How long would it take Dan to do it alone? a. 12 days b. 9 days c. 10 days d. 11 days 104. Robert is 15 years older than his brother Stan. However, "y" years ago, Robert was twice as old as Stan. If Stan is now "b" years old b.y, find the value of (b-y). a. 18 b. 17 c. 15 d. 16 105. Mike, Loui and Joy can mow the lawn in 4, 6 and 7 hours, respectively. What fraction of the yard can they mow in 1 hour if they work together? a. 47/84 hr b. 84/47 hr c. 34/60 hr d. 45/84 hr 106. The volume of hemisphere varies directly as the cube of its radius. The volume of a sphere with 2.54 cm radius is 20.75 cm3. What is the volume of a sphere with 3.25 cm radius of the same kind? a. 4056 cm3 b. 45.98 cm3 c. 43.47 cm3 d. 39.20 cm3 107. Add the following and express in meters: 3 m + 2 cm + 70 mm. a. 3.14 m b. 2.90 m c. 3.12 m d. 3.09 m 108. From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describe an arc of: a. 90o b. 60o c. 540o d. 180o

109. A clock has dial face 304.80 mm in radius. The minute hand is 228.60 mm long while the hour hand is 152.40 mm long. The plane of rotation of the minute hand is 50.80 mm above the plane of rotation of the hour hand. Find the distance between the tips of the hands of the clock at 5:40 AM. a. 228 mm b. 239 mm c. 243 mm d. 233 mm 110. A certain manufactured part can be defective because it has one or more out of the three possible defects: insufficient tensile strength, a burr, or a diameter outside of tolerance limit. In a lot of 500 pieces: 19 have a tensile strength defects, 17 have a burr, 11 have an unacceptable diameter, 12 have tensile strength and burr defects, 7 have tensile strength and diameter defects, 5 have burr and diameter defects and 2 have all three defects. Determine: How many of the pieces have no defects? How many pieces have only burr defects? How many pieces have exactly 2 defects? a. 475, 2, 18 b. 490, 4, 10 c. 465, 3, 7 d. 480, 4, 6 111. Mary is 24 years old. Mary is twice as old as Ana waswhen Mary was as old as Ana is now. How old is Ana? a. 18 b. 16 c. 20 d. 19 112. The electrical resistance of wire made of a certain material varies as its length and inversely as the square of the diameter. If the wire 200 meters long and 1.25 mm in diameter has a resistance of 60 ohms, find the length of the wire of the same material, whose resistance and diameter are 5 ohms and 0.65 mm, respectively. a. 3.96 m b. 4.51 m c. 4.28 m d. 5.72 m 113. A man leaving his office on one afternoon noticed the clock at past two o'clock. Between two three hours, he returned to his office noticing the hands of the clock interchanged. At what time did he leave the office and the time that he returned to the office? a. 2:27.08, 5:11.19 P.M. b. 2:26.01, 5:10.01 P.M c. 2:26.01, 5:10.01 P.M. d. 2:26.01, 5:12.17 P.M. 114. A medium unshaded lamp hangs 8 m directly above the table. To what distance should it be lowered to increase the illumination to 4.45 times the former value? Illumination intensity varies inversely to the square of the distance. a. 4.75 m b. 4.55 m c. 3.79 m d. 3.95 m 115. Roberto is 25 years younger than his father. However, his father will be twice his age in 10 years. Find their ages now. a. 15 and 40 b. 10 and 35 c. None of the choices d. 20 and 45 116. A storage battery discharges at a rate which is proportional to the charge. If the charge is reduced by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge? a. 6 b. 4 c. 3 d. 5 117. Prior to the last IBP elections, a survey was conducted in a certain barangay in Metro Manila to find out which of three political parties they like best. The results indicated that 320 like KBL, 250 like LABAN and 180 liked INDEPENDENTS. But of these, 160 like both KBL and LABAN, 100 liked both LABAN and INDEPENDENTS and 70 like both KBL and INDEPENDENTS. Only 30 said they like all the three parties and none admitted that they did not like any party. How many voters are there in the barangay?

a. 474 b. 525 c. 450 d. 540 118. A man left his home at past 3:00 o'clock P.M as indicated in his wall clock. Between 2 and 3 hours after, he returned home and noticed the hands of the lock interchanged. At what time the man leave his home? a. 3:24.73 P.M b. 3:18.52 P.M c. 3:31.47 P.M d. 3:28.65 P.M 119. Given: f(x) = ( x+ 3) (x - 4) +4. When f(x) is divided by (x - k), the remainder is k. Find k. a. 2 b. 6 c. 4 d. 8 120. A & B working together can finish painting the house in six days. A working alone, can finish it in five days less than B. How long will it take each of them to finish the work alone? a. 15 days for A 20 days for B b. 10 days for A 25 days for B c. 15 days for A 20 days for B d. 10 days for A 15 days for B 121. A statistical clerk submitted the following reports: "The average rate of production of radios is 1.5 units for every 1.5 hours of work by 1.5 workers." How many radios were produced in one month by 30 men working 200 hours during the month? a. 4000 b. 3500 c. 4500 d. 5000 122. A piece of paper is 0.05 in thick. Each time the paper is folded into half, the thickness is doubled. If the paper was folded 12 times, how thick in feet the folded paper will be? a. 15.2 b. 16.25 c. 17.06 d. 18.5 123. A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total number of days it took them to finish the job. a. 22.36 days b. 20.56 days c. 23.22 days d. 21.42 days 124. Six times the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digits, the answer is 51 and the remainder is 11. If the digits are reversed the number becomes smaller by 198, find the number. a. 825 b. 775 c. 725 d. 875 125. Given that "w" varies directly as the product of x and y and inversely as the square of z and that w = 4 when x = 2, y = 6 and z = 3. Find tha value of "w" when x = 1, y = 4 and z = 2. a. 5 b. 4 c. 3 d. 2 126. A man driving his car at a certain speed from his house will reach his office in 6 hours. If he increased his speed 15 mph, he would reach his office 1 hour earlier. Find the distance from his office to his house.

a. 350 miles b. 450 miles c. 520 miles d. 250 miles 127. Determine x, so that x, 2x + 7, 10x - 7 will be a geometric progression. a. 7, -15/6 b. 7, -7/5 c. 7, -5/6 d. 7, -7/6 128. Solve for the values of x and y in 4x + 2y = 5 and 13x - 3y = 2. a. (1, 3) b. (3/2, 1/2) c. (1, 2) d. ( 1/2, 3/2 ) 129. Determine the k so that the equation 4x2 + kx + 1 = 0 will have just one real root. a. 5 b. 6 c. 4 d. 3 130. An airplane travels from points A and B with the distance of 1500 km and a wind along its flight line. If it takes the airplane 2 hours from A to B with the tailwind and 2.5 hours from B to A with the headwind, what is the velocity? a. 700 kph b. 675 kph c. 450 kph d. 750 kph 131. How many numbers between 10 and 200 are exactly divisible by 7? Find their sum. a. 2835 b. 2840 c. 283 d. 2830 e. 27 numbers; sum f. 28 numbers; sum g. 26 numbers; sum h. 26 numbers; sum 132. A gasoline tank of a car contains 50 liters of gasoline and alcohol, the alcohol comprising 25%. How much of the mixture must be drawn off and replaced by alcohol so that the tank will contain a mixture of which 50% is alcohol? a. 10.67 liters b. 20.33 liters c. 16.67 liters d. 16.33 liters 133. In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? a. 16 b. 14 c. 10 d. 12 134. Two thousand (2000) kg of steel containing 8% nickel is to be made by mixing a steel containing 14% nickel with anothercontaining 6% nickel. How much of each is needed? a. 800 kg, 1200 kg b. 500 kg, 1500 kg c. 600 kg, 1500 kg d. 400 kg, 1600 kg

135. A boat man rows to a place 4.8 miles with the stream and black in 14 hours, but that he can row 14 miles with the stream in the same time as 3 miles against the stream. Find the rate of the stream. a. 1 mile per hour b. 0.6 mile per hour c. 0.8 mile per hour d. 1.5 mile per hour 136. Gravity causes a body to fall 16.1 ft in the first second, 48.3 ft in the 2nd second, 80.5 ft in the 3rd second. How far did the body fall during the 10th second. a. 250.1 ft b. 305.9 ft c. 529.45 ft d. 417.3 ft 137. Solve for x : 10x2 + 10 x2 + 1 = 0. a. -0.331, 0.788 b. -0.311, -0.887 c. -0.113, -0.788 d. -0.113, -0.887 138. An airplane travels from points A and B with a distance of 1500 km and a wind along its flight line. If it takes the airplane 2 hours from A and B with the tailwind and 2.5 hours from B to A with the headwind, What is the velocity? a. 700 kph b. 675 kph c. 750 kph d. 450 kph 139. A jogger starts a course at a steady rate of 8 kph. Five minutes later, a second jogger starts the same course at 10 kph. How long will it take the second jogger to catch the first? a. 22 min b. 18 min c. 21 min d. 20 min 140. A rubber ball is made to fall from a height of 50 ft. and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner? a. 300 b. 200 c. 350 d. 250 141. The resistance of the wire varies directly with its length and inversely with its area. If a certain piece of wire 10 m long and 0.10 cm in diameter has a resistance of 100 ohms, what will its resistance be if it is uniformly stretched so that its length becomes 12 m? a. 144 b. 80 c. 120 d. 90 142. Ten liters of 25% salt solution and 25 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10% salt solution. What is the percent concentration of salt in the mixture? a. 0.1955 b. 0.2572 c. 0.2215 d. 0.2705 143. A & B can do the job in 42 days, B & C for the same job in 31 days, C & A also for the same job in 20 days. If A & C work together, how many days can they do the same job? a. 19 b. 17 c. 21 d. 15 144. A pipe can fill a tank in 14 hours. A second pipe can fill the tank in 16 hours. If both pipes are left open, determine the time required to fill the tank? a. 7.92 hr b. 8.47 hr

c. 7.47 hr d. 6.53 hr

145. A man rows downstream at the rate of 5mph and upstream at the rate of 2mph. How far downstream should he go if he is to return in 7/4 hours after leaving? a. 2.5 miles b. 3.3 miles c. 2.7 mlies d. 3.1 miles 146. Solve for the value of x. 2x - y + z = 6 x - 3y - 2z = 13 2x - 3y - 3z = 16 a. 3 b. 1 c. 2 d. 4 147. Find the value of w in the following equations: 3x - 2y + w = 11 x + 5y - 2w = -9 2x + y - 3w = -6. a. 4 b. 2 c. 3 d. -2 148. A boat travels downstream 2/3 of the time as it goes going upstream. If the velocity of the river's current is 8 kph, determine the velocity of the boat in still water. a. 70 kph b. 60 kph c. 30 kph d. 40 kph 149. A survey of 100 persons revealed that 72 of them had eaten at restaurant P and that 52 of them had eaten at restaurant Q. Which of the following could not be the number of persons in the surveyed group who had eaten at both P and Q? a. 23 b. 22 c. 24 d. 25