ALGEBRA

1. An earthquake is usually measured by the magnitude M on 12. Peter and Billy can jog around a circular park in 8 and 12
the Richter scale. The intensity I of an earthquake and the minutes, respectively. If they start at the same instant from
magnitude M are related by the formula: M= log I/Io, where Io the same place, in how many minutes will they pass each
is the intensity of an arbitrary chosen earthquake. The other if they jog around the track in the same direction?
earthquake that hit Kobe, Japan measured 5.7 on the A. 24 min. B. 20 min. C. 15 min. D. 25 min.
Richter scale. The earthquake that hit Baguio, Philippines
measures 7.8. How many times stronger is the earthquake 13. Eight men can excavate15 cu.m. of drainage open canal in
that hit Baguio? 7 hours. Three men can backfill 10 cu.m. in 4 hours. How
A. 148 B. 126 C. 137 D. 37 long will it take 10 men to excavate and backfill 20 cu.m. in
the same project?
2. In a potato race, 8 potatoes are placed 6 feet apart on a A. 11.87hrs B. 10.25hrs C. 9.87hrs D.
straight line, the first being 6 ft from the basket. A contestant 12.87hrs
starts from the basket and puts one potato at a time into the
basket. Find the total distance he must run in order to finish 14. Find the coefficient of the 8th term of the expansion of (2x-
the race. 1/x)10.
A. 532 ft. B. 432 ft C. 342 ft D. 222 ft A. 960 B. 785 C. 890 D. 920

3. Find the value of x if the 8 th term of the expansion of 15. Find the geometric mean between -2 and -8.

(x )
3
12 A. 4 B. 16 C. -4 D. 6
+1
is equal to 25952256.
16. Which of the following is the factor of 2x4+11x2y2-6y4 .
A. 2 B. 4 C. 3 D. 5
A. x2-2y2 B. x2+6y2 C. 2x2+y2 D. 2x2-2y2
4. Two workers A and B together can complete a job in 7 days.
A works twice as fast as B. How many days would it take B 17. Which of the following is a factor of x4-4x3-7x2+22x+24.
A. (x-3) B. (x-2) C. (x-1) D. (x+3)
to do the job working alone?
A. 10.5days B. 21days C. 9 days D. 18 days
18. Find the sum of the numbers divisible by 6 which lie
5. What is the 5th term of the expansion of (ex+e-x)8 ? between 75 and 190.
A. 2508 B. 2580 C. 2058 D. 2850
A. 74 B. 70 C. 65 D. 75
19. Arcadio Corporation’s gross margin is 45% of sales.
6. Find the sum of the first 100 positive integers exactly
divisible by 7. Operating expenses such as sales and administration are
15% of sales. Arcadio is in 40% tax bracket. What percent of
A. 35,350 B. 2,053 C. 53,350 D. 25,536
sales is their profit after taxes?
A. 15% B. 30% C. 18% D. 20%
7. Spheres of equal size are piled in the form of a complete
pyramid with a rectangular base, find the total number of
20. The volume of a hemisphere varies directly as the cube of
spheres in the pile if the number of spheres in the long side
is 5 and that of the short side is 4 until the top layer consists its radius. The volume of the hemisphere with 2.54cm,
radius is 20.75 cm3. What is the volume of a sphere with
of a single row of 2 spheres.
A. 30 B. 40 C. 20 D. 10 3.25cm. radius of the same kind of material?
A. 43.46 B. 57.64 C. 86.92 D. 76.95
8. The speed of the plane is 120 mi/hr in a calm. With the wind
21. The vibration frequency of a string varies as the square root
it can cover a certain distance in 4 hours, but against the
wind it can cover only 3/5 of that distance in the same time. of the tension and inversely as the product of the length and
diameter. Of the testing. If the testing is 3ft long and 0.03
Find the velocity of the wind.
A. 10 mi/hr B. 30 mi/hr C. 20 mi/hr D. 40 inch diameter vibrates at 720 times per second under 90
pounds tension, at what frequency will a 2ft, 0.025 inch
mi/hr
string vibrate under 50 pounds tension.
A. 966 B. 6210 C. 530 D. 855
9. If 1 and -2 are rational roots of the equation
x 4 + x3 + 4x 2 + 6x - 12 = 0. what is the second depressed 22. A lady started a chain letter by writing to four friends and
equation? requesting each to copy the letter and send it to four other
A. x2+6 B. x2-6 C. x2+2 D. x2-2 friends. If the chain was unbroken until the 5 th set of letters
was mailed, how much was spent for postage at P8.00 per
10. A carpenter and his helper together can repair a house in 10 letter?
days. It takes the helper 5 days longer than the carpenter to A. 12,219 C. 21,435
do the repair when each works alone. How many days B. 10,912 D. 11,291
would it take the helper to do the repair if he is to work
alone? 23. A stack of bricks has 61 bricks at the bottom layer, 58 bricks
A. 22.8 days B. 7.2 days C. 17.8 days D. 12.2 days in the 2nd layer, 55 bricks in the 3rd layer and so on, until the
last layer which has 10 bricks. Determine the total number
11. 16 men has a contract to finish the job in 20 days. 20 men of bricks used up.
were hired at the start and four quit the job after 8 days. A. 639 B. 369 C. 539 D. 339
Determine the number of days delayed or ahead of the
scheduled time when they were able to finish the job. 24. A machine costs P50,000.00 and depreciates 20% of the
A. 3 days ahead C. 2 days ahead original cost during the first year, 16% during the second
B. 3 days delayed D. 2 days delayed year, 12% during the third year, and so on, for 5 years. What
is the value at the end of 5 years?
 A. 15,000 C. 30,000 38. Ronnie was four times as old as Randy ten years ago. If he
B. 25,000 D. 20,000 is now twice as old as Randy, how old is Ronnie?
25. If the 5th term in A.P. is 17 and the 3rd term is 10, what is A. 15 B. 20 C. 30 D. 25
the 8th term? 39. The sum of the three numbers in AP is 33, if the sum of their
A. 23.5 B. 27.5 C. 25.5 D. 26.5 squares is 461, find the numbers
A. 4, 11, 18 C. 4, 16, 20
26. z varies directly as x and inversely as y 2. If x = 1 and y = 2, B. 8, 12, 20 D. 8, 12, 18
then z = 2. Find z when x = 3 and y = 4.
A. 1.5 B. 3 C. 2.5 D. 3.5 40. Find the value of x which will satisfy the equation
x -2 x =1.
27. A man who is on diet losses 24 lb. in 3 months, 16lb. in the
A. 1 B. 1,4 C. 4 D. 0,4
next 3 months and so on for a long time. What is the
maximum total weight loss? 41. Find the total distance traveled by the tip of a pendulum if
A. 76 B. 75 C. 72 D. 80 the distance of the first swing is 6 cm. and the distance of
each succeeding swing is 0.98 of the distance of the
28. A group consists of n engineers and n nurses. If two of the previous swing.
engineers are replaced by two other nurses, then 51% of A. 300 B. 200 C. 400 D. 500
the group members will be nurses. Find the value of n.
A. 80 B. 110 C. 55 D. 100 42. Find the equation whose roots are numerically equal but
opposite in sign to the roots of the equation
29. If one root of 9x^2-6x+k=0 exceeds the other by 2, find the x3+7x2+11x+5=0.
value of k. A. x3-7x2+11x-5=0 C. x3+7x2+11x-5=0
A. 8 B. 5 C. -8 D. -6 B. x3+7x2-11x+5=0 D. x3-7x2-11x+5=0
30. Compute the lower bound of the real roots of the polynomial 43. It takes a boat 3 times to travel upstream against a river
equation x3+3x2-5x-6=0. current that it takes the same boat to travel downstream. If
A. -5 B. -4 C. -6 D. -3 the speed of the boat is 40 kph, what is the speed of the
current?
31. A man has P100,000, part of which he invested at 12% A. 24 mph B. 20 mph C. 30 mph D. 18 mph
interest and the rest at 18%. He received a total annual
interest of P15,300. How much did he invest at 18% interest
44. If 3 log x - log y = 0 , express y in terms of x.
rate?
y = x3 B. y = x C. y = x D. y = 3x
2
A. 45,000 C. 55,000
A.
B. 60,000 D. 75,000
45. An Electronics engineering student got a score of 30% on
32. The motion of a particle through a certain medium is such Test I of the five number test in Mathematics. On the last
that it moves two thirds as far each second as in the number he got 90% in which constant difference more on
preceding second. If it moves 6m of the first second, how far each number than he had on the immediately preceding
will it move before coming to rest. one. What was his average score in Mathematics?
A. 20 B. 23 C. 18 D. 12 A. 60 B. 70 C. 80 D. 75
33. The sum of a geometric series is as follows:
S = 1.0 + 1.1 + 1.21 + 1.331 + ...up to the 50th term , 46. If x : y : z = 4 : -3 : 2 and 2x + 4y - 3z = 20 , find x,y,z.
A. 4, -5, 2 B. -8, 6, -4 C. 5, -6, 8 D. 2, -7, 4
A. 1163.91 C. 1180.73
B. 1276.56 D. 1422.34 47. Two racing cars Mazda and Toyota compete for a stretched
of 10000m long. It took 40 min. for Mazda to reach the finish
34. If you owned a sari-sari store in Kuwait, at what price will line. How far was Toyota behind when Mazda reach the
you mark a small camera for sale the cost P600 in order that finish line?
you may offer 20% discount on the marked price and still A. 2400m C. 2000m
makes a profit of 25 % on the selling price? B. 1900m D. 2600m
A. 1000 B. 2000 C. 1200 D. 1500
48. How many terms of the progression 4, 7, 10, 13, . . . must
35. Given two numbers such that the difference of twice the first be taken so that the sum will be 69.
and the second number is 12. If the sum of the first and the A. 6 B. 9 C. 8 D. 12
second number is 36, find the number.
A. 12, 20 B. 14, 28 C. 12, 24 D. 16, 20 49. A golf ball is dropped from a height of 6 meters. On each
rebound it rises 2/3 of the height from which it last fell. What
36. The time required for two examinees to solve the same distance has it traveled at the instant it strikes the ground for
problems differs by two minutes. Together they can solve 32 the 7th time?
problems in one hour. How long will it take for the slower A. 27.89 m C. 20.87 m
problem solver to solve the problem? B. 19.86 m D. 24.27 m
A. 5min B. 6min C. 4min D. 3min
50. The velocity of an airplane in still air is 125 kph. The velocity
37. There are 4 geometric mean between 3 and 729, Find the of the wind due east is 25 kph. If the plane travels east and
sum of the G.P. returns back to its base again in 4 hours, at what distance
A. 1304 B. 1092 C. 2324 D. 1102 does the plane travel due east?
A. 240 km. C. 320 km.
 B. 180 km D. 200 km
63. A pipe can fill up a tank with the drain open in three hours. If
51. What time after 2 o’clock will the hands of the clock extend the pipe runs with the drain open for one hour and then the
in opposite directions for the first time? drain is closed, it will take 45 more minutes for the pipe to fill
A. 2:43.64 B. 2:43.46 C. 2:34.64 D. 2:34.46 the tank, if the drain will be closed at the start of filling, how
52. A battleship started at 7:00AM on a 500 mile voyage on a long will it take the pipe to fill the tank?
special mission but was brought to a full stop an hour after A. 1.15 hrs B. 1.125 hrs C. 1.325 hrs D. 1.525
starting for military reasons, delaying it for a full hour, after hrs
which it was ordered to proceed at a reduced velocity
equivalent to 75% of its original speed. The ship arrived at 64. A man left his home at past 3:00 PM as indicated in his wall
its destination 3¾hr. after scheduled time. Determine the clock. Between two to three hours after, he returned home
original speed of the battleship. and noticed that the hands of the clock interchanged. At
A. 54.05mph C. 64.15mph what time did he left his home?
B. 50.05mph D. 54.15mph A. 3:27.27 B. 3:31.47 C. 3:22.22 D. 3:44.44
53. If the 3rd term of a G.P. is 20, and the 6th term is 160, what is 65. Two numbers differ by 40 and their arithmetic mean exceeds
the first term? their geometric mean by 2. What are these numbers?
A. 4 B. 5 C. 6 D. 2 A. 75 & 115 B. 45 & 85 C. 81 & 121 D. 88
&128
54. The second hand of a clock is 4 inches long. Find the speed
of the tip of the second hand. 66. This states that every integral rational equation has at least
A. 0.32 in/sec C. 0.37 in/sec one root.
B. 0.22 in/sec D. 0.42 in/sec A. Fundamental Theorem of Arithmetic
B. Fundamental Theorem of Counting
55. Missy goes to a bake shop to buy some pastries for resale C. Fundamental Theorem of Algebra
at Book Latte. She spends half her money for Revel Bars, D. Fundamental Theorem of Equations
and one-third of what remains for Triple Chocolate
Brownies. She spends 150 for other pastries and still has 67. The logarithm of the reciprocal of a number is called _____.
200 left from the amount she originally had. How much A. Inverse Logarithm C. Index
money did she have at the start? B. Cologarithm D. Briggsian Logarithm
A. 1050 B. 5100 C. 1500 D. 1250
68. What is the sum of roots of the equation
56. How many liters of a 25% acid solution must be added to 80 ((x – sqrt 2)^2) (x + sqrt 3)(x – sqrt 5) = 0
liters of a 40% acid solution to have a solution that is 30% A. 1.9 B. 3.3 C. 2.2 D. 6.8
acid?
A. 160 L B. 90 L C. 100 L D. 120 L 69. If a1=3 and an = n + an-1, the sum of the first five term is:
A. 30 B. 17 C. 45 D. 42
57. Which of the following is a prime number?
A. 437 B. 483 C. 417 D. 487 70. A radiator contains 5 quarts of 30% antifreeze mixture. How
much of this mixture must be drained and replaced with
58. Your father told you “I was your age now when you were pure antifreeze to obtain an 80% antifreeze mixture?
born”. If you are 21 years old today, how old is your father? A. 25/7 B. 27/7 C. 31/7 D. 29/7
A. 50 B. 42 C. 48 D. 44
71. At one time, Value Rent-A-Car rented compact cars at a
59. Two boys A and B went out hunting and brought home 22 daily rate of P43.95 plus 40 cents per mile. Thrifty Rent-A-
birds. A averages 4 shots per bird at which rate he would Car rented compact cars at a daily rate of P42.95 plus 42
have killed 3 more birds than he did if he had fired as many cents per mile. For what mileage are the costs the same?
times as B. The product of the number shots fired by each A. 50 mi B. 70 mi C. 90 mi D. 110 mi
exceeds the product of the number of birds killed by each by
2760. Determine the number of birds killed by A. 72. Seats for Room 1, Room 2 and Room 3 in a review center
A. 10 B. 17 C. 12 D. 19 are in the ratio 5 : 7 : 8. Mr. Doodles proposed to increase
these seats by 40%, 50% and 75% respectively. What will
60. The distance passed over by a certain pendulum bob in be the ratio of increased seats?
succeeding swings form the geometric progression A. 2 : 3 : 4 B. 6 : 7 : 8 C. 6 : 8 : 9 D. None of these
16,12,9,... feet respectively. Calculate the total distance
traversed by the bob before coming to rest. 73. The numbers a,b,c, in the given order, form a non-constant
A. 64 ft B. 75 ft C. 54 ft D. 96 ft geometric progression. The numbers a,2b,3c form an
arithmetic progression in the given order. Find the quotient q
61. At what price should Book Latte mark a book that costs of the geometric progression.
P300 in order that it may offer a discount of 20% on the A. 1/2 B. 1/4 C. 1/5 D. 1/3
marked price and still make a profit of 25% on the selling
price? 74. A train leaves Stanton travelling east at 35 mi/hr. An hour
A. 400 B. 500 C. 450 D. 700 later, another train leaves Stanton on a parallel track at 40
mph. How far from Stanton will the second (or faster) train
62. The ages of the mother and her daughter are 45 and 5 catch up with the first (or slower) train?
years, respectively. How many years will the mother be A. 240 mi B. 260 mi C. 220 mi D. 280 mi
three times as old as her daughter will?
A. 5 B. 10 C. 15 D. 20
75. The Phil. Army recruited new trainees for its armed forces. 89. In a commercial survey involving 1000 persons on brand
The new trainees were formed into a hollow square, three preferences, 120 were found to prefer brand x only, 200
deep. When it was observed by the commanding officer, that persons prefer brand y only, 150 persons prefer brand z
with the addition of 25 to their number, a solid square might only, 370 prefer either x or y but not z, 450 prefer brand y or
be formed, of which the number of men in each side would z but not x, and 370 prefer either brand z or x but not y, and
be greater by 22 than the square root of the number of men none prefer all the three brands at a time. How many
in each side of the hollow square. Determine the number of persons have no brand preference with any of the three
men that were recruited originally. brands?
A. 396 B. 639 C. 693 D. 936 A. 120 B. 280 C. 70 D. 0

76. The sum of the coefficients in the expansion of (x+y–z) 90. In how many minutes after 2 o’clock will the hands of the
^8 is clock extend in opposite directions for the first time?
A. 1 B. 2 C. 5 A. 2: 43min & 0.636 sec C. 2: 43 min & 38 sec
D. 0 B. 2: 48.636 sec D. 2: 46 min & 30 sec

77. Find the harmonic mean between 3/8 and 75/4. 91. An audience of 540 people is seated in rows having the
A. 25/34 B. 24/35 C. 34/25 D. 35/24 same number of persons in each row. If 3 more persons
seat in each row, it would require 2 rows less to seat the
78. The sum of a geometric series is as follows: S = 1.0 + 1.1 + audience. How many persons were in each row originally?
1.21 + … up to 50th term. Find S. A. 17 B. 30 C. 27 D. 31
A. 2123.51 B. 2654.34 C. 1163.91 D.
1255.82 92. What is the domain of the function f(x) = 4− 3 x 3−7√
?
79. The logarithms of the quotient and the product of two
numbers are 0.352182518 and 1.556302501, respectively. A. X ≥ 1.33 C. X ≥ 1.53
Find the first number. B. X ≥ 2.33 D. X ≥ 3.33
A. 9 B. 10 C. 11 D. 12
93. A mechanical Engineer bought 24 boxes of scews for
80. If 3logx – logy = 0,express y in terms of x. P2200.00. There were three types of screws bought. Screw
A. y=x^3 B. y=x^2 C. y=x D.y=3x A costs P300 per box, screw B costs P150 and screw C
costs P50 per box. How many boxes of screw A did he buy?
81. In the expansion of (2x – 1/x)^10 find the term independent A. 2 B. 4 C. 5 D. 17
of x.
A. 5th term B. 6th term C. 8th term D. 11th 94. A jar contains one quarter red jelly beans and three quarters
term blue jelly beans. If Kuya Dodong removes three quarters of
the red jelly beans and one quarter of the blue jelly beans,
82. If log xy = 6 and log x/y=2. Solve for x and y. what percent of the jelly beans remaining in the jar will be
A. x = 1000, y = 100 C. x = 10500,y = 150 blue?
B. x = 10000,y = 100 D. x = 100000,y = 1000 A. 10 B. 18.75 C. 90 D. 6.25

83. Find the value of x in (3^5)(9^6) = 3^(2x). (Note: The 95. Jerry buys a bottle of 200 pills. Using a standard 12 hour
expression ^ means power.) clock, he sees that the clock reads exactly 12 when he
A. 8.5 B. 9 C. 9.5 D. 8 takes the first pill. If he takes one pill every five hours, what
.
.
hour/s will the clock read when he takes the last pill in the
84. Solve for x: x
x
x
..
bottle?
x =10 A. 1 B. 5 C. 6 D. 11
A. 1.2589 C. 1.1745
B. 2.4156 D. Cannot be solved. 96. A man fires at a target 420 m away and hears the bullet
strike 2 seconds after he pulled the trigger. An observer 525
85. If Juan is 10% taller than Pedro and Pedro is 10% taller than m away from the target and 455 m away from the man
Maria, then Juan is taller than Maria by how many percent? heard the bullet strike the target one second after he heard
A. 20% B. 18% C. 21% D. 11% the report of the rifle. Find the velocity of sound.
A. 652 m/s B. 525 m/s C. 363 m/s D. 350 m/s
86. The sum of three succeeding odd integer is 75. Find the
largest integer. 97. Two turtles Leonardo and Donatello start at the same time
A.31 B. 29 C. 27 D. 25 towards each other at a distance of 150 m. The rate of
Leonardo is 10 m/s. While that of Donatello is 20 m/s. A fly
87. Find the mean proportional between 3 √2 and flies from one turtle to another at the same time that the
turtle starts to move towards each other. The speed of the
6 √ 2. fly is 100 m/s. Find the total distance travelled by the fly until
A. 3 B. √2 C. 6 the turtles meet.
A. 650 B. 600 C. 750 D. 700
D. 2 √2 98. Find the term involving a3b5 in (a + b + c)11
A. 9240a3b5c3 C. -9240a3b5c3
88. If the 5th term in AP is 17 and the 3rd term is 10, what is the
B. 462 a3b5c3 D. -462 a3b5c3
8th term?
A. 23.5 B. 27.5 C. 25.5 D. 26.5
99. What is the remainder of 2^201 divided by 29?
A. 19 B. 21 C. 9 D. 3
100.A policeman is pursuing a thief who is ahead by 72 of his
own leaps. The thief takes 6 leaps while the policeman is
taking 5 leaps, but 4 leaps of the thief are as long as 3 leaps
of the policeman. How many leaps will the thief make before
he is caught?
A. 450 leaps C. 540 leaps
B. 648 leaps D. 486 leaps