1. Find the 30th of an arithmetic progression 4, 7, 10 …
A. 91 B. 90 C. 88 D. 75
2. 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 until
there are 10 bricks in the last layer. How many bricks are there together?
A. 638 B. 637 C. 640 D. 639
3. Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35.
A. 171 B. 182 C. 232 D. 216
4. Find the sum of the first 10th term of the geometric progression 2, 4, 8, 16 …
A. 1023 B. 2046 C. 225 D. 1596
5. Once a month a man put some money into the cookie jar. Each month he put 50 centavos more into the jar than the month
before. After 12 years he counted his money; he had ₱5436. How much money did he put in the jar last month?
A. ₱73.50 B. ₱75.50 C.₱74.50 D. ₱72.50
6. Find the geometric mean of 64 and 4.
A. 16 B.34 C. 32 D. 28
7. The seventh term is 56 and the 12th term is -1792 geometric progression. Find the ratio and the first term. Assume the
ratios are equal.
A. -2, 5/8 B. -1, 5/8 C. -1, 7/8 D. -2, 7/8
8. Find the sum of the infinite geometric progression 6, -2, 2/3.
A. 9/2 B. 5/2 C. 11/2 D. 7/2
9. Find the sum of 1, -1/5, 1/25 ...
A. 5/6 B. 2/3 C. 0.84 D. 0.72
10. Find the ratio of the infinite geometric series if the sum is 2 and the first term is ½.
A. 1/3 B. 1/2 C. 3/4 D. 1/4
11. Factor the expression x2 + 6x + 8 as completely as possible?
A. (x + 8) (x - 2) B. (x + 4) (x - 2) C. (x + 4) (x + 2) D. (x - 4) (x - 2)
12. Find the value of x in the equation 24x2 + 5x – 1 = 0.
A. (1/6, 1) B. (1/6, 1/5) C. (1/2, 1/5) D. (1/8, -1/3)
13. Find the value of k of the equation x2 + kx + 4 = 0, so that the roots are equal.
A. ±4 B. ±8 C. ±12 D. ±2
14. If the roots of the equation are 1 and 2. What is the quadratic equation?
A. x2 – 3x + 2 = 0 B. x2 – 3x - 2 = 0 C. x2 + 3x + 2 = 0 D. x2 + 3x - 2 = 0
15. In the exprension of (x + 4y)12 , the numerical coefficient of the 5th term is :
A. 63,360 B. 126,720 C. 506,880 D. 253,440
16. The polynomial x3 + 4x2 – 3x + 8 is divided b x – 5 , then the remainder is :
A. 175 B. 140 C. 218 D. 200
17. Find the remainder if we divided 4y3 + 18y2 +8y – 4 by (2y + 3)
A. 10 B. 11 C. 15 D. 13
18. Find the rational number equivalent to repeating decimal 2.35242424…
A. 232739900 B. 23261990 C. 232899900 D. 232649900
19. Find the 1987th digit in the decimal equivalent to 17859999 starting from decimal point.
A. 8 B. 1 C. 7 D. 5
20. What is the lowest common factor of 10 and 32?
A.320 B.2 C.180 D. 90
21. The sum of Kim’s and Kelvin’s ages is 18. In three years, Kim will be twice as old as kelvin. What are their ages?
A. 4, 14 B. 5, 13 C. 7, 11 D. 6, 12
22. What time after 3 o’clock will the hands of the clock be together for the first time?
A. 3:16.36 B. 3:14.32 C. 3:12.30 D. 3:17.37
23. The difference of the squares of the digits of a two digit positive number is 27. If the digits are reversed in order and the
resulting number subtracted from the original number, he difference is also 27. What is the original number?
A. 63 B. 54 C. 48 D. 73
24. Ten less than four times a certain number is 14. Determine the number.
A. 6 B. 7 C. 8 D. 9
25. Jojo bought a second-hand Betamax VCR and then sold to Rudy at a profit of 40%. Rudy then sold the VCR to Noel at a
profit of 20%. If Noel paid 2,856 more than it cost to Jojo. How much did Jojo paid for the unit?
A. ₱4,000 B. ₱4,100 C. ₱4,200 D. ₱4,300
26. Ten liters of 25% salt solution and 15 liters of 35% salt solution are poured into a drum originally containing 30 liters of 10%
salt solution. What is the percent concentration in the mixture?
A. 19.55% B. 22.15% C. 27.05% D. 25.72%
27. The boat travels downstream in 2/3 of the time as it does going upstream. If the velocity of the river current is 8kph,
determine the velocity of the boat in still water.
A. 40kph B. 30kph C. 50kph D. 60kph
28. Two engineering student’s attempt to solve a problem that reduces to quadratic equation. One of the students made a
mistake only in the constant term of the quadratic equation and gives an answer of 8 and 2 for the roots. The other student
solving problem made an error in the coefficient of the first degree term only and gives his answer as -9 and -1 for the roots. If
you are to check their solutions, what would be the correct quadratic equation?
A. x2-10x+9=0 B. x2-10x-9=0 C. 10x2-9x-1=0 D. 92+10x-1=0
29. A club of 40 executives, 33 like to smoke Marlboro, and 2o likes to smoke Philip Morris. How many like both.
A. 13 B. 10 C. 11 D. 12
30. A and B working together can finish painting a home in 6 days. A working alone can finish it in five days less than B. How
long will it take each of them alone to finish the work done?
A. 10, 15 B. 15, 20 C. 20, 15 D. 5, 10
31. 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 the value of “w” when x = 1, y = 4 and z = 2.
A. 2 B. 3 C. 4 D. 5
32. A merchant has three items on sale, namely a radio for ₱50, a clock for ₱30 and a flashlight for ₱1.00. At the end of the
day, he has sold a total of 100 of the three items and has taken exactly ₱1000 on the total sales. How many radios did he sell?
A. 16 B. 20 C. 18 D. 24
33. The third term of harmonic progression is 15 and the 9th term is 6. Find the 11th term?
A. 4 B. 5 C. 6 D. 7
34. What is the sum of the coefficients of the expansion of (2x -1)20?
A. 0 B. 1 C. 2 D. 3
35. Determine the sum of the infinite series: s =1/3 +1/9 +1/27+…+ (1/3)n.
A. 4/5 B. 3/4 C. 2/3 D. 1/2
36. Determine the sum of the positive valued solution to the simultaneous equations: xy = 15, yz = 35, zx = 21.
A.15 B13 C17 D19
37. The area of two squares differs by 7 sq. ft. and their perimeters differ by 4ft. Determine the sum of their areas.
A. 25ft2 B. 27 ft2 C. 28 ft2 D. 22 ft2
38. A bookstore purchased bestselling book at ₱200.00 per copy. At what price should this book be sold so that, giving a 20%
discount, the profit is 30%.
A. ₱347 B. ₱280 C. ₱325 D. ₱350
39. In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate, and of the females 70% are
literate. What is the femalPe population?
A. 850 B. 500 C. 550 D. 600
40. Gravity causes a body to fall 16.1 ft in the 1st second, 48.3 in the 2nd second, 80.5 in the 3rd second and so on. How far
did the body fall during the 10th second?
A. 248 .7 ft B. 308.1ft C. 241.5 ft D. 305.9 ft
41. In a commercial survey involving 1,000 persons on brand preference, 120 were found to prefer brand x only, 200 prefer
brand y only, 150 prefer brand z only, 370 prefer either brand x or y but not z, 450 prefer brand y or z but not x, and 420 prefer
either brand z or x but not y. How many persons have no brand preference, satisfied with any of the 3 brands?
A. 230 B. 280 C. 180 D. 130
42. The electric power which a transmission line can transmit it proportional to the product of its design voltage and current
capacity, and inversely to the transmission distance. A 115 kilovolt line rated at 1000 amperes can transmit 140 megawatts
over 150 km. How much power, in Megawatts, can a 230 kilovolt line rated at 1,500 amperes transmit over 100km?
A. 785 B. 485 C. 675 D. 595
43. The number x, 2x + 7, 10x – 7 forms a geometric progression. Find the value of x.
A. -5 & -3/7 B. 7 & 7/6 C. 7 & -7/6 D. 8 & 3/7
44. Solve for x : √20−𝑥 = x
A. 4, -5 B. -4, -5 C. -4, 5 D. no solution
45. Solve for x: 10x2 + 10x + 1 = 0.
A. -0.113, -0.887 B. -0.113, -0.788 C. -0.331, -0.788 D. -0.311 ,-0.887
46. Find the sum of the sequence 25, 30, 35, …
A. 2/5 (𝑛2+9𝑛) B. 5/2 (𝑛2+9𝑛) C. 9/2 (𝑛2+9𝑛) D. 9/2 (𝑛2−9𝑛)
47. If the sum is 220 and the first term is 10, find the common difference if the last term is 30.
A. 2 B.5 C .3 D. 2/3
48. Given the 2 x 2 matrix [974၈ ] find its determinants.
A. 32 B.44 C.-20 D.20
49. If the people won prizes in the state lottery, in how many ways can these 15 people win first, second, third, fourth, and fifth
prizes?
A. 8,845 B.116,280 C.360,360 D.3,003
50. How many 4 digits number can be formed without repeating any digit from the following digits: 1, 2, 3, 4, and 6?
A. 120 B.130 C.140 D.150
51. In how many ways can set of 6 distinct books be arranged in a bookshelf?
A. 720 B.120 C.360 D.180
52. How many permutations are there if the letters PNRCSE are taken 6 at time?
A. 5040 B.140 C.720 D.24
53. What is the number of permutations of the letters in the word BANANA?
A. 36 B.60 C.52 D.42
54. In how many ways can 3 marines and 4 armies be seated on a bench if the armies must be seated together?
A. 640 B.720 C.576 D.144
55. Four different colored flags can be hung in a row to make coded signal. How many signals can be made if a signal consists
of the display of one or more flags?
A. 64 B.66 C.68 D.62
56. How many four-digit numbers can be form by the use of digits 1, 2, 3, 5, 6 and 7 if one digit is used only once in one
number?
A. 240 B.230 C.280 D.360
57. There are four balls of different colors. Two balls are taken at a time and arranged in a definite order. For example if a
while and a red ball are taken, one definite arrangement is white first, red second and another arrangement is red first, white
second, How much such arrangements are possible?
A. 24 B.6 C.12 D.36
58. A factory building has six entrance doors. In how many ways can a person enter and leave:
I by any door
II by a different door
A. 30, 36 B. 36, 30 C.6, 5 D. 36, 6
59. Three A, B and C get into a Bus that has six vacant seats on each side. In how many ways can they be seated if A insists
on sitting on the right side?
A. 660 B. 720 C. 530 D. 410
60. A group of 6 speakers consist of 2 politicians and 4 lawyers who are not politicians. In arrangements for a speaking order
at a meeting, the politicians will speak in succession and the lawyers in succession. In how many ways can the order be
arranged?
A. 69 B. 138 C. 96 D. 192
61. In how many ways can 4 boys and 4 girls be seated alternately in a row of eight chairs?
A. 576 B. 1152 C. 1728 D. 288
62. In how many ways can a IIEE chapter with 15 directors, choose a president, a vice president, a secretary, a treasurer, and
an auditor, if no member can hold more than one position?
A. 15 B. 3,003 C. 36,060 D. 360,360
63. An IIEE unit has 10 REE’s and 6 RME’s, if a committee of 3 members one from each group is to be formed, how many
such committee can be formed?
A. 260 B. 240 C. 120 D. 360
64. There are 5 main roads between the cities A and B, and four between B and C. In how many ways can a person drive from
A to C and return, going through B and both trips without driving on the same road twice?
A. 260 B. 240 C. 120 D.160
65. The lotto use numbers 1-42. A winning number consist of six different numbers in any order. What are your chances of
winning it?
A. 5,245,786 B. 8,437,224 C. 10,127,420 D. 2,546,725
66. In how many ways can you invite one or more if five friends to a party?
A. 25 B. 31 C. 15 D. 62
67. There are four balls of different colors. Two balls at a time are taken and arranged in any way. How many such
combinations are possible?
A. 36 B. 3 C. 6 D. 12
68. A semi-conductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and to
women?
A. 680 B. 540 C.480 D. 840
69. In how many ways can a committee of three consisting of two chemical engineers and one mechanical engineer can be
formed from four chemical engineers and three mechanical engineers?
A. 18 B.64 C. 32 D. none of these
70. In mathematics examination, a student may select 7 problems from a set of 10 problems. In how many ways can he make
his choice?
A. 120 B. 530 C. 720 D. 320
71. How many line segments can be formed with 6 distinct points, no three of which are collinear?
A. 10 B. 15 C. 20 D. 25
72. How many triangles are determined by the vertices of a regular hexagon?
A. 10 B.15 C. 20 D. 25
73. How many committees can be formed by choosing 4 men from an organization of a membership of 15 men?
A. 1390 B. 1240 C. 1435 D. 1365
74. On a certain examination, the student must answer 8 out of the 12 questions, including exactly 5 of the firs 6. In how many
ways can he write the examination?
A. 100 B. 495 C. 792 D. 120
75. How many different sums of money can be made from a penny, a nickel, a dime, and a quarter
A. 24 B. 12 C. 15 D. 20
76. Tony went to drugstore. He bought a bottle of aspirin and bottle of Tylenol. The aspirin cost Php 1.25 more than Tylenol.
He also bought cologne which cost twice as much as the total of the other two combined. How much id the Tylenol cost if the
total (without tax) was Php 24.75?
A. Php 4.50 B. Php 3.50 C. Php 6.25 C. Php 5.75
77. If an alloy containing 30% silver is mixed with a 55% silver alloy to 800 pounds of 40 % alloy, how much of the 30% silver
alloy must be use?
A. 450 lb. B.420 lb. C. 460 lb. D. 480 lb.
78. Lita has Php 40.00. If she has one more Php 5 bill than Php 10 bills, and two more Php 1 bills than Php 5 bills, how many
Php 10 bills does she have?
A. 4 B. 3 C. 2 D. 5
79. In how many ways 7 scientists are assigned to one triple and two double hotel rooms?
A. 210 B. 200 C. 300 D. 230
80. What is the value of x if the logx 1296 =4?
A. 4 B. 5 C. 6 D. 3
81. Express 3 ln x + ½ ln y in Briggsian Logarithm
A. logx3y B. logx3y1/2 C. 0.434 logx3y1/2 D. 2.3 logx3y1/2
82. Simplify :(2𝑦3𝑧−2)−3(𝑥−3𝑦𝑧3)−1/2(𝑥𝑦𝑧−3)5/2
A. 1/(x^2 y^3z^5) B. 1/(x^2 y^7z^5) C. 1/(x^2 y^5z^7) D. 1/(x^5 y^7z^2)
83. The standard acceleration due to gravity is
A. 32.2 ft/s^2 B.980 ft/s^2 C. 32.2m/s^2 D. 62.4m/s^2
84. Given: Log 4 7 =n. find Log 4 1/7
A. 1/n B. n C.-1/n D.-n
85. The number 28, x + 2, 112 form a G.P, What is the 10th term?
A. 14336 B.13463 C.16433 D.16344
86. A goldsmith has two alloys of gold, the first being 70% pure and the second being 60% pure. How many ounces of the 60%
pure gold must be rise to make 100 ounces of an alloy which is 66% gold?
A. 40 B. 35 C. 45 D. 38
87. A box contains 2 blue socks and 2 white socks. Picking randomly, what is the probability that you will pick 2 socks of the
some color?
A. 1/6 B. 1/3 C. 1/2 D. 1/4
88. A plane takes 1 and a half hour to fly from Los Angeles to San Francisco and 2 hours from San Francisco to Los Angeles.
If the wind blows north on both trips at 24 mph, what is speed of the plane in still air?
A. 170 B. 110 C. 120 D. 150
89. In throwing a pair of dice, what is the possible outcome of getting 10?
A. 1/36 B. 1/12 C. 5/36 D. 1/18
90. Determine the number of permutation of 8 distinct objects, taken 3 at a time.
A. 504 B. 210 C. 120 D. 336
91. How many 6 number combinations can be generated from the numbers 1 to 42 inclusive, without repetition and no regard
to the order of the number?
A. 850,668 B. 5,245,786 C. 188,848,296 D. 31,474,716
92. Round off 0.003086 to the three significant figures?
A. .003 B. .00309 C. .0031 D. .00308
93. Round off 2.371 x 10^-8 to two significant figures.
A. 2.4 x 10^-8 B. 2.37 x 10^-8 C. 0.2371 x 10^-9 D. 0.002371 x 10 ^-11
94. The numbers 12 and 16 has the greatest common divisor of ___.
A. 2 B. 4 C. 6 D. 192
95. Find the inverse function of y = f(x) = 2x – 6
A. y=g(x)=2x +6 B. y=g(x)=6x -2 C. y=g(x)=x/2 +3 D. y=g(x)=x/2-3
96. A store advertises a 20% off sale. If an article is marked for the sale at $24.48, what is the regular price?
A. $34.80 B. $28.65 C. $30.60 D. $36.55
97. Mrs. Smith is twice as old as her daughter Sam. Ten years ago, the sum of their ages was 46 years. How old is Sam?
A. 12 B. 15 C. 22 D. 19
98. John, Peter and Charlie are suitors of Susan. The probability that Susan will say yes to john is equal to that of Peter, if the
probability that Susan will say yes to Charlie is twice of either of the two. What is the chance that Charlie will win to Susan?
A. ½ B. 1/3 C. 1/4 D. 2/3
99. What is (1 + i^2 )^3
A. 0 B. 1 C. 1 - I D. 2 + i
100. A 1-inch diameter conduit is equivalent to:
A. 254 mm B. 25.4 mm C. 25.4 cm D. 2.54 cm