Republic of the Philippines
PROFESSIONAL REGULATION COMMISSION
Manila
BOARD OF MECHANICAL ENGINEERING
Registered Mechanical Engineer Licensure Examination
Sunday, August 6, 2017
07:30 a.m. – 12:30 p.m.
-----------------------------------------------------------------------------------MATHEMATICS,ENG’G ECONOMICS & ENG’G SCIENCES
SET A
INSTRUCTION: Select the correct answer for each of the following questions. Mark only
one answer for each item by marking the box corresponding to the letter of your choice
on the answer sheet provided.
STRICTLY NO ERASURES ALLOWED. Use pencil No.2 only.
MULTIPLE CHOICE
1. If the digits 0, 1, and 2 are used to form a three-digit number where repetition of
digits is not allowed, then how many possible numbers can be made?
A. 4
C. 8
B. 6
D. 10
2. An angle is half its supplement. What is its complement?
A. 30
C. 60
B. 45
D. 75
3. It takes 12 men 12 days to build a house. How many days will it take 24 men to
build a house?
A. 2 days
C. 12 days
B. 3 days
D. 6 days
4. The sum of the two numbers is 21.
A. 54
B. 80
If their difference is 9, what is there product?
C. 104
D. 90
5. A term used to describe payment of an employee wherein an employee is called back
to work after his regular days work
A. call back pay
C. call in pay
B. back wages
D. portal to portal pay
6. Manner of liquidating a debt by installment usually at equal intervals of time
A. investment
C. amortization
B. depreciation
D. bonding
7. What kind of process occurs between points 3 and 4? See Figure 8
A. Adiabatic
B. isobaric
C. Isentropic
D. there is insufficient information to determine the process
8. Find the lateral strain, y, of the steel specimen shown if Fx = 600 kips, E = 2.8 x
107psi, and v = 0.29. See figure 3
A. – 4 x 10-4 in.
C. 1.04 x 10-4 in.
B. – 1.04 x 10-4 in.
D. 4 x 10-4 in.
9. What type of power cycle does the following diagram illustrate? See figure 9
A.
A Carnot cycle
B.
an idealized Rankine cycle with reheat
C.
an idealized Diesel cycle
D.
an idealized Stirling cycle
10. The reduction value and marketability due to competition from newest products
A. obsolescence
C. depreciated cost
B. fixed cost
D. indirect cost
11. A goat is tied at the corner of a small building with a square base. If the length
of the rope that ties the goat is 6 meters and the side of the square base is 4
meters, what is the largest grazing area of the goat?
A. 10 sq meters
C. 29 sq meters
B. 25 sq meters
D. 200 sq meters
12. In a group of 50 students, 30 like Math, a certain number like English, 16 like
both English and Math, and 8 like neither subjects.
How many students like
English?
A. 25
C. 30
B. 27
D. 35
13. Terence’s office is 12 km from his house.
If, one day, he drove his car to his
office at a constant speed rate of 30 kph and came back home driving at 20 kph,
what is the average speed for the entire trip?
A. 24 kph
C. 27 kph
B. 25 kph
D. 28 kph
14. During snack break, 1/3 of the total number of snacks were donuts 2/5 were muffins
and the rest were pancakes. If the total number of muffins and pancakes was 20,
how many pieces of snacks were there?
A. 24
C. 35
B. 28
D. 30
15. Together, Lumen and Rey are going home to the province to visit their mothers.
If Lumen visits her mother every 6 days, and Rey visits his mother every 8 days,
after how many days will they visit their mothers together again?
A. 7
C. 18
B. 14
D. 24
16. The sum of the three angles of a triangle
second and the third angle is 20 less than
largest angle?
A. 50 degrees
C. 120
B. 100 degrees
D. 45
is 180 degrees. One angle is twice the
the second. What is the measure of the
degrees
degrees
17. Charlie mixed blue and red paint in the ratio 3 : 5 instead of 5 :3 when he
prepared 24 liters of violet paint. How many liters of the blue paint should he
add to obtain the shade he wants?
A. 2
C. 12
B. 8
D. 16
18. A 140-cm stick is cut so that one part is ¾ of the other.
segment?
A. 105 cm
C. 80 cm
B. 35 cm
D. 60 cm
How long is the shorter
19. If 2/3 of the number of red balls in a box is 1/4 of the total number of balls, and
3/4 of the number of blue balls is 3/8 of the total number of balls, then what is
the ratio of the number of red balls to the number of blue balls?
A. 3 : 8
C. 1 : 2
B. 3 : 4
D. 2 : 3
20. A boy’s age is now three-sevenths of what he will be four years from now.
is he now?
A. 3
C. 7
B. 4
D. 9
How old
21. A ball rolling on an inclined plane rolls 15 cm in the first second. If in every
second thereafter it rolls 7 cm more than in the preceding second, how far will it
roll in 4 seconds?
A. 29
C. 66
B. 36
D. 102
22. Form of summary of assets, liabilities and net worth
A. production
C. balance sheet
B. break even point
D. balance method
23. An index of short term paying ability
A. profit margin ratio
C. acid test ratio
B. current ratio
D. receivable turn over
24. In the ballistic balance shown, a bullet is fired into a block of mass M, which can
swing freely. Which of the following is true for the system after impact?
See figure 7
A. Both mechanical energy and momentum are conserved.
B. Mechanical energy is conserved; momentum is not conserved.
C. Momentum is conserved; mechanical energy is not conserved.
D. Neither mechanical energy nor momentum is conserved.
25. Ratio of annual revenues to the annual expenses
A. benefit ratio
C. rate of return
B. benefit cost ratio
D. income ratio
26. These are the products or services that are required to support human life and
activities that will be purchased in somewhat the same quantity even though the
price varies considerably
A. luxuries
B. utilities
C. necessities
D. produces goods and services
27. The length of time during which the property maybe operated at a profit
A. length of time
C. life
B. physical life
D. economic life
28. Cesar saves P20 in the first week and each week thereafter saves P1 more than in
the preceding week. Hoe much will he have saved after the 3rd month?
A. 63
C. 275
B. 306
D. 22
29. How many times will a clock strike in 36 hours if it strike only at the hour and
strike once at 1, twice at 2, and thrice at 3 and so on?
A. 63
C. 234
B. 306
D. 666
30. The first of the geometric sequences is 1 and the common ratio is 5, determine the
largest 3-digit number that represents a term of this geometric sequence.
A. 625
C. 995
B. 999
D. 125
31. In the geometric sequence whose first element is 0.0001 and whose common ratio is
10, which element is 10,000 ?
A. 8th
C. 10th
th
B. 9
D. 11th
32. Inee was 5 times as old as Luana five years ago.
Inee in ten years, how old is Luana now?
A. 5
C. 15
B. 10
D. 30
If Luana will be half as old as
33. Two cars start at the same time from two places 330 kilometers apart and travel
toward each other. Car A travels at 50 kph and Car B at 45 kph. If Car a rests
for one hour on the way, in how many hours after they left will they meet?
A. 2
C. 4
B. 3
D. 5
34. A motorist set out from A at certain rate and would have reached B in 5 hours if he
had continued at this rate. However, when he had gone three-fourths of the way he
had motor trouble which delayed him for an hour and a half. During the remainder
of the journey he increased his speed by 10 km an hour and reached B one hour and
15 minutes behind schedule. Find the distance from A to B.
A. 150 km
C. 250 km
B. 200 km
D. 220 km
35. The tens digit of a two-digit number is 2 more than three times the units digit.
How many two-digit numbers satisfy this condition?
A. 1
C. 4
B. 2
D. none
36. What is the largest angle of
A. 30
B. 60
triangle whose angles are in the ratio 1:2:3?
C. 120
D. 90
37. It occurs in unique product of services and is available only from a single
supplier and entry of all possible suppliers prevented.
A. competition
C. profitability
B. monopoly
D. inventory
38. The difference between the book value and the actual lower resale value
A. sunk cost
C. resale value
B. salvage value
D. fixed cost
39. Grand total of the assets and operational capability of a corporation
A. earning value
C. investment
B. money market
D. authorized capital
40. An ideal, reversible Carnot cycle is represented on a T-S diagram (See Figure 10)
The efficiency of the cycle is represented by which of the following ratios of
area?
A. ( 1-2-3-6)/(1-2-4-5)
C. (3-4-5-6)/(1-2-4-5)
B. ( 1-2-4-6)/(1-2-3-6)
D. (1-2-4-5)/(3-4-5-6)
41. A cantilever beam with an end mass, m = 7000 kg, deflects 5 cm when a force of 5 kN
is applied at the end. The beam is subsequently mounted on a spring of stiffness,
ks, = 1.5 kN/mcm. What is most nearly the natural frequency of the mass-beam-spring
system (See Fig.12)?
A. 1.5 rad/s
C. 6.0 rad/s
B. 3.1 rad/s
D. 6.3 rad/s
42. What is the angle of twist, for the aluminum bar shown? The shear modulus of
elasticity, G, is 3.7 x 106 psi. See Figure 5
A. 0.000554
C. 0.032
B. 0.00554
D. 0.08
43. What single discount rate is equivalent to successive discount rates of 10% and
10%?
A. 10%
C. 21%
B. 19%
D. none of these
44. To motivate Jose in studying for an examination, his mom promised him some
incentives. For every correct answer, he gets P15.00 and for every mistake, P5.00
will be taken.
How many correct answers did he get in a 100-item exam if he
received P1,000?
A. 15
C. 75
B. 25
D. 100
45. Lines are drawn across a circle so that each line crosses the circle at two points.
If five lines are drawn, what is the maximum number of parts the circle is divided?
A. 12
C. 15
B. 13
D. 16
46. In a certain constant mass system,
How does the change in enthalpy for
B in going from point 1 to point 2?
A. HA > HB
B. HA = HB
the conditions change from point 1 to point 2.
path A differ from the enthalpy change for path
(See figure 11)
C. HA < HB
D. HA / (P1+P2)/2 = HB/P1
47. By how many cubic centimeters does the volume of a cube whose side is 10 cm exceed
that of another cube whose side is 8 cm?
A. 2
C. 498
B. 8
D. 488
48. If the surface area of a cube is 54 square units, what is its volume?
A. 3 cu units
C. 18 cu units
B. 6 cu units
D. 27 cu units
49. A cube whose volume is 64 cubic units is put on top of a table. If another cube
whose volume is 27 cubic units is put on the center of the top of the first cube,
what is the total exposed surface area of the first cube?
A. 16
C. 91
B. 64
D. 71
50. Find the probability of getting a head or a tail in a single toss of a coin?
A. 1/4
C. 1/8
B. 1/2
D. 1
51. A pair of dice is tossed.
other die shows a 5 also?
A. 1/36
B. 1/6
If one die shown a 5, what is the probability that the
C. 1/11
D. 1/12
52. A multiple choice test consists of 5 questions with 3 possible answers but only one
of which is correct. In how many ways can a student answer the 5 questions and get
them all correct?
A. 1
C. 5
B. 3
D. 15
53. How many straight lines can be drawn, given 5 points no three of which are
collinear?
A. 5
C. 15
B. 10
D. 20
54. Mr. Ayala left P 225,000,000 to his 4 children. For every P100 Carlos received,
Ben received P75 Alfred received P50, and Daniel received P150. What was the total
amount received by Ben?
A. P30,000,000
C. P75,000,000
B. P45,000,000
D. P90,000,000
55.
A bookstore raises the prices of all its items by 25% every June. Every October
they offer a Cut-Price Sale, after which they only restore the original prices
before June of that year. To do this, they must reduce the price of each item by
how many percent?
A. 18 %
C. 22 %
B. 20 %
D. 25 %
56. A kaing of lanzones costing P700 was sold partly at 7 % loss and the remaining at
13% profit. The total proceeds were P741. Find the cost of the part that was sold
at 13% profit?
A. P91
C. P450
B. P250
D. P96.33
57. A factory operator bought a diesel generator set for P 10,000 and agreed to pay the
dealer uniform sum at the end of each year for 5 years at 8% compounded annually,
that the final payment will cancel the debt for principal and interest. What is the
annual payment?
A. 12 years
C. 15 years
B. 10 years
D. 17 years
58. An electric motor has a cash price of P8000. It can also be bought on installment
basis with down payment of P2000 and with periodic equal payments at the end of
every 6 months for 5 years if interest is fixed at 8% compounded semi-annually, how
much is each periodic payment?
A. 122.56
C. 739.75
B. 439.56
D. 874.32
59. A polygon with fifteen sides
A. Nonagon
B. Decagon
C.
D.
Pentedecagon
Dodecagon
60. The point where the second derivative of function is equal to zero
A. inflection point
C. point of intersection
B. minima
D. maxima
61. A curve generated by a point which moves in uniform circular motion about an axis
while traveling with a constant speed parallel to the axis.
A. Epicycloid
C. Cycloid
B. Helix
D. Spiral of Archimedes
62. A collateral agreement in a transaction, which gives one of the parties, or both,
the right to choose a course of action. Example, option to buy a thing within a
specific period.
A. executed
C. inventory
B. option
D. interest
63. Statute limiting the time period in which a lawsuit may be brought
A. stipulation
C tender of payment
B. statute of limitations
D. nullity
64. It is the return of the land or property to the state if there is no person legally
entitled to inherent it
A. asset
C. liability
B. escheat
D. cash
65. A ski resort installs two new ski lift at a cost of P 1,800,000. The resort expects
annul gross revenue to increase P 500,000 while it incurs an annual expense of P
50,000 for lift operations and maintenance. What is the pay back period?
A. 4 years
C. 2 years
B. 3 years
D. 7 years
66. How much money should a man invest in a bank account paying 8 percent annual
interest compounded continuously if he wants to use the money to by 20,000
equipment in 4 years?
A. 14,522.98
C. 12,457.45
B. 15,346.76
D. 11,237.45
67. A stock certificate of a mining company guarantees a dividend of P100 at the end of
each year for 10 years and a final additional payment at the end of 10 years of
P1,200. If money is worth 12% effective, what is the certificate worth now?
A. 951.39
C. 1095.54
B. 897.54
D. 789.45
68. A tank is in the form of a frustum of a tight circular cone is filled with oil
weighing 50 pounds per cubic foot. If the height of the tank is 10 feet,
base
radius is 6 ft and the top radius is 4 feet, find the work required in ft-tons to
pump oil to a height 10 feet above the tank.
A. – 312 ft-tons
C. – 325 ft-tons
B. – 324 ft-tons
D. – 435 ft-tons
69. Find the rate of change of the volume of the sphere with respect to its radius when
its radius is 5.
A. 100 
B. 200 
C. 150
D. 250
70. A savings association pays 4% interest compounded quarterly.
annual interest rate?
A. 18.045%
C. 17.155%
B. 16.985%
D. 17.230%
What is the effective
71. A bank offers 1.2% effective monthly interest. What is the effective annual rate
with monthly compounding?
A. 15.4%
C. 8.9%
B. 14.4%
D. 7.9%
72. What is the present worth of P27,000.00 due in 6 years if money is worth 13% and is
compounded semi-annually?
A. P12,681.00
C. P13,500.00
B. P15,1250.00
D. P21,931.00
73. The nominal interest rate is 4%.
continuous compounded account?
A. P13,500.10
B. P13,498.60
How much is my P10,000.00 worth in 10 years in a
C. P13,620.10
D. P13,650.20
74. An equilateral polygon or sometimes known as a regular polygon.
A. equigon
C. perigon
B. isogon
D. decagon
75. The base of a number system.
A. radius
B. radix
C. characteristics
D. matrix
76. 20000 PS to hp:
A. 17920
B. 19720
C. 17290
D. 19270
77. The product of the n consecutive integers from 1 to n.
A. serial
C. differential
B. integral
D. factorial
78. Which is not a qualification for an applicant for ME Board Examination?
A. Certified Plant Mechanic
B. Holder of BSME degree
C. At least 18 years of age
D. A citizen of the Philippines
79. The column shown has a cross-sectional area of 13 m2. What can be the approximate
maximum load if the compressive stress cannot exceed 9.6 kPa? See figure 2
A. 125 kN
C. 200 kN
B. 102 kN
D. 125 kN
80. The figure below shows a two-member truss with a load F=11,500 kips applied
statically. Given that L1 = 4 feet, L2 = 5 feet, and that the beams have crosssectional area A= 6 in2, find the elongation of member AB after F is applied. Use E
= 29,000,000 psi. See figure 4
A. -2.48 in.
C. – 1.98 in.
B. – 1.48 in.
D. 1.48 in.
81. Find the expression for the bending moment as a function of x for the following
beam. See Figure 6
A. M(x) = - x2 + 2x
C. M(x) = - x2 +
B. M(x) = -x2 + 1
D. M(x) = x2 – 2x
2x
82. A series of numbers which are perfect square such as the series ( 1,4,9,16,25…….)
A. Fermat’s numbers
C. Fibonacci’s numbers
B. Euler’s numbers
D. Fourier series
83. It is point on the axis midway between the focus and the directrix of the parabola.
A. vertex
C. latus rectum
B. origin
D. eccentrity
84. The highest point of figure with respect to the base or the plane of the base.
A. apothem
C. apex
B. peak
D. altitude
85. What is the MOST nearly the stress at the surface S of the cylindrical object
shown? The specific weight of the material is gamma = 76.9 kN/m^3. See figure 1
A. 310 kPa
C. 250 kPa
B. 180 kPa
D. 275 kPa
86. How much must be invested on January 1 year 1, in order to accumulate P2,000 on
January 1, year 6 at 6%?
A. P1,495.00
C. P1.595.00
B. P1,295.00
D. P1,695.00
87. A bank charges 12% simple interest on a P300.00 loan. How much will be repaid if
the loan is paid back in one lump sum after three years?
A. P408.00
C. P551.00
B. P415.00
D. P450.00
88. If P5000.00 shall accumulate for 10 years at 8% compounded quarterly.Find the
compounded interest at the end of 10 years.
A. P6,005.30
C. P6,040.20
B. P6,000.00
D. P6,010.20
89. XYZ Corporation manufactures bookcases that it sells for P65.00 each. It cost XYZ
P35,000.00 per year to operate its plant.
This sum includes rent, depreciation
charges on equipment, and salary payments. If the cost to produce one bookcase is
P50.00, how many cases must be sold each year for XYZ to avoid taking a loss?
A. 2334 cases
C. 750 cases
B. 539 cases
D. 2333 cases
90. An asset is purchased for P9,000.00. Its estimated life is 10 years, after which it
will be sold for P1,000.00. Find the book value during the third year if the sumof-the-year’s digit (SYD) depreciation is used.
A. P6,100.00
C. P5,072.00
B. P4,500.00
D. P4,800.00
91. A company issued 50 bonds of P1,000.00 face value each, redeemable at par at the
ends of 15 years to accumulate the funds for redemption, the firm established a
sinking fund consisting of annual deposits, the interest rate of the fund being 4%.
What was the principal in the fund at the end of the 12th year?
A. P35,983.00
C. P41,453.00
B. P38,378.00
D. P37,519.00
92. A sum of P1,000.00 is invested now and left for eight years, at which time the
principal is withdrawn.
The interest that has accrued is left for another eight
years. If the effective annual interest rate is 5%, what will be the withdrawal
amount at the end of the 16th year?
A. P706.00
C. P774.00
B. P500.00
D. P799.00
93. How much of a 40% solution of alcohol and how much of an 80% solution should be
mixed to give 150 liters of a 50% solution?
A. 112.5 liters/37.5 liters
C. 211 liters/3.5liters
B.121.5 liters/53.7liters
D. 212 liters/ 53.7 liters
94. How much water must be evaporated from the 18 kg of 20% salt solution to produce a
50% solution.
A. 2.25 kg
C. 7.5 kg
B. 5.0 kg
D. 10.5 kg
95. It is straight line towards which a curve approaches but never meets.
A. directrix
C. asymptotes
B. major axis
D. conjugate axis
96. Consist of the totality of property belonging to a deceased person, which must be
administered and distributed in accordance with a last will and testament and/or
the laws on succession
A. payee
C. title
B. tax
D. estate
97. Used in sales or ordinary contracts, describes any person who requires property or
negotiable instruments in good faith and for valuable consideration.
A. liability
C. bonafide purchaser for value
B. asset
D. owner
98. It is rule used for differentiating a function, that is , if z is function if y and
y is function of x, then dz/dx= (dz/dx)(dy/dx)
A. L. Hospital’s rule
C. Crammer’s rule
B. Chain rule
D. slide rule
99. The process of plotting points to give rise to the graph of a curve. It includes
the use of techniques of symmetry, maxima and minima, curvature and asymptote.
A. drafting
C. dimensional analysis
B. curve tracing
D. correlation
100.
A court writ issued to compel the performance of a public or official duty owed
by the person to whom the order is directed.
A. arrest
C. mandamus
B. bail
D. payee
***END***
SUBMIT THIS TEST QUESTION SET TOGETHER WITH THE ANSWER SHEET TO YOUR
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DISCIPLINARY ACTION.