Refresher 01: Engineering Sciences – Mechanical Engineering Online Review Center

Handouts
Exercises

Topics:

Worded Problems in Algebra
Analytic and Plane Geometry
Logarithms
Probabilities and Statistics
Engineering Economy
PSME Code
Mechanical Engineering Law
Engineering Mechanics
Strength of Materials
Fluid Mechanics
Board of Mechanical Engineering Code of Ethics

In a commercial survey involving 1200 persons on brand preferences, 130 were found to prefer brand A only, 200 prefer bran B only, 160 prefer brand C only, 380 prefer brand A or B but not C, 450 prefer either brand B or C but not A, and 380 prefer either C or A but not B. How many persons have no brand preference, satisfied with any of the three brands?
- a. 480
- b. 450
- c. 430
- d. 420
In a survey concerning the number of students enrolled in mathematics subject, it was found out that 40 enrolled in Algebra, Calculus and Geometry, 50 in Algebra and Geometry, 45 in Geometry and Calculus, 55 in Algebra and Calculus, 85 in Algebra and 75 in Calculus. If there are 150 students in all, how many students enrolled purely in Geometry only?
- a. 45
- b. 50
- c. 55
- d. 60
In the set of 150 triangles, 85 are right and 75 are isosceles triangles. How many are right isosceles triangles?
- a. 15
- b. 20
- c. 10
- d. 25
A club of 50 students, 34 like to eat in Jolibee and 22 like to eat in McDonalds, how many like both?
- a. 4
- b. 6
- c. 8
- d. 10
How many lbs of water must be evaporated from 60 lbs of 4% solution so that the remaining solution will be 5% salt?
- a. 14
- b. 16
- c. 18
- d. 12
A gold smith has two alloys of gold, the first alloy being 75% pure gold and the second alloy of 55% pure gold. How many ounces of the first alloy must be used to make 100 ounces of a new alloy which will be 65% pure gold?
- a. 50
- b. 45
- c. 65
- d. 35
Ten liters of 30% salt solution and 20 liters of 40% salt solution are poured into a drum originally containing 40 liters of 15% salt solution, what is the percent concentration of the resulting mixture?
- a. 22.6%
- b. 24.3%
- c. 26.1%
- d. 20.3%
A man drives from station A to station B 50 km away at an average speed of 40 kph and return to A at an average speed of 30 kph. What was the average speed of the man in the whole journey?
- a. 32.2 kph
- b. 36.8 kph
- c. 34.3 kph
- d. 30.5 kph
Kinematic viscosity is an SI derived unit described as:
- a. Pascal second
- b. Newton per meter
- c. sq. meters per second
- d. watt per meter Kelvin
The length of time during which the property may be operated at a profit.
- a. life
- b. Length of time
- c. Physical life
- d. Economic Life
In a cantilever beam with a concentrated load at the free end, the moment is:
- a. Maximum at the wall
- b. Constant along the beam
- c. Maximum at the free end
- d. ¼ maximum half way out on the beam
A situation whereby payment is made for work not done. The term also applies to the case where more worker are used than are reasonable requirement for efficient operation.
- a. Downtime pay
- b. Moon lighting
- c. Feather bedding
- d. Check-in pay
Locus of points on a side which rolls along a fixed line:
- a. Cycloid
- b. Cardioid
- c. Epicycloid
- d. Hypocycloid
Grand total of the asset and operational capability of a corporation.
- a. Authorized capital
- b. Investment
- c. Earning value
- d. Money Market
The Economic Order Quantity (EOQ) is defined as the order quantity which minimizes the inventory cost per unit time. Which of the following is not assumption of the basic EOQ with no shortages?
- a. There is an upper bound on the quantity ordered
- b. The entire reorder quantity is delivered instantaneously
- c. The demand rate is uniform and constant
- d. There is a positive cost on each unit inventoried
Ductile cast iron and gray cast iron both contains 4% carbon. Ductile cast iron, however, has a higher tensile strength and is considerably more ductile. Which of the following is the major difference that accounts for the superior properties of the ductile iron?
- a. The graphite particles of the gray cast iron are excessively large
- b. The gray cast iron contains iron carbide whereas the ductile iron contains graphite.
- c. The gray cast iron contains flakes of graphite, whereas the ductile cast iron contains spheroids of graphite.
- d. The ductile iron is tempered to give better properties.
When using net present worth calculations to compare two projects, which of the following could invalidate the calculations?
- a. Evaluation over different time periods
- b. Mutually exclusive projects
- c. Difference in the magnitude of the projects
- d. Nonconventional cash flows
At section 35 of ME LAW, pressurized pipes will have a working pressure of not less than ___.
- a. 70 kPa
- b. 95 kPa
- c. 100 kPa
- d. 150 kPa
An airplane, flying with the wind, took three hours to travel 1500 km and 3 ½ hours to fly back. What is the wind velocity?
- a. 30.2 kph
- b. 35.7 kph
- c. 38.9 kph
- d. 28.4 kph
It takes A twice as it takes B to do a certain piece of work. Working together, they can do the work in 7 days. How long would it take B to do it alone?
- a. 12.5
- b. 16.5
- c. 10.5
- d. 8.5
The boat travels downstream in 2/3 of the time as it does going upstream. If the velocity of the river current is 9 kph, determine the velocity of the boat in still water.
- a. 45 kph
- b. 48 kph
- c. 42 kph
- d. 38 kph
What time after 3 o’clock will the hands of the clock be together for the first time?
- a. 3:18:18
- b. 3:16:36
- c. 3:12:34
- d. 3:14:13
In how many minutes after 7 o’clock will the hands of the clock be directly opposite to each other for the first time?
- a. 5:45
- b. 6:45
- c. 5:40
- d. 5:38
A man is 40 years old has a son of 12 years. In how many years will be the father be three times as old as his son?
- a. 2
- b. 3
- c. 4
- d. 5
A Mario is three times as old as his Sonny. Six years ago, he was six times as old as Sonny was at that time. How old is Sonny?
- a. 8
- b. 10
- c. 14
- d. 12
The sum of Mike’s and Alberto’s ages is 20. In 3 years, Mike will be twice as old as Alberto. How old is Mike now?
- a. 12.33
- b. 10.33
- c. 16.33
- d.14.33
A simply supported beam 12 m long carries a uniformly distributed load of 30 kN/m. What is the value of the maximum moment of the beam due to the load?
- a. 520 kN-m
- b. 510 kN-m
- c. 540 kN-m
- d. 530 kN-m
A cylindrical tank with 12 inches inside diameter contains oxygen has at 3,800 psi. Calculate the required wall thickness (in mm) under the stress of 30,000 psi.
- a. 16.3mm
- b. 17.2mm
- c. 19.3mm
- d. 18.1mm
The quantity of chlorine in parts per million required to satisfactorily chlorinate sewage is usually:
- a. 30 – 60
- b. 65 – 90
- c. 0 – 25
- d. 95 – 120
How is the material purchase price variance defined?
- a. (quantity issued – std. quantity)(std. price)
- b. (quantity purchased*actual price) – (quantity purchased*std. price)
- c. (actual price – std. price)(quantity used)
- d. (quantity purchased – quantity used)(actual price)
Additional information to prospective bidders on contract documents issued prior to bidding date:
- a. Bid bulletin
- b. Delicts
- c. Escalatory clause
- d. Technology assessment
Gross profit, sales less cost of good sold, as a percentage of sales is called:
- a. Profit margin
- b. Price earnings
- c. ROI ratio
- d. Gross margin
In an Imhoff tank:
- a. There are no settling compartments
- b. The sludge and fresh sewage are well mixed to give complete digestion
- c. The effluent contains very little dissolved oxygen
- d. The sludge and raw sewage are not mixed
What is the acid test ratio?
- a. The ratio of owner’s equity to the total current liabilities
- b. The ratio of current assets (exclusive of inventory) to the total current liabilities
- c. The ratio of all assets to total liabilities
- d. The ratio of gross margin to operating sales and administrative expenses.
What is the formula for a straight-line depreciation rate?
- a. 100% minus % net salvage value all over the estimated service life
- b. 100% net salvage value all over estimated service life
- c. Average net salvage value all over the estimated service life
- d. % net salvage value all over estimated service life
The peso amount as earned from investment or project is called
- a. Surplus
- b. Interest
- c. ROI
- d. ROR
Modes of extinguishing obligations when creditor abandons his right to collect:
- a. Forfeiture
- b. Condonation
- c. Debt cancellation
- d. Liquidated damages
What is the color of steam pipe?
- a. Light blue
- b. Green
- c. Silver gray
- d. Violet
Compute for the safe wall thickness of 78.3 cm diameter steel tank. The tank is subjected to a 8.33 MPa pressure and the steel material has a yield stress of 216.3 MPa. The factor of safety to use is 4.
- a. 6 cm
- b. 7 cm
- c. 5 cm
- d. 8 cm
Determine the thickness of a steel air receiver with 28-in diameter and pressure load of 150 psi assuming design stress of 8000 psi
- a. 0.2625 in
- b. 0.3912 in
- c. 0.4521 in
- d. 0.5021 in
A hollow shaft has an inner diameter of 0.040 m and an outer diameter of 0.065 m. Find the polar moment of inertia of this hollow shaft.
- a. 1.5×10^-4m⁴
- b. 1.8×10^-4m⁴
- c. 1.3 x10-4m⁴
- d. 1.9×10^-4m⁴
What is the minimum distance can a truck slide on a horizontal asphalt road if it is traveling at 28 m/s? the coefficient of sliding friction between the asphalt and rubber is 0.55. The weight of the truck is 8000 kgs.
- a. 70.6 m
- b. 72.7 m
- c. 76.2 m
- d. 78.1 m
A highway curve has a super elevation of 6.5 degrees. What is the radius of the curve such that there will be no lateral pressure between the tires and the roadway at the speed of 50 mph?
- a. 447.2 m
- b. 457.6 m
- c. 432.9 m
- d. 468.1 m
One of the best known safety practices in industrial plant is:
- a. To maintain fire brigade
- b. To provide alert security guards
- c. To train deliver personnel
- d. To provide machine with appropriate guards
The volume of a circular cylinder is equal to the product of its base and altitude:
- a. Corollary
- b. Theorem
- c. Axiom
- d. Postulate
Which of the four does not belong to the group?
- a. Class D Fire – Fire caused by LPG
- b. Class A Fire – Fire caused by light combustible materials like paper and wood
- c. Class C Fire – Electrical fire
- d. Class B Fire – fire caused by oil and other hydrocarbons
All heavy machinery should be supported on solid foundations of sufficient mass and base area to prevent or minimize transmission of:
- a. Better control of the drainage system
- b. Objectionable sound coming from the exhaust
- c. Objectionable vibration to the building and occupied space
- d. Objectionable vibration or forces from nearby machines
What is the name of vector that represents the sum of two vectors
- a. Scalar
- b. Resultant
- c. Tangent
- d. Tensor
The statement of equality between two ratios:
- a. Theorem
- b. Power factor
- c. Proportion
- d. Valuation
The coefficient of friction for dry surfaces:
- a. Depend on the materials and the finish condition on the surface
- b. Does not depend on the materials
- c. Depends on the composition of the materials only
- d. Depends only on the finish condition of the surfaces
The dimension of “Acceleration*mass” is the same as that of:
- a. Weight
- b. Work
- c. Power
- d. Length
Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.
- a. Axiom
- b. Corollary
- c. Postulate
- d. Theorem
A plane closed curve, all points of which are the same distance from a point within, called the center is:
- a. Chord
- b. radius
- c. Circle
- d. Radius
A 350 kg block tends to slide down a 30 degree inclined plane. If the angle of friction between the block and the inclined plane is 15 degrees, solve for the horizontal force P to maintain equilibrium.
- a. 93.8 kg
- b. 95.2 kg
- c. 98.1 kg
- d. 96.1 kg
A shot is fired at an angle of 45 degrees with the horizontal and a velocity of 400 fps. Find the maximum height.
- a. 1,352.1 ft
- b. 1,652.0 ft
- c. 1,483.2 ft
- d. 1,242.2 ft
A stone is thrown upward with an angle of 35 degrees with the horizontal and returns to earth in 8 seconds. How high does it go?
- a. 1,209.1 ft
- b. 1,872.9 ft
- c. 1,600.0 ft
- d. 1,029.7 ft
A baseball is thrown from a horizontal plane following a parabolic path with an initial velocity of 120 m/s at an angle of 30 degrees above the horizontal. How far from the throwing point will the ball attain its original level?
- a. 1,827.8 m
- b. 1,271.2 m
- c. 1,320.0 m
- d. 1,778.1 m
The sum of the numbers is 12. Find the possible largest product.
- a. 30
- b. 24
- c. 36
- d. 32
Evaluate the limit of (x2 – 1)/(x2 + 3x – 4) as x approaches 1.
- a. 2/3
- b. 3/2
- c. ¾
- d. 2/5
Find the distance from the vertex to focus of a parabola y2 – 4y – 12x – 40 = 0.
- a. 3
- b. 4
- c. 5
- d. 6
Compute the area of the ellipse 9×2 + 4y2 = 40.
- a. 18.2 units
- b. 20.9 units
- c. 22.7 units
- d. 24.5 units
Find the center of the circle of the equation x2 + y2 – 2x + 4y – 28 = 0.
- a. (1, 2)
- b. (1, -2)
- c. (-1, -2)
- d. (-1, 2)
Find the distance from the line 5x – 4y + 6 = 0 to point (3, 2).
- a. 2
- b. 3
- c. 5
- d. 4
Find the equation of the line with slope 4 and a y-intercept of 1.
- a. 4x+y+1=0
- b. y-4x+1=0
- c. 4x-y+1=0
- d. 4x-y+2=0
The side of opposite the right angle of a right triangle is:
- a. Apothem
- b. Median
- c. Quadrilateral
- d. Hypotenuse
An instrument for measuring specific gravity of fluids is:
- a. Flow meter
- b. Hygrometer
- c. Hydrometer
- d. Calorimeter
The National Association for Mechanical Engineers accredited by the Professional Regulation Commission:
- a. PSME
- b. PAMEE
- c. AGMEEP
- d. IIEE
Minimum grade of Mechanical Engineer required in the design and preparation of plans of a 280 kW diesel power plant:
- a. PME
- b. RME
- c. MPE
- d. CPM
The difference between the book value and the actual lower resale value is:
- a. Salvage value
- b. Resale value
- c. Fixed costs
- d. Sunk cost
It occurs when a unique product or service is available only from a single supplier and entry of all other possible suppliers prevented:
- a. Inventory
- b. Monopoly
- c. Competition
- d. Profitability
A rivet is double shear
- a. Is always hand driven
- b. Has four times the strength of a rivet in simple shear
- c. Has twice the strength as a rivet in single shear
- d. Has the same strength as a rivet in single shear
Kind of obligation which has no condition attached
- a. Pure
- b. Private
- c. Analytic
- d. Gratuitous
In fluid dynamics, there is what is called conservation laws. One of the laws state that fluids mass is always conserved in fluid systems, regardless of the pipeline’s complexity orientation of the flow or type of fluid flowing. The law is called:
- a. Conservation of volume
- b. Conservation of mass
- c. Conservation of energy
- d. Conservation of power
The type of vibration which is caused by fluctuating vertical couples which tend to make the ends of the engine rise and fall:
- a. Pitching
- b. Blanking
- c. Splitting
- d. Bleaching
The line connecting (x, 5) and (10, y) is bisected by the point (8, 4). Find the value of x and y.
- a. x=6, y=2
- b. x=-3, y=-6
- c. x=3, y=5
- d. x=6, y=3
Given three vertices of a triangle whose coordinates are A(1, 1), B(4, -4) and C(6, -4). Find the area of the triangle.
- a. 4 sq. units
- b. 8 sq. units
- c. 5 sq. units
- d. 7 sq. units
Find the distance between A(5, -4) and B(-3, 6).
- a. 10.7 units
- b. 12.8 units
- c. 14.9 units
- d. 16.5. units
Each interior angle of a regular dodecagon is equal to ____ degrees.
- a. 150 deg
- b. 130 deg
- c. 120 deg
- d. 110 deg
Each interior angle of a sector is 35 degrees and the radius is 20 cm. What is the area of the sector?
- a. 110.2 cm²
- b. 135.1 cm²
- c. 122.2 cm²
- d. 141.9 cm²
Given a triangle of sides 12 cm and 18 cm and an included angle of 60 degrees. Find the area of the triangle.
- a. 90.1 cm²
- b. 95.0 cm²
- c. 92.9 cm²
- d. 93.5 cm²
If an equilateral triangle is circumscribed about a circle of radius 12 cm, determine the side of the triangle.
- a. 16.2
- b. 18.3
- c. 20.8
- d. 21.7
Determine the value of log of 45 to base 9.
- a. 2.31
- b. 1.73
- c. 3.22
- d. 4.01
If log 3 = x and log 4 = y, find log 1.5 in terms of x and y.
- a. 3x-y+4
- b. 3x+y+1
- c. 3x-2y+1
- d. 3x+y-2
If the log of 4 to the base 4 plus log of x to the base 4 is equal to 5, then the value of x is ___.
- a. 225
- b. 256
- c. 267
- d. 232
If the sides of parallelogram and an included angle are 7, 11 and 100 deg, respectively, find the length of the shorter diagonal.
- a. 12.71
- b. 13.21
- c. 11.97
- d. 14.82
Which of the following flow meters measure the average fluid velocity in a pipe rather than a point or local velocity?
- a. Humeter
- b. Venturi meter
- c. Speedometer
- d. Flow meter
The speed at which an exact model of the pump would run if it were designed to deliver 1 gpm against 1 ft per stage
- a. Pump capacity
- b. Linear speed
- c. RPM
- d. Specific Speed
Fluid which exhibits linear stress-strain rate relationship. If the shear in a fluid varies linearly with the velocity gradient, which of the following describes the fluid?
- a. It is a Newtonian Fluid
- b. It is a viscous fluid
- c. It is a less viscous fluid
- d. None of the above.
Mario is standing on a weighing scale attached to the floor of an elevator which reads zero. What does this indicate
- a. Mario is still accelerating
- b. Mario is at rest
- c. Mario is moving at constant speed
- d. Mario is freely falling
At what angle does a projectile go farthest?
- a. 75 deg
- b. 60 deg
- c. 45 deg
- d. 30 deg
What causes space capsules to become hot when they re-enter the earth’s atmosphere?
- a. The firing of its rocket engine
- b. The earth atmosphere is hot
- c. The friction of the air
- d. All of the above
Why should a person weigh less on the moon than on earth?
- a. The mass of the moon is smaller than the mass of the earth
- b. The moon is only a satellite of the earth
- c. The force of earth’s gravity is greater than that of the moon
- d. None of the above
Turbulence is said to exist when:
- a. Pipe friction exists
- b. The velocity distribution in cross section is uniform
- c. Cross current exists
- d. Streamline, parallel in direction
An obtuse angle is ____ than a right angle.
- a. Equal
- b. Greater than 180 deg
- c. greater
- d. Lesser
What solid figure that has many faces?
- a. Decagon
- b. Polygon
- c. Octagon
- d. Polyhedron
sin (270^o + A) is equal to ___.
- a. –cosA
- b. cosA
- c. –sinA
- d. cscA
If sin A = 3.522x, cos A = 4.155x and sin 2A = 4.945x, find the value of x.
- a. 0.1321
- b. 0.1690
- c. 0.1872
- d. 0.1291
If sec 2A = 1/sin 3A, find the angle A in degrees.
- a. 18 deg
- b. 20 deg
- c. 16 degd. 22 deg
If sin 3A = cos 6B then:
- a. A–B=30
- b. A-2B=28
- c. A+2B=30
- d. A-3B=30
If sin A = ¾, what is the value of 1 – cos A?
- a. 0.6721
- b. 0.4522
- c. 0.3121
- d. 0.3386

Answer Key (Handwritten)