April 2024 MSTC EERC Exam PDF

# Engineering Review and Learning Center ## APRIL 2024 Exams ### 1. (APRIL 2024) A package of floor tiles contains 24 one-foot-square tiles. Find how many packages should be bought to cover a square ballroom floor whose side measures 64 feet. A. 161 packages B. **171 packages** C. 151 packages...

# Engineering Review and Learning Center ## APRIL 2024 Exams ### 1. (APRIL 2024) A package of floor tiles contains 24 one-foot-square tiles. Find how many packages should be bought to cover a square ballroom floor whose side measures 64 feet. A. 161 packages B. **171 packages** C. 151 packages D. 141 packages ### 2. (APRIL 2024) A geology professor has five silicates, seven pyrites, and eight carbonates in a rock collection. He picks six rocks at random for a student to analyze. Find the probability that the professor picked two silicates, one pyrite, and three carbonates. A. 0.202 B. **0.101** C. 0.303 D. 0.404 ### 3. (APRIL 2024) There are nine cities which served by two competing airlines. One or the other airline (but not both) has a flight between every pair of cities. What is the minimum number of triangular flights (i.e., trips from A to B to C and back to A on the same airline)? A. 12 B. **16** C. 18 D. 20 ### 4. (APRIL 2024) One lane of a two-lane highway was observed for an hour during the day. The following data were gathered: Average distance between front bumpers of successive cars: 80 ft Average mean speed during the study: 30 mph Space mean speed: 29 mph A. **1.9 sec/veh** B. 2.9 sec/veh C. 4.9 sec/veh D. 3.9 sec/veh ### 5. (APRIL 2024) Find the expected production in loose cubic meters (Lm3) per hour of a small hydraulic excavator. Heaped bucket capacity is 0.57 m3. The material is sand and gravel with bucket fill factor of 0.95. Job efficiency is 50 min/h. Average depth of cut is 4.3 m. Maximum depth of cut is 6.1 m and average swing is 90. Hint: Productions (LCY/h) = C×S×V×B×E Cycle output = 250 cycles/60 min Swing depth factor = 1.0 A. 111 LCM/h B. **131 LCM/h** C. 133 LCM/h D. 113 LCM/h ### 6. (APRIL 2024) Find the volume generated when the first quadrant area bounded by y = x2, the y-axis, and the lines y = 1 and y = 4 is rotated about the y-axis. A. 17π/2 B. 13π/2 C. **15π/2** D. 11π/2 ### 7. (APRIL 2024) Northern Gold Mining bought a mine site with 500,000 tons of recoverable ore for $800,000. Of this total, $50,000 is the land's estimated value. If 40,000 tons are processed this year, the revenue from 5500 ounces of gold is $1.8M, and the expenses (other than depletion) are $1.6M. What is the percentage depletion, and should cost or percentage depletion be claimed? A. No, because the percentage depletion of $100K exceeds the cost depletion of $60K. B. **Yes, because the percentage depletion of $100K exceeds the cost depletion of $60K.** C. Yes, because the percentage depletion of $60K exceeds the cost depletion of $100K. D. No, because the percentage depletion of $60K exceeds the cost depletion of $100K. ### 8. (APRIL 2024) Two linear waves have the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transits more energy and by what factor? A. The wave with the shorter wavelength will transmit two times as much energy as the other wave. B. **The wave with the shorter wavelength will transmit four times as much energy as the other wave.** C. The wave with the longer wavelength will transmit two times as much energy as the other wave. D. The wave with the longer wavelength will transmit four times as much energy as the other wave. ### 9. (APRIL 2024) A company determines that in the production of x units of a commodity its revenue and cost functions are, respectively, R(x) = -3x3 + 970X and C(x) = 2x2 + 500. Find the maximum profit and maximum average cost. A. Php 54.32 B. **Php 25.43** C. Php 32.54 D. Php 43.25 ### 10. (APRIL 2024) What is the proper sequence of the following polygons? I. Quadrilateral II. Parallelogram III. Rectangle IV. Square A. I, II, IV, III B. II, I, III, IV C. **I, II, III, IV** D. IV, III, I, II ### 11. (APRIL 2024) A rectangular field bounded on one side by a building is to be fenced on the other 3 sides. If 3000 ft of fence is to be used, find the dimensions (in feet) of the largest field that can be fenced in. A. 800 by 1,600 B. 1,500 by 750 C. 400 by 1,200 D. **750 by 1,500** ### 12. (APRIL 2024) A car travels over the crest of a hill at 10.0 m/s. The radius of curvature at the crest is 12.0 m. Determine the minimum speed required for the passenger to feel momentarily weightless. A. 10.58 m/s B. 10.88 m/s C. **10.85 m/s** D. 10.55 m/s ### 13. (APRIL 2024) For a water treatment plant having a flow of flowrate of 432 cubic meter per hour, what is the required plan area of a type I settling tank to remove 90% of the particles having a setting velocity of 0.12 cm/sec? A. 120 m2 B. 111 m2 C. **90 m2** D. 100 m2 ### 14. (APRIL 2024) The following table shows areas of cut and fill sections at locations 50 ft apart. Assume a shrinkage = 12% and bulking = 25%. Cumulative earthwork (yd3) between stations 0+00 and 3+00 is most nearly? | Station | Area (ft²) | |:------------|:----------:| | | Cut | Fill | | 0+00.00 | 536.2 | 342.2 | | 0+50.00 | 213.5 | 213.6 | | 1+00.00 | 123.5 | 343.3 | | 1+50.00 | 654.6 | 111.0 | | 2+00.00 | 973.1 | 762.4 | | 2+50.00 | 567.3 | 342.9 | | 3+00.00 | 451.6 | 190.4 | A. 2,200 B. **2,500** C. 1,850 D. 1,340 ### 15. (APRIL 2024) A horizontal compound curve connects two tangents. The bearing of the back tangent is N46°25'32"E and the bearing of the forward tangent is S17°56'21"E. The curve radii to be used are R1 = 1,800 and R2 = 900. The PC is located at station 138 + 34.12 and the PI at station 158 + 12.98. A. 145 + 12.54 B. 147+05.23 C. **148 + 50.61** D. 151 + 03.32 ### 16. (APRIL 2024) An athlete performing a long jump leaves the ground at 27 degrees and lands 7.80 m away. What was the takeoff speed? A. 9.37 B. **9.73** C. 7.39 D. 7.93 ### 17. (APRIL 2024) How much will a man have at the end of thirty days, when he received 1 cent on the day one and on each other day he received double the amount of the previous day? A. 5,368,709.12 B. **5,368,790.12** C. 5,368,709.21 D. 5,368,790.21 ### 18. (APRIL 2024) A hoisting mechanism uses a cable system as shown below. If the load, W = 3 tons, the effort required (lb) at point B is most nearly. **Note:** The image of the cable system is not provided, therefore, a solution cannot be provided for this problem. A. 1345 B. **1715** C. 2065 D. 2350 ### 19. (APRIL 2024) A 4-lane divided highway (2 lanes in each direction) currently has ADT of 23,000 vehicles (each way). Approximately 12% of the traffic consists of trucks. Traffic is expected to grow by a 4% annual rate over the next 20 years. Table 1 shows data collected from a weigh station during a typical day for 1,078 trucks. | Axle Load (k) | Number of Single Axles | Number of Tandem Axles | |:--------------|:-----------------------|:-----------------------| | 10 | 2420 | | | 14 | 630 | | | 18 | 301 | | | 20 | 22 | | | 22 | 6 | 24 | | 25 | 1 | 15 | | 28 | | 12 | | 32 | | 11 | | Axle Load (k) | Load Equivalence Factor (Single Axles) | |:--------------|:---------------------------------| | 10 | 0.0877 | | 14 | 0.360 | | 18 | 1.0 | | 20 | 1.51 | | 22 | 2.18 | | 25 | 3.53 | | Axle Load (k) | Load Equivalence Factor (Tandem Axles) | |:--------------|:---------------------------------| | 22 | 0.180 | | 25 | 0.308 | | 28 | 0.495 | | 32 | 0.857 | Using the Asphalt Institute Load Equivalence Factors (LEF) shown in Table 2, the design 20-year 18-k ESAL (W18) is most nearly. A. 9 × 106 B. 15 × 106 C. 20 × 106 D. **23 × 106** ### 20. (APRIL 2024) It is the purpose for which a building or other structures or part thereof, is used for intended to be used. A. Residential B. Commercial C. **Occupancy** D. None of the Above ### 33. E-mail Messages Use the frequency polygon below to answer the following questions. **Note:** The image of the frequency polygon is not provided, therefore, a solution cannot be provided for this problem. ### 37. A crest on a section of highway consists of a vertical curve with a 1500 m radius and a positive 1% grade followed by a negative 3% grade. The design requirements are as follows. design speed = 80 km/h driver eye height = 1.2 m object (to be avoided) height = 0.2 m stopping sight distance = 300 m The minimum required length of vertical curve needed to satisfy the design stopping sight distance is most nearly (A) 680 m (B) 700 m (C) 760 m (D) **840 m** ### 38. A superpave design mixture for a highway with ESALS < 107 has a nominal maximum aggregate size of 19 mm. The mixture has been tested and has the following characteristics: air voids = 4.0% VMA = 13.2% VFA = 70% dust-to-asphalt ratio = 0.97 at N = 8 gyrations, Gmm = 87.1% at N = 174 gyrations, Gmm = 97.5% Do these characteristics satisfy their corresponding superpave requirements? (A) **Yes, all the parameters are within an acceptable range.** (B) No, the VMA is excessive. (C) No, the dust-to-asphalt ratio is too high. (D) ) No, Gmm at Nmax is too high. ### Problems 31 and 31 are based on the following information. The connection matrix shown represents a road transportation network between six locations. | Node | 1 | 2 | 3 | 4 | 5 | 6 | |:-----|:---|:---|:---|:---|:---|:---| | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 2 | 1 | 0 | 1 | 0 | 0 | 1 | | 3 | 0 | 1 | 0 | 1 | 1 | 0 | | 4 | 0 | 0 | 1 | 0 | 1 | 0 | | 5 | 1 | 0 | 1 | 1 | 0 | 1 | | 6 | 1 | 1 | 0 | 0 | 1 | 0 | ### Problem 32 The total number of arcs in the network is (A) 0 (B) 1 (C) **2** (D) 3