MSTE LOOKS-FAM
C
Dr. Irving Weiman, who is always in a hurry, walks up an up going escalator at the rate of one step per second. Twenty steps bring him to the top. Next day he goes up at two steps per second, reaching the top in 32 steps. How many steps are there in the escalator? 30 90 80 40
C
A ball was dropped from the height of 10 feet. It rebounds one-half the distance on each bounce. What is the total distance it travels? 10 20 30 40
C
A billiard table is in the form of an ellipse with one axis two feet longer than the other. A ball is stuck from one focus and after bounding against two cushions returns to its starting point. At the halfway point in its trip the ball is eight feet from the source. How big is the table? 13 and 15 ft 14 and 16 ft 15 and 17 ft 16 and 18 ft
A
A passenger ferry makes trips from a town to an island community that is 7 miles down shore from the town and 3 miles off a straight shoreline. The ferry travels along the shoreline to some point and then proceeds directly to the island. If the ferry travels 12 mi hour along the shoreline and 10 mi hour as it moves out to sea, determine the routes that have a travel time of 45 minutes. 1.9 miles 2 miles 2.7 miles 1 miles
A
A radiator contains 8 quarts of a mixture of water and antifreeze. If 40% of the mixture is antifreeze, how much of the mixture should be drained and replaced by pure antifreeze so that the resultant mixture will contain 60% antifreeze? 8/3 7/2 5/4 2/9
C
A record enthusiast decided to calibrate his 33 1/3 rpm player by placing equally spaced dots around the rim. What is the minimum number of dots required in order that they appear stationary under 60 cycles light? 211 147 216 136
C
A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder of altitude 10 feet with a hemisphere attached to each end. The radius r is yet to be determined. Express the volume V (in ft^3 ) of the tank a function of r (in feet). 3/2πr^2(2r - 15) 2/5πr^2(2 + 15r) 2/3πr^2(2r + 15) 4/7πr^2(2r - 15r)
A
A surveyor observes that at a point A, located on level ground a distance 25.0 feet from the base B of a flagpole, the angle between the ground and the top of the pole is 30°. Approximate the height h of the pole to the nearest tenth of a foot. 14.4 ft 9.7 ft 11.2 ft 13.8 ft
C
A, B, and C are three towns, each pair being connected by a network of roads. A motorist notices that there are 82 routes from A to B, including those via C and 62 routes from B to C, including those via A. He also notices that there are fewer than 300 routes from A to C, including those via B. How many are there? 44 45 46 47
A
An Origami expert started making a Nani-des-ka by folding the top left corner of a sheet of paper until it touched the right edge and the crease passed through the bottom left corner. He then did the same with the lower right corner, thus making two slanting parallel lines. The paper was 25 inches long and the distance between the parallel lines was exactly 7/40 of the width. How wide was the sheet of paper? 24 19 37 54
D
An electric iron is in the form of two arcs of circles 20 inches in diameter, each are being 9inches long. The back of the iron is on the line of centers of the two circles. What is the angle at the point? 52°32' 52°24' 51°34' 52°34'
D
An engineer must take three space suits in two test chambers. Each suit must be tested for 1 hour at each of two low pressures. He takes ten minutes to load a suit in a chamber, set the pressure, and start the test; 4 min. to change the pressure, and ten min. to unload the suit from a chamber. What is the minimum time to complete the tests? 5hr and 42 mins 2hr and 55 mins 5hr and 37 mins 3hr and 54 mins
C
By the time the radius of a certain pearl has increased 1 mm, the area will have increased as much (in square mm) as the volume (in cubic mm). If the pearl is an exact sphere, what is the radius now? 1.254 1.704 1.457 1.344
A
The rhythmic process of breathing consists of alternating periods of inhaling and exhaling. One complete cycle normally takes place every 5 seconds. If F(t) denotes the air flow rate at time t (in liters per second) and if the maximum flow rate is 0.6 liter per second, find a formula of the form F(t)= a sin bt that fits this information. 0.6 sin (2π/5)(t) 0.5 cos (2/5)(t) 0.3 tan (2t/5)(π) 0.1 sin (2π/5)(π)
D
There are four volumes of an encyclopedia on a shelf, each volume containing 300 pages, (that is numbered 1 to 600), but these have been placed on the shelf in random order. A bookworm starts at the first page of Vol.1 and eats his way through to the last page of Vol 4. What is the expected number of pages (excluding covers) he has eaten through? 100 400 700 500
C
A hospital nursery contains only two baby boys; the girls have not yet been counted. At 2:00 pm s new baby is added to the nursery. A baby is then selected at a random to be the first to have its footprint taken. It turns out to be a boy. What is the probability that the last addition to the nursery was girl? 1/7 3/8 2/5 1/4
D
A lighthouse shows successive one-second flashes of red, white, green, green, white, red. A second lighthouse does the same only with two second flashes. The six-second sequence of the first lighthouse is repeated steadily, as is the twelve- second sequence of the other lighthouse. What fraction of the time do the two lights show the same color if the given sequences start at the same time? 4/6 2/6 5/6 1/6
D
A logistic curve is the graph of an equation of the form y =k/1+be^−ex , where k, b and c are positive constants. In the famous study of growth of protozoa by Gause, a population of Paramecium caudate was found to be described by a logistic equation with c=1.1244, k=105 and x the time in days. Find b if the initial population was 3 protozoa. 31 32 33 34
D
Find the slope-intercept form for the line through P(5,7) that is perpendicular to the line 6x + 3y =4 17/3 −15/4 13/5 −19/2
B
For a drug to have a beneficial effect, its concentration in the bloodstream must exceed a certain value, which is called the minimum therapeutic level. Suppose that the concentration c (in mg L) of a particular drug t hours after it is taken orally is given by c =20t/t^2+4 , if the minimum therapeutic level is 4 mg/L. Determine when this level is exceeded. 1> t > 4 1< t < 4 2< t < 4 2> t > 4
C
How many people would you expect to meet before you met one who was born on a Wednesday? 2 5 7 3
B
Ian barista 10 9 17 7
A
A bridge across a river is in the form of an arc of s circle. A boy walking across the bridge finds that 27 feet from the shore the bridge is 9 feet above the water. He continues on to the center of the span and finds that the bridge is now 10 feet above the water. How deep is the river? 80 45 60 70
B
A candle 15 inches long will burn in 9 hours, 1 inch at the lesser end will be consumed in 20 minutes less than the same length at the larger end. How long will it take for an inch at the lesser end to be consumed? 26.34 26.43 24.62 24.26
A
A commercial fishing boat uses sonar equipment to detect a school of fish 2 miles east of the boat and traveling in the direction of N51°W at a rate of 8 mi/hour. If the boat travels at 20 mi/hour. Approximate to the nearest 0.1°. The direction it should head to intercept the school of fish is? N75.4°E N45.7°W S35.4°E S34.5°W
D
A cross section through the center of a football is a circle x inches in circumference. The football is x-8 inches long from tip to tip and each seam is an arc of a circle 3/4 of x inches in diameter. Find x. 24 m x 46 m 24 m x 16 m 23 m x 26 m 24 m x 36 m
D
A grain-elevator hopper is to be constructed as shown in Figure 4, with a right circular cylinder of radius 2 feet and altitude h feet on top of a right circular cone whose altitude is one-half that of the cylinder. What value of h will make the total volume V of the hopper 500 ft? 27.4 ft 19.5 ft 43.7 ft 34.1 ft
A
Immediately after Mayon volcano showed tell-tale signs of activity, the PHIVOLCS set up stations to monitor the volcano. Two of such stations were located at points A and B, 7 km apart and on the same horizontal plane as the base of the volcano. From station A, the angle of elevation of the top of Mayon is 8°. When the volcano erupted, the volcanic ash emitted above its crater suspended an angle of 64° from each station A and B. Assuming that the points of observations are on the same vertical plane, find the height of the ash. 32.3 km 36.8 km 30.8 km 28.4 km
A
In Bristol 90% of the citizens drink tea; 80% drink coffee; 70% drink whiskey; and 60% drink gin. No one drinks all four beverages. What percent of Bristol's citizens drink liquor? 100 99 98 97
C
In a certain community there are 1000 married couples. Two thirds of the husbands who are taller that their wives are also heavier and three quarters of the husbands who are heavier than their wives are also taller. If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller and heavier that their wives? 360 200 480 560
A
In the battle of Small Tuba, the troopers always outnumbered 3 to 1, made every shot count. Ultimately both sides were wiped out. What fraction of braves' shot hit their mark? 1/8 3/4 2/9 6/7
B
Lazy Levy wishes to toss a snowball over a building 144 ft x 144 ft and133 ft high with the least expenditure of energy. How far away from the building should he stand? Hint: Derive constraints to specify the required parabola. 83 ft 84 ft 85 ft 86 ft
A
Metal sphere 264.5 cm 214.8 cm 325.8 cm 526.3 cm
B
Obviously the smaller the compounding period, the greater the interest. How much does one dollar amount to after one year at 100% per annum interest, compounded continuously, i.e., instantaneously? 2.65 2.71 2.88 2.44
A
Passenger on an excursion bus A. included among the 18 children were 8 married couples. B. included among the 18 children were 6 married couples. C. included among the 18 children were 10 married couples. D. included among the 18 children were 4 married couples.
D
Samsung 1246 1428 1086 1194
D
Sand pouring from a conveyor form into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute. 4π ft/min 2π ft/min 5π ft/min 3π ft/min
B
Some Civil Engineering students decide to have a parade during Engineering Week. When the students form ranks of 3 abreast, two are left over. In ranks of 5, four students are left over. In ranks of 7, six are left over. In ranks of 11, ten are left over. What is the least possible number of students in the parade? 1362 1154 986 1028
D
The slope distance and zenith angle between points A and B were observed with a total station instrument as 9585.26 feet and 81°42'20" respectively. The H.I. and rod readings r were equal. If the elevation of A is 1238.42 ft, compute the elevation of B. Consider the effect of curvature and refraction correction. Hint: Ho = 0.0206M? where M is in thousands of feet 2621 ft 2612 ft 1632 ft 2623 ft
C
The weight that can be safely supported by a beam with a rectangular cross section varies directly as the product of the width and square of the depth of the cross section and inversely as the length of the beam. If a 2-inch by 4-inch beam that is 8 feet long safely supports a load of 500 pounds, what weight can be safely supported by a 2-inch by 8-inch beam that is 10 feet long? (Assume that the width is the shorter dimension of the cross section.) 1344 lb 2400 lb 1600 lb 3500 lb
D
There are nine cities which are served by two competing airlines. One or the other airline (but not both) have 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)? 18 9 14 12
C
Tv weather forecaster 25% 76.7% 83.3% 50%
A
Two motorists set out at the same time to go from A to B, a distance 100 miles. They both followed the same route and traveled at different, though uniform, speeds of an integral number of mile per hour. The difference in their speeds was a prime number of miles per hour, and after they had been driving for two hours the slower car was five times further from A than the faster car was from B. How fast did the two motorists drive? 42 and 40 32 and 41 30 and 65 43 and 41
B
Two ships leave port at the same time, one sailing west at a rate of 17 mi/hr and the other sailing south at 12 mi/hr. If t is the time (in hours) after their departure, express the distance d between the ships as a function of t. 19.9(t) 20. 8(t) 23.4(t) 21.3(t)