C. Silver = 5 oz.; Gold = 10 oz.
D. Silver = 7.8 oz.; Gold = 4.2 oz.
Problem 164(ME April 1998)
A pump can pump out a tank in 11 hours. Another pump can pump out the same tank in 20 hours. How long it will take both pumps together to pump out the tank?
A. ½ hour B. ½ hour C. 6 hours D. 7 hours Problem 165
Mr. Brown can wash his car in 15 minutes, while his son John takes twice as long as the same job. If they work together, how many minutes can they do the washing?
A. 6
B. 8 C. 10 D. 12 Problem 166
One pipe can fill a tank in 5 hours and another pipe can fill the same tank in 4 hours. A drainpipe can empty the full content of the tank in 20 hours. With all the three pipes open, how long will it take to fill the tank?
A. 2 hours B. 2.5 hours C. 1.92 hours D. 1.8 hours Problem 167
A swimming pool is filled through its inlet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters through its inlet and simultaneously allowed to leave through its
outlet, the pool is filled in 7 ½ hours. Find how long will it take to fill the pool with the outlet closed.
A. 6 B. 2 C. 3 D. 5
Problem 168
Three persons can do a piece of work alone in 3 hours, 4 hours and 6 hours respectively. What fraction of the job can they finish in one hour working together?
A. ¾ B. 4/3 C. ½ D. 2/3 Problem 169
A father and his son can dig a well if the father works 6 hours and his son works 12 hours or they can do it if the father works 9 hours and son works 8 hours. How long will it take for the son to dig the well alone?
A. 5 hours B. 10 hours C. 15 hours D. 20 hours Problem 170
Peter and Paul can do a certain job in 3 hours. On a given day, they work together for 1 hour then Paul left and Peter finishes the rest work in 8 more hours. How long will it take for Peter to do the job alone?
A. 10 hours B. 11 hours C. 12 hours D. 13 hours
Problem 171 (ECE November 1995)
Pedro can paint a fence 50% faster than Juan and 20% faster than Pilar and together they can paint a given fence in 4 hours. How long will it take Peter to paint the same fence if he had to work alone?
A. 10 hrs.
B. 11hrs.
C. 13hrs.
D. 15hrs.
Problem 172
Nonoy can finish a certain job in 10 days if Imelda will help for 6 days. The same work can be done by Imelda in 12 days if Nonoy helps for 6 days. If they work together, how long will it take for them to do the job?
A. 8.9 B. 8.4 C. 9.2 D. 8 Problem 173
A pipe can fill up a tank with the drain open in three hours. If the pipe runs with the drain open for one hour and then the drain is closed it will take 45 more minutes for the pipe to fill the tank.
If the drain will be closed right at the start of filling, how long will it take for the pipe to fill the tank?
A. 1.15hrs.
B. 1.125hrs C. 1.325hrs.
D. 1.525hrs.
Problem 174
Delia can finish a job in 8 hours. Daisy can do it in 5 hours. If Delia worked for 3 hours and then Daisy was asked to help her finish it, how long will Daisy have to work with Delia to finish the job?
A. 2/5 hours B. 25/14 hours C. 28 hours D. 1.923 hours
Problem 175 (CE November 1998)
A job could be done by eleven workers in 15 days. Five workers started the job. They were reinforced with four more workers at the beginning of the 6th day. Find the total number of days it took them to finish the job.
A. 22.36 B. 21.42 C. 23.22 D. 20.56
Problem 176
On one job, two power shovels excavate 20000m3 of earth, the larger the shovel working for 40 hours and the smaller shovel for 35 hours. Another job, they removed 40000m3 with the larger shovel working for 70 hours and the smaller working 90 hours. How much earth can the larger shovel move in one hour?
A. 173.91 B. 347.83 C. 368.12 D. 162.22
Problem 177 (EE April 1996)
A and B can do a piece of work in 42 days, B and C in 31 days, and A and C in 20 days.
Working together, how many days can all of them finish the work?
A. 18.9 B. 19.4 C. 17.8 D. 20.9 Problem 178
Eight men can dig 150 ft of trench in 7hrs. Three men can backfill 100ft of the trench in 4hrs.
The time it will take 10 men to dig and fill 200 ft of trench is:
A. 9.867hrs.
B. 9.687hrs.
C. 8.967hrs.
D. 8.687hrs.
Problem 179
In two hours, the minute hand of the clock rotates through an angle of : A. 45°
B. 90°
C. 360°
D. 720°
Problem 180
In one day (24 hours), how many times will the hour hand and minute hand of a continuously driven clock be together
A. 21 B. 22
C. 23 D. 24 Problem 181
How many minutes after 3:00 will the minute hand of the clock overtakes the hour hand?
A. 14/12 minutes B. 16-11/12 minutes C. 16-4/11 minutes D. 14/11 minutes Problem 182
How many minutes after 10:00 o’clock will the hands of the clock be opposite of the other for the first time?
A. 21.41 B. 22.31 C. 21.81 D. 22.61 Problem 183
What time between the hours of 12:00 noon and 1:00 pm would the hour hand and the minute hand of a continuously driven clock be in straight line?
A. 12:33 pm B. 12:30 pm C. 12:37 pm D. 12:287 pm
Problem 184 (GE February 1997)
At what time after 12:00 noon will the hour hand and the minute hand of a clock first form a n angle of 120°?
A. 21.818 B. 12:21.818 C. 21.181 D. 12:21.181
Problem 185 (GE February 1994)
From the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describes an arc of:
A. 360°
B. 120°
C. 540°
D. 720°
Problem 186
It is now between 3 and 4 o’clock and in twenty minutes the minute hand will be as much as the hour-hand as it is now behind it. What is the time now?
A. 3:06.06 B. 3:07.36 C. 3:09.36 D. 3:08.36
Problem 187 (EE October 1990)
A man left his home at past 3:00 o’clock PM as indicated in his wall clock. Between two to three hours after, he returned home and noticed that the hands of the clock interchanged. At what time did he left his home?
A. 3:27.27 B. 3:31.47 C. 3:22.22 D. 3:44.44 Problem 188
The sum of the reciprocals of two numbers is 11. Three times the reciprocal of one of the numbers is three more than twice the reciprocal of the other number. Find the numbers.
A. 5 and 6 B. 7 and 4 C. 1/5 and 1/6 D. 1/7 and ¼ Problem 189
If a two digit number has x for its unit’s digit and y for its ten’s digit, represent the number.
A. yx B. 10y + x C. 10x + y D. x + y Problem 190
One number if five less than the other number. If their sum is 135, what are the numbers?
A. 70&75 B. 60&65 C. 65&70 D. 75&80
Problem 191
In a two-digit number, the unit’s digit is 3 greater than the ten’s digit. Find the number if it is 4 times as large as the sum of its digits.
A. 47 B. 58 C. 63 D. 25 Problem 192
Find two consecutive even integers such that the square of the larger is 44 greater than the square of the smaller integer.
A. 10&12 B. 12&14 C. 8&10 D. 14&16 Problem 193
Twice the middle digit of a three-digit number is the sum of the other two. If the number is divided by the sum of its digit, the answer is 56 and the remainder is 12. If the digits are reversed, the number becomes smaller by 594. Find the number.
A. 258 B. 567 C. 852 D. 741 Problem 194
The product f three consecutive integers is 9240. Find the third integer.
A. 20 B. 21 C. 22 D. 23 Problem 195
The product if two numbers is 1400. If three (3) is subtracted from each number, their product becomes 1175. Find the bigger number.
A. 28 B. 50 C. 32
D. 40 Problem 196
The sum of the digits of the three-digit number is 14. The hundreds digit being 4 times the units digit. If 594 is subtracted from the number, the order of the digits will be reversed. Find the number.
A. 743 B. 563 C. 653 D. 842
Problem 197 (ECE March 1996)
The sum of two numbers is 21, and one number is twice the other. Find the numbers.
A. 7 and 14 B. 6 and 15 C. 8 and 13 D. 9 and 12
Problem 198 (ECE March 1996)
Ten less than four times a certain number is 14. Determine the number.
A. 4 B. 5 C. 6 D. 7
Problem 199 (ECE November 1997)
The denominator of a certain fraction is three more than twice the numerator. If 7 is added to both terms of the fraction, the resulting fraction is 3/5. Find the original fraction.
A. 8/5 B. 5/13 C. 13/5 D. 3/5 Problem 200
Three times the first of the three consecutive odd integers is three more than twice the third. Find the third integer.
A. 9 B. 11 C. 13 D. 15
Motion Variation, Percent, Miscellaneous Problems Problem 201
Nonoy left Pikit to drive to Davao at 6:15 PM and arrived at 11:45 PM averaged 30 mph and stopped 1 hour for dinner, how far is Davao from Pikit.
A. 128 B. 135 C. 160 D. 256 Problem 202
A man fires a target 420 m away hears the bullet strikes to 2 second after he pulled the trigger.
An observer 525 m away from the target and 455 m from the man heard the bullet strike the target one second after he heard the report of the rifle. Find the velocity of the bullet.
A. 525 m/s B. 360 m/s C. 350 m/s D. 336 m/s Problem 203
A man travels in a motorized banca at rate of 12 kph from his barrio to the poblacion and come back to his barrio at the rate of 10 kph. If his total time of travel back and forth is 3 hours and 10 minutes, the distance from the barrio to the poblacion is :
A. 17.27 km B. 17.72 km C. 12.77 km D. 17.32 km Problem 204
It takes Michael 60 seconds to run around a 440-yard track. How long does it take Jordan to run around the track if they meet in 32 second after they start together in a race around the track in opposite direction?
A. 58.76 seconds B. 68.57 seconds C. 65.87 seconds D. 86.57 seconds
Problem 205
Juan can walk from his home to his office at the rate of 5 mph and back at the rate 2 mph. What is his average speed in mph?
A. 2.86 B.3.56 C.4.12 D.5.89
Problem 206
Kim and Ken traveled at the same time at the rate of20m/min,from the same pointon a circular track of radius 600 m. If Kim walks along a circumference and Kim towards the center,find their distance after 10 minutes.
A.193 m B.202 m C.241 m D.258 m Problem 207
Two ferryboats ply back and forth across a river with constant but different speeds, turning at the river banks without loss of time. They leave the opposite shores at the same instant, meet for the first time 900 meters from one shore, and meet for the second time 500 meters from the opposite shore. What is the width of the river?
A. 1500 m B. 1700 m C. 2000 m D. 2200 m
Problem 208 (CE May 1998)
A boat takes 2/3 as much time to travel downstream from C to D, as to return, If the rate of the river’s current is 8 kph, what is the speed of the boat in still water?
A. 38 B. 39 C. 40 D. 41
Problem 209 (ECE November 1998)
A man rows downstream at the rate of 5mph and upstream at the rate of 2mph. How far downstream should he go if he is to return in 7/4 hours after leaving?
A. 2 mi
B. 3.5 mi C. 3 mi D. 2.5 mi
Problem 210 (EE April 1997)
A jogger starts a course at a steady rate of 8kph. Five minutes later, a second jogger the same course at 10 kph. How long will it take for the second jogger to catch the first?
A. 20 min B. 25 min C. 30 min D. 35 min
Problem 211 (CE May 1999)
At 2:00 pm, an airplane takes off at 340mph on an aircraft carrier. The aircraft carrier moves due south at 25kph in the same direction as the plane. At 4:05 pm, the communication between the plane and aircraft carrier was lost. Determine the communication range in miles between the plane and the carrier.
A. 656 miles B. 785 miles C. 557 miles D. 412 miles Problem 212
A boat going across a lake 8km wide proceed 2 km at a certain speed and then completes the trip at a speed 1/2kph faster. By doing this, the boat arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the boat.
A. 2 kph B. 4 kph C. 9 kph D. 5 kph
Problem 213 (CE May 1993)
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 w when x=1, y=4 and z=2.
A. 4 B. 2 C. 1 D. 3
Problem 214 (ECE November 1993)
If x varies directly as y and inversely as z, and x=14 when y=7 and z=2, find x, when z=4 and y=16.
A. 14 B. 4 C. 16 D. 8
Problem 215
The electrical resistance of a cable varies directly as its length and inversely as the square of its diameter. If a cable 600 meters long and 25 mm in diameter has a resistance of 0.1 ohm, find the length of the cable 75 mm in diameter with resistance of 1/6 ohm.
A. 6000 m B. 7000 m C. 8000 m D. 9000 m Problem 216
The electrical resistance offered by an electric wire varies directly as the length and inversely as the square of the diameter of the wire. Compare the electrical resistance offered by two pieces of wire of the same material, one being 100 m long and 5 mm diameter, and the other is 50 m long and 3 mm in diameter.
A. R1 = 0.57 R2
B. R1 = 0.72 R2
C. R1 = 0.84 R2 D. R1 = 0.95 R2
Problem 217
The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motors. If it takes 20 seconds for a 5-hp motor to lift 50 lbs. through 40 feet, what weight can an 80-hp motor lift through a
distance of 40 feet within 30 seconds?
A. 1000 lbs.
B. 1150 lbs.
C. 1175 lbs.
D. 1200 lbs.
Problem 218 (ECE November 1995)
The time required by an elevator to lift a weight, vary directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30 seconds for a 10-hp motor to lift 100lbs through 50 feet, what size of motor is requires to lift 800 lbs. in 40 seconds through a distance of 40 feet?
A. 48 hp B. 50 hp C. 56 hp D. 58 hp
Problem 219
In a certain department store, the salary of saleslady is partly constant and varies as the value of her sales for the month, when the value of her sales for the month is P10000.00, her salary for that month is P900.00. When her sales goes up to P 2000.00 her monthly salary goes up to P1000.00. What must be the value of her sales for the month so that her salary for that month will be P2000.00?
A. P25000.00 B. P28000.00 C. P32000.00 D. P36000.00 Problem 220
A man sold 100 eggs, eighty of them were sold at gain of 30% while the twenty eggs were sold at a loss of 40%. What is the percentage gain or loss of the whole eggs?
A. 14%
B. 15%
C. 16%
D. 17%
Problem 221
The population of the country increases 5% each year. Find the percentage it will increase in three years.
A. 5%
B. 15%
C. 15.15%
D. 15.76%
Problem 222
Pedro bought two cars, one for P600000.00 and the other for P400000.00. He sold the first at a gain of 10% and the second at a loss of 12%. What was his total percentage gain or loss?
A. 6% gain B. 0% gain C. 1.20% gain D. 6% loss Problem 223
A grocery owner raises the prices of his goods by 10%. Then he starts his Christmas sale by offering the customers a 10% discount. How many percent of discount does the customers actually get?
A. nothing B. 1% discount C. 9% discount D. they pay 1% more Problem 224
Kim sold a watch for P3500.00 at a loss of 30% on the cost price. Find the corresponding loss or gain if he sold it for P5050.00.
A. 1% loss B. 10% loss C. 1% gain D. 10% gain Problem 225
By selling balut at P5.00 each, a vendor gains 20%. The cost price of egg rises by 12.5%. If he sells the balut at the same price as before, find his new gain in percent.
A. 7.5%
B. 5%
C. 8%
D. 6.25%
Problem 226
The enrollment at college A and college B both grew up by 8% from 1980 to 1985. If the enrollment in college A grew up by 800 and the enrollment in college B grew up by 840, the enrollment at college B was how much greater than the enrollment in college A in 1985?
A. 650 B. 504 C. 483 D. 540
Problem 227
A group consists of n boys and n girls. If two of the boys are replaced by two other girls, then 49% of the group members will be boys. Find the value of n.
A. 100 B. 49 C. 50 D. 51
Problem 228
On his Christmas Sale, a merchant marked a pair of slipper P180.00, which is 20% off the normal retail price. If the retail price is 50% higher than the whole sale price, what is the wholesale price of the slipper?
A. P18.00 B. P17.00 C. P15.00 D. P22.50 Problem 229
A certain XEROX copier produces 13 copies every 10 seconds. If the machine operates without interruption, how many copies will it produce in an hour?
A. 780 B. 46800 C. 1835 D. 4680 Problem 230
At a certain printing plant, each of the machines prints 6 newspapers every second. If all
machines work together but independently without interruption, how many minutes will it take to print the entire 18000 newspapers? ( Hint: let x = number of machines)
A. 50x B. 3000/x C. 50/x D. 3000x
Problem 231 (ME April 1996)
A manufacturing firm maintains one product assembly line to produce signal generators. Weekly demand for the generators is 35 units. The line operates for 7 hours per day, 5 days per week.
What is the maximum production time per unit in hours required for the line to meet the demand?
A. 1 hour B. 0.75 hour C. 3 hours D. 2.25 hours Problem 232
Of the 316 people watching a movie, there a re 78 more children than women and 56 more women than men. The number of men in the movie house is:
A. 176 B. 98 C. 42 D. 210 Problem 233
A certain department store has an inventory of Q units of a certain product at time t=0. The store sells the product at a steady rate of Q/A units per week, and exhausts the inventory in A weeks.
The amount of product in inventory at any time t is:
A. Q – (Q/A) t B. Q + (Q/A) t C. Qt – Q/A D. Qt – (Q/A) t
Problem 234 (ECE March 1996)
A merchant has three items on sale: namely, a radio for P50, a clock for P30, and a flashlight for P1. At the end of the day, she has sold a total of 100 of three items and has taken exactly 1000 on the total sales. How many radios did he sale?
A. 80 B. 4 C. 16 D. 20 Problem 235
The price of 8 calculators ranges from P200 to P1000.If their average price is P950,what is the lowest possible price of any one of the calculators?
A. 500 B. 550
C. 600 D. 650 Problem 236
A deck of 52 playing cards is cut into two piles. The first pile contains 7 times as many black cards as red cards. The second pile contains the number of red cards that is an exact multiple as the number of black cards. How many cards are there in the first pile.
A. 14 B. 15 C. 16 D. 17
Problem 237 (ECE November 1997)
The population of the Philippines doubled in the last 30 years from 1967 to 1997.Assuming that the rate of population rate increase will remain the same in what year wills the population triple?
A. 2030 B. 2027 C. 2021 D. 2025 Problem 238
Determine the unit digit in the expansion of 3855. A. 3
B. 9 C. 7 D. 1
Problem 239 (ECE April 1998)
Find the 1987th digit in the decimal equivalent of 1785/9999 starting from the decimal point.
A. 1 B. 7 C. 8 D. 5 Problem 240
Find the sum of all positive integral factors of 2048.
A. 4095 B. 3065 C. 4560
D. 1254 Problem 241
In how many ways can two integers be selected from the numbers 1,2,3,…50 so that their difference is exactly 5?
A. 50 B. 5 C. 45 D. 41 Problem 242
A box contains 8 balls, 6 black balls.a8 red balls, and 13 yellow balls. How many balls must be drawn to ensure that there will be three balls of the same color?
A. 8 B. 9 C. 10 D. 11 Problem 243
A shore sells 10 different sizes of shoes, each in both high-cut and low-cut variety, each either rubber or leather, and each with white or black color. How many different kinds of shoes does he sell?
A. 64 B. 80 C. 72 D. 92
Problem 244(ME October 1999)
An engineer was told that a survey had been made on a certain rectangular field but the
dimension had been lost .An assistant remembered that if the field had been 100 ft longer and 25 ft narrower, the area would have been increased by 2500 sq. ft, and that if it had been 100 ft shorter 50 ft wider, the area would have been decreased 5000 sq.ft. What was the area of the field?
A. 25.000 ft2 B. 15,000 ft2 C. 20,000 ft2 D. 22,000 ft2
Problem 245 (EE April 1994)
A 10-meter tape is 5 mm short. What is the correct length in meters?
A. 9.995 m B. 10.05 m C. 9.95 m D. 10.005 m
Problem 246 (ME OCTOBER 1997)
The distance between two points measured with a steel tape was recorded as 916.58 ft. later. The tape was checked and to be only 99.9 ft long. What is the true distance between the points?
A. 035.66 ft B. 966.15 ft C. 955.66 ft D. 915.66 ft
Problem 247 (ME April 1996)
A certain steel tape is known to be 100000 feet long when the temperature of 70 . When the tape is at a temperature of 10 , what reading corresponds to a distance of 90 ft? Coefficient of linear expansion of the tape is 5.833 10-6 per .
A. 85.935 B. 88.031 C. 90.031 D. 93.031
Problem 248 (ME April 1996)
A line was measured with a steel tape when the temperature was 30 . The measured length of the line was found to be 1,256.271 feet. The tape was afterwards tasted when the temperature was 10 and it was found to be 100.042 feet long. What was the true length of the line if the
A line was measured with a steel tape when the temperature was 30 . The measured length of the line was found to be 1,256.271 feet. The tape was afterwards tasted when the temperature was 10 and it was found to be 100.042 feet long. What was the true length of the line if the