Algebra - Sample Problems
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Sample Problems
Worded Problems
Work Problems
Problem (CE Board)
You can design a web site in 30 hours. Your friend can design the same site in 20 hours. How long will it take to design the web site if you both work together?
A. 15 hrs C. 18 hrs
B. 12 hrs D. 16 hrs
Problem(CE Board)
If one pump can fill the tank in 16 hours, two pumps can fill the thank in 6 hours, how fast can the other pump can fill the tank?
A. 9.6 hours C. 8.2 hours
B. 6.5 hours D. 7.6 hours
Problem (CE Board)
A contractor has 50 men of the same capacity at work on a job. They can complete the job in 30 days, the working day being 8 hours, but the contract expires in 20 days. All men get P450 per day for a full or part day and the liquidated damages are P10,000 for every full or part day he requires over his contract. If he decides to put 20 additional men, how many days could he finish the job.
A. 25 C. 20
B. 18 D. 22
Average Problems
Problem (CE Board)
On the first six tests in her Mathematics subject, her scores were 92, 82, 86, 93, 96, and 91. If she took a seventh test and raised the mean of her scores exactly one point, what is her score on the 7th test?
A. 84 C. 97
B. 98 D. 96
Problem (CE Board)
Diego has scored 72, 67, 82 and 79 on his algebra tests. Use an inequality to find the scores he must take on the final exam to pass the course with an average of 77 or higher, given that the final exam counts as two test.
A. greater than or equal to 71
B. greater than or equal to 51
C. greater than or equal to 81
D. greater than or equal to 61
Money/Investment Problems
Problem (CE Board)
Your local computer store is having a sale. After 30% price reduction, you purchase a new computer for P53,900. What was the computer’s price before the reduction?
A. P77,000 C. P85,000
B. P82,000 D. P75,000
Problem (CE Board)
ABC car rental agency charges P400 a day plus P15 per km, whereas DEF rental agency charges P2000 a day and P5 per km. How many km must be driven to make the daily cost of the ABC rental a better deal than DEF rental?
A. 140 C. 130
B. 150 D. 160
Problem (CE Board)
DITG Corporation has a total operating costs of P455,000.00. Having invested in radio campaign, the company’s sales have increased from P625,000.00 to P821,000.00. In addition to one-off cost of P80,000.00 for the radio adverts, these extra sales have added P63,000.00 in variable costs. Thus, the total operating costs for the firm now stand at P598,000.00. By what percentage has EBIT ( Earnings Before Interest and Taxes) improved as a result of the marketing campaign?
A. 31% C. 23%
B. 30% D. 35%
Miscellaneous Worded Problems
Problem (CE Board)
GERTC corporation, had been mailing out coupons for a clearance sale at a constant rate for 4 days, when they counted the coupons they still had mail out and discover they had 120,000 left. After 7 total days of work they had 75,000 left. At what rate are they mailing coupons out?
A. 17,000 coupons per day
B. 11,000 coupons per day
C. 15,000 coupons per day
D. 13,000 coupons per day
Motion/Rate Problems
Problem (CE Board)
In still water, your small boat average 8 km per hour. It takes you the same amount of time to travel 15 km downstream, with the current, as 9 km upstream, against the current. What is the rate of water’s current?
A. 3 kph C. 2 kph
B. 4 kph D. 5 kph
Problem (CE Board)
A plane flies 465 miles with the wind and 345 miles against the wind in the same length of time. If the speed of the wind is 20 mph, find the speed of the plane in still air.
A. 125 mph C. 165 mph
B. 155 mph D. 135 mph
Progression/Sequence
Arithmetic Progression
Problem
Very few people are aware of the growth pattern of Jack' beanstalk. On the first day it increased its height by 1/2, on the second day by 1/3, on the third day by 1/4, and so on. How long will it take to achieve its maximum height (100 times its original height)?
A. 99 days C. 198 days
B. 100 days D. 200 days
Problem
My house is on a road where the numbers run 1, 2, 3, 4, - consecutively. My number is a three-digit one and, by curious coincidence, the sum of all house numbers less than mine is the same as the sum of all houses greater than mine. what is my house number and how many houses are there on the road?
A. House No. 170; 240 houses
B. House No. 211; 298 houses
C. House No. 175; 247 houses
D. House No. 204; 288 houses