ALGEBRA

ALGEBRA Q1. From the equation 7x2 + (2k 1)x 3k + 2 = 0, determine the value of k so that the sum and product of the roots are equal.2 C. 14D. 3Q2. In the equation kx2 6x + 3 = 0, determine the value of k so that the roots are equal.4 C. 12 D. 3

Q3. Four positive integers form an arithmetic progression. If the product of the 1st and the last term is 70 and that of the 2nd and 3rd term is 88, what is the first term?A. 5B. 3C. 14D. 8

Q4. If one-third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?3561/5000C. 4061/5000 3061/5000D. 665/729

Q5. There are 4 geometric means between 1/4 and 8. What is the sum of all the six terms?10.5C. 9.512.5D. 5.25

Q6. A certain ball when dropped from a height rebounds 2/3 of the distance from which it fell. Find the total distance traveled by the ball from the time it is dropped from a height of 60 ft. until it comes to rest.300 ft. C. 180 ft. 185 ft. D. 175 ft.Q10. Find x if 7 is the fourth proportional to 36, 28 and x.A. 6B. 8C. 7D. 9Q11. Given f(x) = (x 4)(x + 3) + 4. When f(x) is divided by (x k), the remainder is k. What is the value of k?A. 12 B. 4 C. 8 D. 2

Q12. If (log10 x) / (1 log10 2) = 2, what is the value of x?C. 254D. 5Q13. A multimillionaire left his entire state to his wife, daughter, son and bodyguard. His daughter and son got half the total value of the estate sharing in the ratio 3:2. His wife got twice as much as the share of the son. If the bodyguard received half a million pesos, what is the total value of the estate? A. 6.5 M B. 5 M C. 7 MD. 6 MQ14. Ann is 5 years older than Beth. In 5 years, the product of their ages will be 1.5 times the product of their present ages. How old is Beth now?A. 27 B. 20 C. 25 D. 18

Q15. The sum of the digits of a two-digit number is 11. If the digits are reversed, the resulting number is seven more than twice the original number. What is the original number? A. 92B. 83C. 38D. 29

Q16. Mike, Louie and Joy can mow the lawn in 4, 6 and 7 hours, respectively. What fraction of the yard can they mow in 1 hour if they work together?47/84C. 37/8445/84D. 27/84

Q17. The time required for two examinees to solve the same problem differ by two minutes. Together they can solve 32 problems in one hour. How long, in minutes, will it take the slower problem solver to solve a problem?A. 5B. 2C. 3D. 4

Q18. The average rate of production of PCBs is 1 unit for every 2 hours work by two workers. How many PCBs can be produced in one month by 60 workers working 200 hours during the month? 4000C. 60005000D. 3000

Q19. It takes an airplane one hour and 45 minutes to travel 500 miles against the wind and covers the same distance in one hour and 15 minutes with the wind. What is the speed of the airplane in mph?342.85 C. 450.5375.5D. 285.75Q20. A and B are running on a circular track having a certain perimeter. The rates of A and B are 1100 m/min and 880 m/min, respectively. If they travel in the same direction from the same starting point, it requires 3 min. for A to overtake B. How long is the circular track?660 m.C. 580 m.780 m.D. 480 m.

Q21. The gasoline tank of a car contains 50 liters of gasoline and alcohol, the alcohol comprising 25%. How much of the mixture must be drawn off and replaced by alcohol so that the tank contain a mixture of which 50% is alcohol?12.67 litersC. 18.75 liters16.67 litersD. 14.25 liters