1. Find the 10th term of the harmonic progression 3, 2, 3/2.
2. If x varies directly as y and inversely as z, and x = 12 when y = 6 and z = 4, find the value of x when y = 16 and z = 4.
3. Find the value of k so that 2x^2 + 8x + k is a perfect square.
4. What is the least common multiple of 25 and 205?
5. A pump can pump out water from a tank in 18hours. Another pump can pump out water from the same tank in 10 hours. How long will it take both pumps to pump out the water in the tank?
6. Find the remainder if we divide 4y^3 + 8y^2 + y – 6 by (2y + 3).
7. What is the sum of the first 50 terms of the series 10 + 85 +160 + 235 ?
8. A goldsmith has two alloys of gold, the first being 70 % pure and the second being 60 % pure. How many ounces of the 70 % pure gold must be used to make 100 ounces of an alloy which will be 66 % gold?
9. It takes Butch twice as long as it takes Dan to do a certain piece of work. Working together they can do the work in 6 days. How long would it take Butch to do it alone?
10. A girl is one-third as old as her brother and 8 years younger than her sister. The sum of their ages is 38 years. How old is the brother?
11. Given: lo3 (x^2-2x)=0 . Find x.
12. What is the discriminant of the equation 4x^2 = 8x + 5?
13. Two men will meet at an intersection. One travels southward while the other travels north. If one of the drivers drives 30 mph and the other drives 40mph, when will they be 35 miles apart?
14. A mixture containing 16% of a drug is combined to a 28% of a drug to obtain a 15mL of 24% of a mixture. How many 28% of a drug should be added?
15. Truncate 3.14159876 to 5 decimal places.
16. A calculator manufacturer wants to earn $18000. They produce the calculator for $6 and sell it for $11. If the overhead runs $150000, what is the number of calculator to be produced?
17. Find the value of w in the following equations: 3x + 2y - w = 11 x + 5y - 2w = -9 2x + y – 3w = 6
18. 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 Juan to paint the same fence if he had to work alone?
19. Multiply the following: (3x + 5y)(2x – 2y)
20. The numbers 12 and 26 has the greatest common divisor of ___.