Algebra 1

1. What is the value of the 20^th term of this sequence: 8, 12, 16, 20, …?

64

84

75

80

2. 50 grams of solution L has 50% benzene by mass and 250 grams of the solution M has 90% benzene by mass. If 40 grams of solution L is added to 40 grams of solution M, what is the percent of benzene by mass in the resulting mixture?

80%

85%

60%

70%

3. Car X traveled 180 miles and averaged 20 miles per gallon of gasoline. If car Y traveled 15 miles for each gallon of gasoline, how many miles had car Y traveled when it had used the same amount of gasoline that car X used to travel 180 miles?

130

120

135

140

4. Suppose that d is 10% of e, e is 50% of g and d is x% of g. What is the value of x?

10

7

5

15

5. The average of 12 consecutive odd integers is 20. What is the greatest of these 12 integers?

31

33

27

29

6. Given that P= . What is the minimum value of P?

3

1

2

0

7. What is the 50^th number of the series: 7, 14, 21, 28, …

343

357

350

364

8. A broken car costs $2000 to repair and the cost of a new car is $10.400. Fortunately, the new fuel-efficient car will save you $210 per month on gas compared to the old one. How many months of savings from the new car will it take to equal the difference in cost between buying a new car and repairing the old one?

40

35

45

50

9. Given that while a and b are 2 positive integers, a + b = 4. What is the possible value of ab so that S is a positive integer?

5

3

2

7

10. (hard question) Suppose that S=. What is the minimum value of S?

6

7

9

10

11. A book-binding machine makes ten books per minute. If the book-binding machine runs for ten hours each day, how many days will it need to run to produce 6,000,000 books?

2000

1000

1500

2200

12. If the average of 2a and b is equal to 50% of 8b, what is the value of ?

4

2

3.5

3

13. 25% of the students in A class are boys. 20% of the boys come from Vietnam. of them come from Hanoi. What is the smallest number possible of students of A class?

60

50

120

80

14. Solve for x:

X=5

X=2

X=2 or 5

No Solution

Please note that X must be inside [1;3] so when you solve this equation, the solution x=5 should be declined.

Explanation

Please note that X must be inside [1;3] so when you solve this equation, the solution x=5 should be declined.

15. (***): Difficult question X is a real number >0.Given that What is the minimum value of P?

0

1

3

2

Let X=Y x Y => P=(Y-1)(Y-1) + 2 so the minimum value of P will be 2

Explanation

Let X=Y x Y => P=(Y-1)(Y-1) + 2 so the minimum value of P will be 2

16. Solve for "X":

X=-0.5

X=1

X=2

X=-1

17. The first term of a certain sequence is 3 and the second term is 13. The third term and each term thereafter are found by taking the average of the two terms preceding it. What is the value of the first term in the sequence that is not an integer?

10.5

9.5

8.5

7.5

18. Mary earns p dollars per hour. At this rate, how many hours will it takes Mary to earn x dollars?

10px

60p

P/x

X/p

19. If a=4b=5c, what is the average of a, b and c in terms of a?

1

29/60

2

2/3

20. If , which of the following cannot be the value of x?

7

4

-3

-5