# Advanced Algebra Practice Questions

- Posted by Brian Stocker MA
- Date Published October 18, 2012
- Date modified June 17, 2020
- Comments 3 comments

### Algebra is a common subject for the following exams:

College Entrance, ACCUPLACER, CHSPE

**Some Advanced Algebra Tutorials**

### Practice Problems

**1. Find x+y, if: 5x+8y=67 and 2x-y=31 **

a. 98

b. 46

c. 21

d. 14

e. 7

**2. Peter’s salary is twice Ann’s salary and half of David’s salary. Then the average salary of Ann and David is Peter’s salary.
**

a. equal to

b. larger than

c. depends on salary

d. there is no correct answer

**3. Ann and Kate have 80 dollars together. If Kate buys ice-cream for 5 dollars, then Kate will have double Ann’s money. How much money does Ann have?**

a. $20

b. $25

c. $40

d. $50

e. $55

**4. Given: a=b+2c, b=3c. What is the average of numbers a, b and c?**

a. c

b. 1.5c

c. 2c

d. 2 1/3 c

e. 3c

**5. In a forest 4/7 of all the trees are conifer and the rest are leaf-bearing. Among the leaf-bearing trees 7/15 are oak and 2/3 of these oaks are new. There are 160 old oaks in the forest. How many trees in all are in the forest?**

a. 2400

b. 2800

c. 3200

d. 3600

e. 4000

**6. Find x+y, if: 2x+3y=8 and 3x+5y=13 **

a. 1.5

b. 2

c. 2.5

d. 3

e. 3.5

**7. The speed of one car is 20% less than the speed of a second car. What per cent more time does the first car need to travel the same route as the second car?**

a. 12.5%

b. 20%

c. 25%

d. 30%

e. 33%

**8. Number of boys in a class is twice the number of girls. 20% of the girls are brunettes and of the rest – half are blondes: Mary, Clara, Gina and Trisha. How many boys study in this class?**

a. 20

b. 24

c. 30

d. 32

e. 40

**9. In the previous question – what part of all the students are brunette girls?**

a. 20%

b. 1/10

c. 1/2

d. 1/15

e. 15%

**10. If the average of three numbers is V. If one of the numbers is Z and another is Y, what is the remaining number?**

a. ZY – V

b. Z/V – 3 – Y

c. Z/3 – V – Y

d. 3V- Z – Y

e. V- Z – Y

**11. Two cyclists start biking from a trail’s start 3 hours apart. The second cyclist travels at 10 miles per hour and starts 3 hours after the first cyclist who is traveling at 6 miles per hour. How much time will pass before the second cyclist catches up with the first from the time the second cyclist started biking?**

a. 2 hours

b. 4 ½ hours

c. 5 ¾ hours

d. 6 hours

e. 7 ½ hours

**12. Jim can fill a pool carrying buckets of water in 30 minutes. Sue can do the same job in 45 minutes. Tony can do the same job in 1 ½ hours. How quickly can all three fill the pool together?**

a. 12 minutes

b. 15 minutes

c. 21 minutes

d. 23 minutes

e. 28 minutes

**13. Mary is reviewing her algebra quiz. She has determined that one of her solutions is incorrect. Which one is it?**

a. 2x + 5 (x-1) = 9 x = 2

b. p – 3(p-5) = 10 p = 2.5

c. 4 y + 3 y = 28 y = 4

d. 5 w + 6 w – 3w = 64 w = 8

e. t – 2t – 3t = 32 t = 8

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### Answer Key

1. D

2. B

3. B

4. E

5. A

6. D

7. C

8. A

9. D

10. D

11. B

12. B

13. E

**Written by:**Brian Stocker MA, Complete Test Preparation Inc.

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## 3 Comments

nice! thanks

I believe your answer to #6 is incorrect (B, 2). As this is a simple system of linear equations it is..

X=1 Y=2, so X+Y = 3 which is D.

2(1) + 3(2) = 8 –> 2 + 6 = 8

3(1) + 5(2) = 13 –> 3 + 10 = 13

thanks! corrected