# Basic Algebra Practice Test Questions

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Basic Algebra questions are common on most College Entrance exams, High School exams, Nursing Entrance Exams and High School Equivalence exams.

# Algebra Practice Test Questions

1. It is known that x2+4x=5. Then x can be

- 0
- -5
- 1
- Either (b) or (c)

2. (a+b)2 = 4ab . What is necessarily correct?

- a>b
- a<b
- a=b
- None of the Above

3. Sum of the digits of a 2-digit number is 12. If we switch the digits, the number we get will be greater than the initial one by 36. Find the initial number

- 39
- 48
- 57
- 75

4. Two friends traveled to a nearby city. In the second day they travelled 75 miles more than the first day, and in the third day, they travelled a third of the distance covered in the second day. How many miles did they cover in the first day, if the total travelled was 170 miles?

- 30 miles
- 35 miles
- 105 miles
- 135 miles

5. Kate’s father is 32 years older than Kate. In 5 years he will be five times older than his daughter. How old is Kate?

- 2
- 3
- 5
- 6

6. If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?

- 5/p
- p – 5
- p + 5
- p/5

7. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

- 2 hours and 24 minutes
- 3 hours and 12 minutes
- 3 hours and 44 minutes
- 4 hours and 10 minutes

8. Employees of a discount appliance store receive an additional 20% off of the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

- $280.90
- $287
- $292.50
- $306

Answer Key

**1.** **D** x2 +4x=5, x2+4x-5=0, x2+5x-x-5=0, factorize x(x+5)-1(x+5)=o, (x+5)(x-1)=0. x+5=0 or x-1=0, x=0-5 or x=0+1, x= -5 or x=1, either b or c

**2. C** Open parenthesis: 2a + 2b = 4ab, divide both sides by 2 = a+b=2ab or a+b=ab + ab, therefore a=ab and b=ab, therefore a=b

**3. B** Let the XY represent the initial number, X + Y = 12, YX=XY+ 36, Only b=48 satisfies both equations above from the given options

**4. A**

**5. B**

Let the father’s age=Y, and Kate’s age=X, therefore Y=32+X, in 5yrs y=5x,substituting for Y will be 5x = 32+X, 5x – x = 32, 4X=32,X= 32/8, x = 8, Kate will be 8 in 5 yrs time, so Kate’s present age = 8-5=3

**6. D**

**7. A**

Let X represent the house, Sally paints X in 4hrs or ¼ X per 1hr or 60 minutes, John paints X in 6 hours or at 1/6X per 1hr or 60mins. Working together, they will paint 1/4x + 1/6x in 1hr or 60minutes = 10/24x = 5/12x every 60 minutes, to paint x = 60 minutes x 12/5 = 144 minutes or 2 hrs and 24 minutes

**8. D**

Cost of dishwasher = $450, 15% discount = 15/100 x 450 = $67.5, new price = 450 – 67.5 = $382.5, 20% discount on lowest price = 20/100 x 382.5 = $76.5, final price = $306

Algebra tutorial at Wikipedia