There are several reasons colleges give these exams. For one thing, there are thousands of high schools across the country, and no two of them are exactly alike. Some schools do a great job when it comes to preparing their students for college level math, some are fairly competent at the task, and others do a poor job. So the fact that a student has a high school diploma isn’t very helpful when colleges seek to match students with the right coursework.

##### 1. If Lynn can type a page in p minutes, what piece of the page can she do in 5 minutes?

- 5/p
- p – 5
- p + 5
- p/5
- 1- p + 5

##### 2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, 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
- 4 hours and 33 minutes

##### 3. Employees of a discount appliance store receive an additional 20% off of the lowest price on an 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
- $287.00
- $292.50
- $306.00
- $333.89

##### 4. The sales price of a car is $12,590, which is 20% off the original price. What is the original price?

- $14,310.40
- $14,990.90
- $15,290.70
- $15,737.50
- $16,935.80

##### 5. Solve the following equation for *A* : 2A/3 = 8 + 4A

- -2.4
- 2.4
- 1.3
- -1.3
- 0

##### 6. If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

- 8
- 10
- 14
- 19
- 21

##### 7. Alfred wants to invest $4,000 at 6% simple interest rate for 5 years. How much interest will he receive?

- $240
- $480
- $720
- $960
- $1,200

##### 8. Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?

- $496.30
- $512.40
- $555.40
- $574.90
- $588.20

##### 9. The city council has decided to add a 0.3% tax on motel and hotel rooms. If a traveler spends the night in a motel room that costs $55 before taxes, how much will the city receive in taxes from him?

- 10
- 11 cents
- 15 cents
- 17 cents
- 21 cents

##### 10. A student receives his grade report from a local community college, but the GPA is smudged. He took the following classes: a 2 hour credit art, a 3 hour credit history, a 4 hour credit science course, a 3 hour credit mathematics course, and a 1 hour science lab. He received a “B” in the art class, an “A” in the history class, a “C” in the science class, a “B” in the mathematics class, and an “A” in the science lab. What was his GPA if the letter grades are based on a 4 point scale? (A=4, B=3, C=2, D=1, F=0)

- 2.7
- 2.8
- 3.0
- 3.1
- 3.2

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## Answers & Explanations

## 1. A

The following proportion may be written: 1/p=x/5. Solving for the variable, x, gives xp = 5, where x=5/p. So, Lynn can type 5/p pages, in 5 minutes.

## 2. A

Sally can paint 1/4 of the house in 1 hour. John can paint 1/6 of the same house in 1 hour. In order to determine how long it will take them to paint the house, when working together, the following equation may be written: 1/4 x+1/6 x=1. Solving for x gives 5/12 x=1, where x= 2.4 hours, or 2 hours, 24 minutes.

## 3. D

Sale Price = $450 – 0.15($450) = $382.50, Employee Price = $382.50 – 0.2($382.50) = $306

## 4. D

$12,590 = Original Price – 0.2(Original Price) = 0.8(Original Price), Original Price = $12,590/0.8 = $15,737.50

## 5. A

In order to solve for A, both sides of the equation may first be multiplied by 3. This is written as 3(

^{2A}/_{3})=3(8+4A) or 2A=24+12A. Subtraction of 12A from both sides of the equation gives -10A=24. Division by -10 gives A = -2.4.## 6. A

Three equations may initially be written to represent the given information. Since the sum of the three ages is 41, we may write, l + s + j = 41, where l represents Leah’s age, s represents Sue’s age, and j represents John’s age. We also know that Leah is 6 years older than Sue, so we may write the equation, l = s + 6. Since John is 5 years older than Leah, we may also write the equation, j = l + 5. The expression for l, or s + 6, may be substituted into the equation, j = l + 5, giving j = s + 6 + 5, or j = s + 11. Now, the expressions for l and j may be substituted into the equation, representing the sum of their ages. Doing so gives: s + 6 + s + s + 11 = 41, or 3s = 24, where s = 8. Thus, Sue is 8 years old.

## 7. E

Simple interest is represented by the formula, I = Prt, where P represents the principal amount, r represents the interest rate, and t represents the time. Substituting $4,000 for P, 0.06 for r, and 5 for t gives I = (4000)(0.06)(5), or I = 1,200. So, he will receive $1,200 in interest.

## 8. A

$670 = Cost + 0.35(Cost) = 1.35(Cost), Cost = $670/1.35 = $496.30

## 9. D

The amount of taxes is equal to $55*0.003, or $0.165. Rounding to the nearest cent gives 17 cents.

## 10. C

The GPA may be calculated by writing the expression, ((3*2)+(4*3)+(2*4)+(3*3)+(4*1))/13, which equals 3, or 3.0.

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