# TSI Math Practice Test 3

#### Danilo is now five years older than Mary was ten years ago. What is Danilo's current age in terms of m if Mary is presently m years old?

Mary’s age ten years ago is:

m−10

So Danilo’s age is:

5 (m−10)

= 5m−50

#### The overall area of a house in square feet is directly proportionate to its market price. What is the price of a 2,000 square foot home if a 1,500 square foot home costs $300,000?

We may answer this by calculating a proportion based on the area-to-price ratio:

^{1,500}⁄_{$300,000} = ^{2,000}⁄_{x}

Cross multiply and solve for x:

1,500x = $600,000,000

x = $400,000

#### If 2+5=8, what is 12x?

The simplest solution is as follows:

2x+5 = 8x

8x−2x = 5

6x = 5

6x⋅2 = 5⋅2

12x = 10

#### The point (1,2) is intersected by line A. Which of the following CANNOT be line A's equation?

A line's slope-intercept form is:

y = mx+b

There are three alternatives because the line crosses through (1,2). The line will be vertical (x=1), horizontal (y=2), or have a slope (the "m" in front of the "x" variable).

To determine which equation is not satisfied, substitute x=1 into each of the four equations. The only option that does not result in y = 2 is y = x+1.

#### In a school, there are 80 students. Each student is required to take either algebra or pre-calculus, and some students must take both. In the algebra class, there are 60 students. What is the probability that a randomly picked student is doing pre-calculus but not algebra if 15 students take both algebra and pre-calculus?

The correct answer:

^{1}⁄_{4}

#### What are the solutions to the equation below?

x^{2} + 8x + 15 = 0

Explanation:

To factor the quadratic equation, we must find the two 15 (constant term) components that add up to 8 (the coefficient of x):

15 = 3⋅5

8 = 3+5

As a result, 3 and 5 are the two factors that satisfy our criteria. The quadratic's completely factored form is:

(x+3)(x+5)=0

Recall that if ab=0, then either a=0, or b=0.

If (x+3)(x+5) = 0

Then either (x+3)=0, or (x+5)=0

That is, either: x=−3, or x=−5

The roots of the quadratic are: −3, and −5

#### Find the x-intercept of a line whose equation is as follows:

2y=3x−6

At the x-intercept, the value of y is equal to zero. By setting y=0 in the equation of the line, we may solve for the x-intercept:

2y = 3x−6

2(0) = 3x−6

0 = 3x−6

3x = 6

x = 2

#### In 5 days, ten people can paint a building. How much of the building could 7 individuals paint in 5 days if each person paints as quickly as the others?

In 5 days, ten people can paint a building. In 5 days, each person paints a tenth of the building.

7 individuals would paint 7/10 of the building in 5 days.

Seven individuals would paint 7/10 of the building in five days.

#### Pens are 60 cents each and pencils are 40 cents each at the office supplies emporium. Donna spent $8.20 on a total of 17 products (pens and pencils). What was the total number of pens Donna bought?

Explanation:

The first step is to determine which variables will be used:

Let the number of pens Donna purchased =x

Let the number of pencils Donna purchased =y

By creating two equations and solving for x, we can figure out how many pens Donna bought.

0.6x+0.4y=8.2

x+y=17

y=17−x

0.6x+0.4(17−x)=8.2

0.6x+6.8−0.4x=8.2

0.2x=1.4

x = ^{1.4}⁄_{0.2} = ^{14}⁄_{2} = 7

#### 50 square feet of rectangular space makes up Bill's new porch. What is the perimeter of the porch if the length is two times the width?

The correct answer is (A). The formula for the area of a rectangle:

A=Width⋅Length

From the question, we know that L=2W and that A=50. So we can plug these values into our equation and solve for W:

50=W⋅L

50=W⋅2W

50=2W2

W2=25

W=5

We know that L=2W , so L=10

Perimeter =2L+2W

Perimeter =2⋅10+2⋅5

Perimeter =30

#### Solve for x:

3(x+1)=5(x−2)+7

We can simplify the equation as follows:

3(x+1)=5(x−2)+7

3x+3=5x−10+7

3x+3=5x−3

We can add 3 to both sides to get the following:

3x+6=5x

We can subtract 3x from both sides and then divide the resulting equation by 2 to solve for x as follows:

**
6=2x
3=x**

**
**

**
Correct!
Wrong!
Correct!
Wrong!
Correct!
Wrong!
Correct!
Wrong!
Correct!
Wrong!
**

#### Point (1,2) is where Line A passes through. Which one of the following CANNOT be line A's equation?

The correct answer is (B). The slope-intercept form of a line is:

y=mx+b

Since the line passes through (−1,2), there are three possibilities: The line will have a slope (the “m” in front of the “x” variable), it will be vertical (x=−1), or it will be horizontal (y=2).

Plug x=−1 into all four equations to see which equation is not satisfied. The only answer choice that doesn’t give us y=2 is y=x+1.

#### Martina was five times older than Diego was 10 years ago. What is Diego's current age in terms of m if Martina is presently m years old?

The correct answer is (C). Martina’s age ten years ago is:

m−10

So Diego’s age is:

5(m−10)

=5m−50

#### If 2x+5=8x, then 12x=?

Here is the easiest way to solve this:

2x+5=8x

8x−2x=5

6x=5

6x⋅2=5⋅2

12x=10

#### The square footage of a home's overall floor area closely relates to its market value. What is the cost of a 2,000 square foot home if a 1,500 square foot home costs $300,000?

#### Determine the x-intercept of the line with the equation 2y=3x6.

The correct answer is (D). At the x-intercept, y=0. We can solve for the x-intercept by setting y=0 in the equation of the line:

2y=3x−6

2(0)=3x−6

0=3x−6

3x=6

x=2