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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #22 : Inequalities

The Spanish club wants to make and sell some pizzas for a fundraiser. It will cost $300 to rent the equipment to make the pizzas and $2 worth of ingredients to make each pizza. The pizzas will be sold for $5.50 apiece.

How many pizzas must be made and sold for the Spanish club to make a profit of at least $600?

Possible Answers:

258

134

120

Correct answer:

258

Explanation:

Let be the number of pizzas made and sold. Each pizza will require $2 worth of ingredients, so the ingredients in total will cost . Add this to the cost to rent the equipment and the cost will be 2N + 300 .

The pizzas will cost $5.50 each, so the money raised will be 5.5N .

The profit will be the difference between the revenue and the cost -

$5.5 N - \left (2N + 300\right )$

The Spanish club wants a profit of at least $600, so we set up and solve the inequality:

$5.5 N - \left (2N + 300\right ) \geq 600$

$5.5 N - 2N - 300\right ) \geq 600$

$3.5 N - 300 \geq 600$

$3.5 N - 300 + 300 \geq 600 + 300$

$3.5 N \geq 900$

$3.5 N \div 3.5 \geq 900 \div 3.5$

$N \geq 257.14$

The Spanish club must sell at least 258 pizzas to earn a profit.

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Example Question #22 : Inequalities

Solve the inequality.

$\small 4 - 2n \leq 1$

Possible Answers:

$\small n\geq \frac{3}{2}$

$\small \small n\geq \frac{-3}{2}$

$\small \small n\leq \frac{3}{2}$

$\small \small \small \small n\leq \frac{-3}{2}$

$\small \small \small \small n\geq \frac{5}{2}$

Correct answer:

$\small n\geq \frac{3}{2}$

Explanation:

$\small 4 - 2n \leq 1$

$\small \small \small 4 - 2n - 4 \leq 1- 4$

$\small \small - 2n \leq -3$

$\small \small \frac{-2n}{-2}\leq \frac{-3}{-2}$

* Notice that when we multiply or divide both sides by a negative number the ineqaulity sign changes orientation.

$\small n\geq \frac{3}{2}$

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Example Question #154 : Algebra

Solve for :

7x+12>3x-13

Possible Answers:

$x>-\frac{25}{4}$

$x<-\frac{1}{4}$

$x>-\frac{35}{8}$

$x>-\frac{12}{25}$

$x<-\frac{25}{4}$

Correct answer:

$x>-\frac{25}{4}$

Explanation:

Begin by moving all of the values to the left side of the inequality:

7x+12>3x-13

becomes

4x+12>-13

Next, move the to the right side:

4x>-25

Finally, divide both sides by :

$x>-\frac{25}{4}$

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Example Question #155 : Algebra

Solve for :

4x-23<7x+5

Possible Answers:

$x<-\frac{28}{3}$

$x<\frac{18}{3}$

$x>\frac{18}{3}$

$x<\frac{31}{4}$

$x>-\frac{28}{3}$

Correct answer:

$x>-\frac{28}{3}$

Explanation:

First, move the values to the left side of the inequality:

4x-23<7x+5

becomes

-3x-23<5

Next, move the to the right side:

-3x<28

Finally, divide by . Remember: you must flip the inequality sign when you multiply or divide by a negative number.

$x>-\frac{28}{3}$

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Example Question #151 : Algebra

Solve for :

17x +122>20x-22

Possible Answers:

x > 48

$x < \frac{137}{3}$

$x > \frac{130}{4}$

x < 48

x < 92

Correct answer:

x < 48

Explanation:

First, get the factors on the left side of the inequality:

17x +122>20x-22

becomes

-3x +122>-22

Next, subtract 122 from both sides:

-3x>-144

Now, divide by . Remember: Dividing or multiplying by a negative number requires you to flip the inequality sign:

x < 48

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Example Question #2 : How To Find The Solution To An Inequality With Division

Solve the inequality

$\frac{3x}{5} > 6$

Possible Answers:

x > 9

x < 10

x > 3

x > 10

Correct answer:

x > 10

Explanation:

First, multiplying each side of the equality by gives 3x > 30 . Next, dividing each side of the inequality by will solve for ; x > 10 .

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Example Question #4 : Inequalities

What is the solution set of the inequality $\dpi{100} \small 3x+8<35$ ?

Possible Answers:

$\dpi{100} \small x<9$

$\dpi{100} \small x<35$

$\dpi{100} \small x>9$

$\dpi{100} \small x>27$

$\dpi{100} \small x<27$

Correct answer:

$\dpi{100} \small x<9$

Explanation:

We simplify this inequality similarly to how we would simplify an equation

$\dpi{100} \small 3x+8-8<35-8$

$\dpi{100} \small \frac{3x}{3}<\frac{27}{3}$

Thus $\dpi{100} \small x<9$

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Example Question #6 : Inequalities

What is a solution set of the inequality 2x+12>42 ?

Possible Answers:

x>4

x>15

x<9

$x>\frac{3}{2}$

x<15

Correct answer:

x>15

Explanation:

In order to find the solution set, we solve 2x+12>42 as we would an equation:

2x+12>42

2x>30

x>15

Therefore, the solution set is any value of x>15 .

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Example Question #2 : Equations / Inequalities

Find the solution to the following equation if x = 3:

y = (4x² - 2)/(9 - x²)

Possible Answers:

no possible solution

Correct answer:

no possible solution

Explanation:

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

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Example Question #112 : Equations / Inequalities

Undefined_denom3

I. x = 0

II. x = –1

III. x = 1

Possible Answers:

III only

II only

I only

I, II, and III

II and III only

Correct answer:

I only

Explanation:

Undefined_denom2

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #22 : Inequalities

Example Question #22 : Inequalities

Example Question #154 : Algebra

Example Question #155 : Algebra

Example Question #151 : Algebra

Example Question #2 : How To Find The Solution To An Inequality With Division

Example Question #4 : Inequalities

Example Question #6 : Inequalities

Example Question #2 : Equations / Inequalities

Example Question #112 : Equations / Inequalities

All PSAT Math Resources

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