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PSAT Math : How to evaluate algebraic expressions

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Example Questions

Example Question #15 : Evaluating Expressions

x * y = –a, a – x = 2a. What is y?

Possible Answers:

-2

-a

Insufficient Information.

Correct answer:

Explanation:

Use the second equation to find x in terms of a. Plug it back in the second equation, that will give you 1 = y.

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Example Question #21 : Evaluating Expressions

The projected sales of a movie are given by the function s(p) = 3000/(2p + a) where s is the number of movies sold, in thousands; p is the price per movie, in dollars; and a is a constant. If according to projections, 75,000 cartidges will be sold at $15 each, how many movies are sold at $20 each?

Possible Answers:

200,000

50,000

60,000

20,000

150,000

Correct answer:

60,000

Explanation:

You set up the equation to solve for a.

75 = 3000/(2(15) + a)

a = 10

You then set up the formula again for each movie costing $20, s(20) = 3000/(2(20) + 10), and solve for x, the number sold, giving you 60.

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Example Question #22 : Evaluating Expressions

Half of one hundred divided by five and multiplied by one-tenth is __________.

Possible Answers:

1/2

Correct answer:

Explanation:

Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.

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Example Question #23 : Evaluating Expressions

Let x&y be defined as (x – y)^xy . What is the value of –1&2?

Possible Answers:

–1/3

1/9

–3

–1/9

Correct answer:

1/9

Explanation:

We are told that x&y = (x – y)^xy.

–1&2 = (–1 – 2)^(–1)(2) = (–3)^–2

To simplify this, we can make use of the property of exponents which states that a^–^b = 1/(a^b).

(–3)^–2 = 1/(–3)² = 1/9

The answer is 1/9.

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Example Question #21 : Expressions

If 18 – w is 8 less than 32, what is the value of $\dpi{100} \small -\frac{1}{3}w$ ?

Possible Answers:

–3

–2

–6

Correct answer:

Explanation:

We need to rewrite this problem in mathematic terms.

8 less than 32 can be written as 32 – 8

so we will get the equation

18 – w = 32 – 8.

Now, we need to solve for w.

–w = 32 – 8 – 18

–w = 6

w = –6

Find the value of the given expression, $\dpi{100} \small -\frac{1}{3}w$ , by plugging in –6 for w.

$\dpi{100} \small -\left (\frac{1}{3} \right )\left ( -6 \right )=2$

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Example Question #23 : Evaluating Expressions

If x and y are integers such that x > y > 0 and x²+ y²= 100

Which of the following can be the value of x + y?

I. 10

II. 12

III. 14

IV. 16

V. 18

Possible Answers:

Correct answer:

Explanation:

Note that x must be greater than y and that y must be greater than 0. This means that x and y are different, positive integers. In addition, the sum, x²+ y²must equal to 100. If we list squares beginning from the square of the first integer greater than 0 (1²) up to the square of the greatest integer less than 100 (9²) we will get:

1, 4, 9, 16, 25, 36, 49, 64, 81

We must observe that the only two numbers that will add up to 100 are 36 and 64.

Remember that x > y > 0 and that x²+ y²=100.

This means that x must be $\dpi{100} \small \sqrt{64}$ and y must be $\dpi{100} \small \sqrt{36}$

When we solve for x and y we get:

x = 8

and y = 6.

Therefore, x + y can only be 14.

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Example Question #24 : Evaluating Expressions

If $m > n$ , which of the following has to be true?

Possible Answers:

$m^{2} > n^{2}$

$\frac{m}{2} > \frac{n}{2}$

$mn > 0$

$\left | m \right | > \left | n \right |$

$mn > -mn$

Correct answer:

$\frac{m}{2} > \frac{n}{2}$

Explanation:

Plug in numbers for each alternative. If both sides of the inequality $\frac{m}{2} > \frac{n}{2}$ are multiplied by 2, the result is the original inequality, $m > n$ . The other options fail (if confused, try plugging in $m$ as a positive, $n$ as a negative).

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Example Question #22 : Evaluating Expressions

Billy began lifting weights in February. After 6 months, he can lift 312 lbs, a 20% increase in the amount he could lift in February. How much weight could Billy lift in February?

Possible Answers:

$250\ lbs.$

$280\ lbs.$

$260\ lbs.$

$290\ lbs.$

$270\ lbs.$

Correct answer:

$260\ lbs.$

Explanation:

$1.2w = 312$

$w = 260 lbs$

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Example Question #733 : Algebra

A metal rod is 36 inches long and divided into 3 sections. The middle section is twice as long as the first section. The third section is 4 inches shorter than the first section. How long are the sections?

Possible Answers:

None of the above answers

The first piece is 6 inches, the second piece is 10 inches and the third piece is 20 inches

First piece is 20 inches, the second piece is 10 inches and the third piece is 6 inches

The first piece is 15 inches, the second piece is 15 inches and the third piece is 6 inches

First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.

Correct answer:

First piece is 10 inches, the middle piece is 20 inches, and third piece is 6 inches long.

Explanation:

Assume the first section equals $x$ inches, then the second(or the middle section) must be equal to $2x$ and the third piece must be equal to $x-4$ .

$x+2x+(x-4)=36$ and now you solve for $x$ which equals 10. Hence the middle piece must be equal to 20 inches and the third piece is only 6 inches long.

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Example Question #734 : Algebra

A B

1 2

2 4

3 10

5 34

Using the table above, please select the answer below that expresses the relationship between A and B.

Possible Answers:

$B=A^3-2A^2+2A+1$

$B=A^2+A-2$

$B=2A$

$B=8A-6$

$B=2A^2-4A+4$

Correct answer:

$B=2A^2-4A+4$

Explanation:

By testing the answers, it can be seen that the only equation to satisfy all cases in the table above is

$B=2A^2-4A+4$

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PSAT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #15 : Evaluating Expressions

Example Question #21 : Evaluating Expressions

Example Question #22 : Evaluating Expressions

Example Question #23 : Evaluating Expressions

Example Question #21 : Expressions

Example Question #23 : Evaluating Expressions

Example Question #24 : Evaluating Expressions

Example Question #22 : Evaluating Expressions

Example Question #733 : Algebra

Example Question #734 : Algebra

All PSAT Math Resources

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