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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #492 : Algebra

Solve for $x$ :

$4^{4}+4^{4}+4^{4}+4^{4}=2^{x}$

Possible Answers:

$6$

$9$

$8$

$11$

$10$

Correct answer:

$10$

Explanation:

Combining the powers, we get $1024=2^{x}$ .

From here we can use logarithms, or simply guess and check to get $x=10$ .

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Example Question #13 : Exponents

If $\dpi{100} \small r$ and $\dpi{100} \small s$ are positive integers, and $\dpi{100} \small 25\left ( 5^{r} \right )=5^{s-2}$ , then what is $\dpi{100} \small s$ in terms of $\dpi{100} \small r$ ?

Possible Answers:

$\dpi{100} \small r$

$\dpi{100} \small r+1$

$\dpi{100} \small r+2$

$\dpi{100} \small r+3$

$\dpi{100} \small r+4$

Correct answer:

$\dpi{100} \small r+4$

Explanation:

$\dpi{100} \small 25\left ( 5^{r} \right )$ is equal to $5^{2}\left ( 5^{r}\right )$ which is equal to $\dpi{100} \small \left ( 5^{r+2} \right )$ . If we compare this to the original equation we get $\dpi{100} \small r+2=s-2\rightarrow s=r+4$

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Example Question #1111 : Psat Mathematics

If m and n are integers such that m < n < 0 and m² – n² = 7, which of the following can be the value of m + n?

I. –5

II. –7

III. –9

Possible Answers:

II and III only

I only

I and II only

I, II and III only

II only

Correct answer:

II only

Explanation:

m and n are both less than zero and thus negative integers, giving us m² and n² as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.

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Example Question #1112 : Psat Mathematics

$\frac{7^5+7^4}{8}=$

Possible Answers:

$\frac{7^9}{8}$

$\frac{14^4}{8}$

$\frac{7}{8}$

$\frac{7^4}{8}$

7^4

Correct answer:

7^4

Explanation:

To simplify, we can rewrite the numerator using a common exponential base.

$\frac{7^5+7^4}{8}=\frac{7(7^4)+7^4}{8}$

Now, we can factor out the numerator.

$\frac{7(7^4)+7^4}{8}=\frac{7^4(7+1)}{8}=\frac{7^4(8)}{8}$

The eights cancel to give us our final answer.

$\frac{7^4(8)}{8}=7^4$

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Example Question #1113 : Psat Mathematics

If $x\star y=x^2-y^2$ , then what is $4\star (5\star 3)$ ?

Possible Answers:

240

Correct answer:

Explanation:

$4\star (5\star 3)$

Follow the order of operations by solving the expression within the parentheses first.

$x\star y=x^2-y^2$

$5\star 3=(5)^2-(3)^2$

$5\star 3=25-9=16$

Return to solve the original expression.

$4\star(5\star3)=4\star(16)$

$x\star y=x^2-y^2$

$4\star16=(4)^2-(16)^2$

$4\star(16)=-240$

$4\star(5\star3)=-240$

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Example Question #1114 : Psat Mathematics

Solve:

$4^{8}\div2^{10}=$

Possible Answers:

-0.5

Correct answer:

Explanation:

$4^{8}=\left ( 2^{2}\right )^{8}=2^{16}$

Subtract the denominator exponent from the numerator's exponent, since they have the same base.

$\frac{2^{16}}{2^{10}}=2^{16-10}=2^{6}=64$

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Example Question #1115 : Psat Mathematics

5⁴/ 25 =

Possible Answers:

5⁴ / 5

Correct answer:

Explanation:

25 = 5 * 5 = 5². Then 5⁴ / 25 = 5⁴ / 5².

Now we can subtract the exponents because the operation is division. 5⁴ / 5²= 5^{4 – 2} = 5² = 25. The answer is therefore 25.

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Example Question #1 : How To Divide Exponents

For all real numbers n, (2ⁿ * 2) / (2ⁿ * 2ⁿ) =

Possible Answers:

2^{1 – n}

2n/2n

2n – 1

Correct answer:

2^{1 – n}

Explanation:

(2ⁿ * 2) / (2ⁿ * 2ⁿ) simplifies to 2/2ⁿ or 2¹/2ⁿ.

When dividing exponents with the same base, you subtract the divisor from the dividend, giving 2^1–n.

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Example Question #2 : How To Divide Exponents

If x⁹/x³ = xⁿ, solve for n.

Possible Answers:

Correct answer:

Explanation:

When dividing terms with the same base, we can subtract the exponents:

9 – 3 = 6

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Example Question #3 : How To Divide Exponents

Simplify the following expression: (x²y⁴)/(x³y³z²)

Possible Answers:

y/xz²

z²xy

xy/z²

xz²/y

Correct answer:

y/xz²

Explanation:

According to the rules of exponents, a^x/a^y = a^x-y

In this expression, we can follow this rule to simplify x²/x³and y⁴/y³

x^2–3 = x^–1 = 1/x. y^4–3 = y¹= y.

Therefore, y/xz²

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #492 : Algebra

Example Question #13 : Exponents

Example Question #1111 : Psat Mathematics

Example Question #1112 : Psat Mathematics

Example Question #1113 : Psat Mathematics

Example Question #1114 : Psat Mathematics

Example Question #1115 : Psat Mathematics

Example Question #1 : How To Divide Exponents

Example Question #2 : How To Divide Exponents

Example Question #3 : How To Divide Exponents

All PSAT Math Resources

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