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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #1321 : Psat Mathematics

Solve for $\displaystyle x$.

$\frac{1}{3}(3x-6)+\frac{1}{2}(2x+4)=\frac{1}{5}(15x -5)$ $\displaystyle \frac{1}{3}(3x-6)+\frac{1}{2}(2x+4)=\frac{1}{5}(15x -5)$

Possible Answers:

$2$ $\displaystyle 2$

$-2$ $\displaystyle -2$

$-3$ $\displaystyle -3$

$0$ $\displaystyle 0$

$\displaystyle 1$

Correct answer:

$\displaystyle 1$

Explanation:

First distribute the fractions:

$\displaystyle x-2 +x+2 =3x-1$

Combine like terms:

2x=3x-1 $\displaystyle 2x=3x-1$

x=1 $\displaystyle x=1$

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Example Question #1322 : Psat Mathematics

Solve for $x$ $\displaystyle x$.

$(2x+3)-3(x+5)=-(3x-4)$ $\displaystyle (2x+3)-3(x+5)=-(3x-4)$

Possible Answers:

$\displaystyle 8$

$0$ $\displaystyle 0$

$-4$ $\displaystyle -4$

$-8$ $\displaystyle -8$

$4$ $\displaystyle 4$

Correct answer:

$\displaystyle 8$

Explanation:

First distribute to eliminate the parentheses:

$2x+3-3x-15=-3x+4$ $\displaystyle 2x+3-3x-15=-3x+4$

Then combine like terms:

$2x=16$ $\displaystyle 2x=16$

$x=8$ $\displaystyle x=8$

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Example Question #1323 : Psat Mathematics

x = 1/2

What does 1/x + 1/(x + 4) equal?

Possible Answers:

20/9

9/2

4/9

Correct answer:

20/9

Explanation:

1/x + 1/(x+4) =

1/(1/2) + 1/ (1/2 + 4) =

1/ (1/2) + 1 / (9/2) =

2 + 2/9

20/9

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Solve for $\displaystyle x$.

$\frac{16}{x + 7} = \frac{2}{6}$ $\displaystyle \frac{16}{x + 7} = \frac{2}{6}$

Possible Answers:

$\displaystyle 36$

$\displaystyle 41$

$\displaystyle 12$

$\displaystyle 24$

$\displaystyle 28$

Correct answer:

$\displaystyle 41$

Explanation:

Cross multiply. $\displaystyle 96 = 2 (x+7)$

Dsitribute. $\displaystyle 96 = 2x + 14$

Solve for $\displaystyle x$. $\displaystyle 96 - 14 = 2x$

82 = 2x $\displaystyle 82 = 2x$

41 = x $\displaystyle 41 = x$

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Example Question #1324 : Psat Mathematics

If x=-5 $\displaystyle x=-5$, what is the value of $\frac{x^{2}+20}{x-4}$ $\displaystyle \frac{x^{2}+20}{x-4}$?

Possible Answers:

$\displaystyle 25$

$\displaystyle -5$

$\displaystyle 9$

$\displaystyle 45$

Correct answer:

$\displaystyle -5$

Explanation:

To solve this question, substitute -5 in for x in the numerator and denominator. Remember that the square of a negative number is positive.

45 / -9 = -5

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

If $\frac{6}{x}=\frac{9}{19}$ $\displaystyle \frac{6}{x}=\frac{9}{19}$ , then what is the value of $\displaystyle x$?

Possible Answers:

none of these

38/3

3/38

9/114

7/12

Correct answer:

38/3

Explanation:

cross multiply:

(6)(19) = 9x

114=9x

x = 38/3

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

$\dpi{100} \small \frac{4 }{x} = \frac{2}{25}$ $\displaystyle \dpi{100} \small \frac{4 }{x} = \frac{2}{25}$

Find x.

Possible Answers:

$\dpi{100} \small 50$ $\displaystyle \dpi{100} \small 50$

None

$\dpi{100} \small 0.25$ $\displaystyle \dpi{100} \small 0.25$

$\dpi{100} \small \frac{25}{8}$ $\displaystyle \dpi{100} \small \frac{25}{8}$

$\dpi{100} \small \frac{8}{25}$ $\displaystyle \dpi{100} \small \frac{8}{25}$

Correct answer:

$\dpi{100} \small 50$ $\displaystyle \dpi{100} \small 50$

Explanation:

Cross multiply:

$\dpi{100} \small 4 \times 25 = 2x$ $\displaystyle \dpi{100} \small 4 \times 25 = 2x$

$\dpi{100} \small 100 = 2x$ $\displaystyle \dpi{100} \small 100 = 2x$

$\dpi{100} \small x = 50$ $\displaystyle \dpi{100} \small x = 50$

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Example Question #1 : How To Solve For A Variable As Part Of A Fraction

The numerator of a fraction is the sum of 4 and 5 times the denominator. If you divide the fraction by 2, the numerator is 3 times the denominator. Find the simplified version of the fraction.

Possible Answers:

$\displaystyle 12$

$\displaystyle 6$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 18$

Correct answer:

$\displaystyle 6$

Explanation:

Let numerator = N and denominator = D.

According to the first statement,

N = (D x 5) + 4.

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

–N = –6D

+[N = (D x 5) + 4]

–6D + (D x 5) + 4 = 0

–1D + 4 = 0

D = 4

Thus, N = 24.

Therefore, N/D = 24/4 = 6.

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Example Question #1325 : Psat Mathematics

Solve for $\displaystyle x$:

$\frac{24x-8}{3}=12$ $\displaystyle \frac{24x-8}{3}=12$

Possible Answers:

$3\frac{1}{4}$ $\displaystyle 3\frac{1}{4}$

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$2\frac{7}{8}$ $\displaystyle 2\frac{7}{8}$

$1\frac{5}{6}$ $\displaystyle 1\frac{5}{6}$

$\displaystyle 2$

Correct answer:

$1\frac{5}{6}$ $\displaystyle 1\frac{5}{6}$

Explanation:

Solve for $\displaystyle x$:

$\frac{24x-8}{3}=12$ $\displaystyle \frac{24x-8}{3}=12$

Step 1: Cross-multiply to eliminate the fraction

$3(\frac{24x-8}{3})=12 \cdot 3$ $\displaystyle 3(\frac{24x-8}{3})=12 \cdot 3$

$\displaystyle 24x-8 = 36$

Step 2: Solve for $\displaystyle x$:

24x=44 $\displaystyle 24x=44$

$x=\frac{44}{24}=\frac{22}{12}=\frac{11}{6}=1\frac{5}{6}$ $\displaystyle x=\frac{44}{24}=\frac{22}{12}=\frac{11}{6}=1\frac{5}{6}$

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Example Question #1 : Data Analysis

This semester, Mary had five quizzes that were each worth 10% of her grade. She scored 89, 74, 84, 92, and 90 on those five quizzes. Mary also scored a 92 on her midterm that was worth 25% of her grade, and a 91 on her final that was also worth 25% of her class grade. What was Mary's final grade in the class?

Possible Answers:

Correct answer:

Explanation:

To find her average grade for the class, we need to multiply Mary's test scores by their corresponding weights and then add them up.

The five quizzes were each worth 10%, or 0.1, of her grade, and the midterm and final were both worth 25%, or 0.25.

average = (0.1 * 89) + (0.1 * 74) + (0.1 * 84) + (0.1 * 92) + (0.1 * 90) + (0.25 * 92) + (0.25 * 91) = 88.95 = 89.

Looking at the answer choices, they are all spaced 2 percentage points apart, so clearly the closest answer choice to 88.95 is 89.

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1321 : Psat Mathematics

Example Question #1322 : Psat Mathematics

Example Question #1323 : Psat Mathematics

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #1324 : Psat Mathematics

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #1 : How To Solve For A Variable As Part Of A Fraction

Example Question #1325 : Psat Mathematics

Example Question #1 : Data Analysis

All PSAT Math Resources

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