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Correct Answer **C.** 0.15 --- ## 2. Evaluation **A.** 0.2 This is too large. The product simplifies to $\frac{3}{20}=0.15$, not $0.2$. **B.** 0.5 This is much too large. Multiplying fractions less than 1 gives a result less than each factor, and the exact product is $\frac{3}{20}=0.15$. **C.** 0.15 Multiply and simplify: \[ \frac{2}{3}\cdot\frac{3}{5}\cdot\frac{5}{10}\cdot\frac{6}{8} \] Cancel common factors: - $\frac{2}{3}\cdot\frac{3}{5}=\frac{2}{5}$ - $\frac{2}{5}\cdot\frac{5}{10}=\frac{2}{10}=\frac{1}{5}$ - $\frac{1}{5}\cdot\frac{6}{8}=\frac{6}{40}=\frac{3}{20}=0.15$ So this is the correct answer. **D.** 0.25 This is incorrect. The simplified product is $\frac{3}{20}$, which equals $0.15$, not $0.25$. **E.** 0.333333333 This decimal equals about $\frac{1}{3}$, but the actual product is $\frac{3}{20}=0.15$. --- ## 3. Overall Explanation The correct answer is **C**. Compute the product by simplifying as you go: \[ \frac{2}{3}\cdot\frac{3}{5}\cdot\frac{5}{10}\cdot\frac{6}{8} \] Notice that common factors cancel: - $3$ cancels with $3$ - $5$ cancels with $5$ So the expression becomes: \[ \frac{2}{10}\cdot\frac{6}{8}=\frac{1}{5}\cdot\frac{6}{8}=\frac{6}{40}=\frac{3}{20} \] Convert to decimal: \[ \frac{3}{20}=0.15 \] So the simplified result is **0.15**. The community reference also points to **C**, which matches the correct computation.37:T52d,## 1. Correct Answer **E.** 12 minutes --- ## 2. Evaluation **A.** 20 minutes Using \[ \text{time} = \frac{\text{distance}}{\text{speed}} = \frac{10}{50} = 0.2 \text{ hours}, \] and converting to minutes gives $0.2 \times 60 = 12$ minutes. So this is not correct. **B.** 10 minutes Using \[ \text{time} = \frac{10}{50} = 0.2 \text{ hours} = 12 \text{ minutes}, \] so 10 minutes is too short. **C.** 15 minutes The travel time is \[ \frac{10}{50} = 0.2 \text{ hours}. \] Since $0.2$ hours is 12 minutes, not 15 minutes, this choice is incorrect. **D.** 30 minutes At 50 miles per hour, Dave covers 10 miles in \[ \frac{10}{50} = 0.2 \text{ hours}. \] Converting to minutes: $0.2 \times 60 = 12$. Therefore, 30 minutes is incorrect. **E.** 12 minutes Use the formula \[ \text{time} = \frac{\text{distance}}{\text{rate}} = \frac{10}{50} = 0.2 \text{ hours}. \] Then convert hours to minutes: \[ 0.2 \times 60 = 12 \text{ minutes}. \] So this is the correct choice. --- ## 3. Overall Explanation To find how long the trip takes, use \[ \text{time} = \frac{\text{distance}}{\text{speed}}. \] Substitute the given values: \[ \text{time} = \frac{10}{50} = \frac{1}{5} \text{ hour}. \] Since 1 hour is 60 minutes, \[ \frac{1}{5} \times 60 = 12 \text{ minutes}. \] So the correct answer is **E. 12 minutes**.38:T43b,## 1. Correct Answer **B.** 4/5 --- ## 2. Evaluation **A.** 5/4 This is the reciprocal of the slope. Rewriting the equation as `y = (4/5)x - 4` shows the slope is `4/5`, not `5/4`. **B.** 4/5 Rewriting `4x - 5y = 20` in slope-intercept form gives `y = (4/5)x - 4`. The coefficient of `x` is the slope, so the slope is `4/5`. **C.** - 4/5 This would be the slope if the equation were `4x + 5y = 20`. For `4x - 5y = 20`, solving for `y` gives `y = (4/5)x - 4`, so the slope is positive `4/5`. **D.** - 5/4 This has both the wrong sign and the reciprocal. From `y = (4/5)x - 4`, the slope is `4/5`. **E.** - 4 This is the y-intercept, not the slope. In `y = (4/5)x - 4`, the slope is `4/5` and the intercept is `-4`. --- ## 3. Overall Explanation The equation is best interpreted as `4x - 5y = 20`. Put it into slope-intercept form: `4x - 5y = 20` `-5y = -4x + 20` `y = (4/5)x - 4` In `y = mx + b`, the slope is `m`, so the slope is **`4/5`**, which is **B**. The prompt appears slightly garbled, but the answer choices strongly support the minus-sign interpretation.2f:["$","$L30",null,{"examId":2223,"initialBookmarkedIds":[],"children":["$","$L31",null,{"initialTab":"practice","allowBookmarked":false,"tabResetKey":"implicit","children":[["$","$L32",null,{"className":"mb-6","children":[["$","$L33",null,{"value":"practice","children":"Practice Questions"}],null]}],["$","$L34",null,{"value":"practice","children":[["$","$L35",null,{"questions":[{"id":368106,"sortOrder":1,"type":"multiple_choice","domain":null,"visibility":"full","questionText":"

\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tIf x = -5, then |x - 7| =
\n

","questionPreview":null,"options":[{"id":1441608,"position":0,"text":"-12","imageUrl":null},{"id":1441609,"position":1,"text":"2","imageUrl":null},{"id":1441610,"position":2,"text":"10","imageUrl":null},{"id":1441611,"position":3,"text":"-2","imageUrl":null},{"id":1441612,"position":4,"text":"12","imageUrl":null}],"correctOptions":[4],"correctAnswerHtml":null,"explanation":"","aiExplanation":"## 1. Correct Answer\n**E.** 12\n\n---\n\n## 2. Evaluation\n\n**A.** -12\n\nSubstituting gives \$|-5-7|=|-12|\$. Absolute value is never negative, so it cannot be \$-12\$.\n\n**B.** 2\n\nAfter substitution, the expression is \$|-12|\$, which equals 12, not 2.\n\n**C.** 10\n\nThe quantity inside the absolute value is \$-12\$, and its absolute value is 12, not 10.\n\n**D.** -2\n\nAbsolute value cannot be negative. Also, \$|-5-7|=|-12|=12\$, not \$-2\$.\n\n**E.** 12\n\nSubstitute \$x=-5\$: \$|x-7|=|-5-7|=|-12|=12\$. This is correct.\n\n---\n\n## 3. Overall Explanation\n\nReplace \$x\$ with \$-5\$:\n\n\\[\n|x-7| = |-5-7| = |-12| = 12\n\\]\n\nSo the correct answer is **E**. The community reference also suggests **E**, which matches the calculation.","revealAnswer":{"schemaVersion":"mcq_option_analysis_v1","correctOptionPositions":[4],"isMultiSelect":false,"overallExplanationHtml":"

Replace \$x\$ with \$-5\$:

\\[
|x-7| = |-5-7| = |-12| = 12
\\]

So the correct answer is E. The community reference also suggests E, which matches the calculation.

","options":[{"position":0,"label":"A","explanationHtml":"

Substituting gives \$|-5-7|=|-12|\$. Absolute value is never negative, so it cannot be \$-12\$.

","isCorrect":false},{"position":1,"label":"B","explanationHtml":"

After substitution, the expression is \$|-12|\$, which equals 12, not 2.

","isCorrect":false},{"position":2,"label":"C","explanationHtml":"

The quantity inside the absolute value is \$-12\$, and its absolute value is 12, not 10.

","isCorrect":false},{"position":3,"label":"D","explanationHtml":"

Absolute value cannot be negative. Also, \$|-5-7|=|-12|=12\$, not \$-2\$.

","isCorrect":false},{"position":4,"label":"E","explanationHtml":"

Substitute \$x=-5\$: \$|x-7|=|-5-7|=|-12|=12\$. This is correct.

","isCorrect":true}]},"images":null},{"id":368107,"sortOrder":2,"type":"multiple_choice","domain":null,"visibility":"full","questionText":"

\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tSolve and simplify: 2/3 x 3/5 x 5/10 x 6/8 =
\n

","questionPreview":null,"options":[{"id":1441613,"position":0,"text":"0.2","imageUrl":null},{"id":1441614,"position":1,"text":"0.5","imageUrl":null},{"id":1441615,"position":2,"text":"0.15","imageUrl":null},{"id":1441616,"position":3,"text":"0.25","imageUrl":null},{"id":1441617,"position":4,"text":"0.333333333","imageUrl":null}],"correctOptions":[2],"correctAnswerHtml":null,"explanation":"Fractions are multiplied by multiplying numerators by numerators and denominators by denominators. Some of the fractions in this problem can be simplified.","aiExplanation":"$36","revealAnswer":{"schemaVersion":"mcq_option_analysis_v1","correctOptionPositions":[2],"isMultiSelect":false,"overallExplanationHtml":"

The correct answer is C.

Compute the product by simplifying as you go:

\\[
\\frac{2}{3}\\cdot\\frac{3}{5}\\cdot\\frac{5}{10}\\cdot\\frac{6}{8}
\\]

Notice that common factors cancel:

\$3\$ cancels with \$3\$
\$5\$ cancels with \$5\$

So the expression becomes:

\\[
\\frac{2}{10}\\cdot\\frac{6}{8}=\\frac{1}{5}\\cdot\\frac{6}{8}=\\frac{6}{40}=\\frac{3}{20}
\\]

Convert to decimal:

\\[
\\frac{3}{20}=0.15
\\]

So the simplified result is 0.15. The community reference also points to C, which matches the correct computation.

","options":[{"position":0,"label":"A","explanationHtml":"

This is too large. The product simplifies to \$\\frac{3}{20}=0.15\$, not \$0.2\$.

","isCorrect":false},{"position":1,"label":"B","explanationHtml":"

This is much too large. Multiplying fractions less than 1 gives a result less than each factor, and the exact product is \$\\frac{3}{20}=0.15\$.

","isCorrect":false},{"position":2,"label":"C","explanationHtml":"

Multiply and simplify:

\\[
\\frac{2}{3}\\cdot\\frac{3}{5}\\cdot\\frac{5}{10}\\cdot\\frac{6}{8}
\\]

Cancel common factors:

\$\\frac{2}{3}\\cdot\\frac{3}{5}=\\frac{2}{5}\$
\$\\frac{2}{5}\\cdot\\frac{5}{10}=\\frac{2}{10}=\\frac{1}{5}\$
\$\\frac{1}{5}\\cdot\\frac{6}{8}=\\frac{6}{40}=\\frac{3}{20}=0.15\$

So this is the correct answer.

","isCorrect":true},{"position":3,"label":"D","explanationHtml":"

This is incorrect. The simplified product is \$\\frac{3}{20}\$, which equals \$0.15\$, not \$0.25\$.

","isCorrect":false},{"position":4,"label":"E","explanationHtml":"

This decimal equals about \$\\frac{1}{3}\$, but the actual product is \$\\frac{3}{20}=0.15\$.

","isCorrect":false}]},"images":null},{"id":368108,"sortOrder":3,"type":"multiple_choice","domain":null,"visibility":"full","questionText":"

\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tIf Dave drives at a steady speed of 50 miles per hour, how long will it take him to drive 10 miles?
\n

","questionPreview":null,"options":[{"id":1441618,"position":0,"text":"20 minutes","imageUrl":null},{"id":1441619,"position":1,"text":"10 minutes","imageUrl":null},{"id":1441620,"position":2,"text":"15 minutes","imageUrl":null},{"id":1441621,"position":3,"text":"30 minutes","imageUrl":null},{"id":1441622,"position":4,"text":"12 minutes","imageUrl":null}],"correctOptions":[4],"correctAnswerHtml":null,"explanation":"Since there are 60 minutes in an hour, this problem can be solved with the following equation: 50/60 = 10/x","aiExplanation":"$37","revealAnswer":{"schemaVersion":"mcq_option_analysis_v1","correctOptionPositions":[4],"isMultiSelect":false,"overallExplanationHtml":"

To find how long the trip takes, use
\\[
\\text{time} = \\frac{\\text{distance}}{\\text{speed}}.
\\]
Substitute the given values:
\\[
\\text{time} = \\frac{10}{50} = \\frac{1}{5} \\text{ hour}.
\\]
Since 1 hour is 60 minutes,
\\[
\\frac{1}{5} \\times 60 = 12 \\text{ minutes}.
\\]
So the correct answer is E. 12 minutes.

","options":[{"position":0,"label":"A","explanationHtml":"

Using
\\[
\\text{time} = \\frac{\\text{distance}}{\\text{speed}} = \\frac{10}{50} = 0.2 \\text{ hours},
\\]
and converting to minutes gives \$0.2 \\times 60 = 12\$ minutes. So this is not correct.

","isCorrect":false},{"position":1,"label":"B","explanationHtml":"

Using
\\[
\\text{time} = \\frac{10}{50} = 0.2 \\text{ hours} = 12 \\text{ minutes},
\\]
so 10 minutes is too short.

","isCorrect":false},{"position":2,"label":"C","explanationHtml":"

The travel time is
\\[
\\frac{10}{50} = 0.2 \\text{ hours}.
\\]
Since \$0.2\$ hours is 12 minutes, not 15 minutes, this choice is incorrect.

","isCorrect":false},{"position":3,"label":"D","explanationHtml":"

At 50 miles per hour, Dave covers 10 miles in
\\[
\\frac{10}{50} = 0.2 \\text{ hours}.
\\]
Converting to minutes: \$0.2 \\times 60 = 12\$. Therefore, 30 minutes is incorrect.

","isCorrect":false},{"position":4,"label":"E","explanationHtml":"

Use the formula
\\[
\\text{time} = \\frac{\\text{distance}}{\\text{rate}} = \\frac{10}{50} = 0.2 \\text{ hours}.
\\]
Then convert hours to minutes:
\\[
0.2 \\times 60 = 12 \\text{ minutes}.
\\]
So this is the correct choice.

","isCorrect":true}]},"images":null},{"id":368109,"sortOrder":4,"type":"multiple_choice","domain":null,"visibility":"full","questionText":"

\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tJohn will be x in 7 years. How old was he last year?
\n

","questionPreview":null,"options":[{"id":1441623,"position":0,"text":"x + 7","imageUrl":null},{"id":1441624,"position":1,"text":"1 ג€\" x - 7","imageUrl":null},{"id":1441625,"position":2,"text":"x + 8","imageUrl":null},{"id":1441626,"position":3,"text":"x - 8","imageUrl":null},{"id":1441627,"position":4,"text":"7x","imageUrl":null}],"correctOptions":[3],"correctAnswerHtml":null,"explanation":"The target age can be found by subtracting first seven and then one year from x.","aiExplanation":"## 1. Correct Answer\n**D.** x - 8\n\n---\n\n## 2. Evaluation\n\n**A.** x + 7\n\nIf John will be **x** in 7 years, then his **current** age is **x - 7**. Last year, he would have been **(x - 7) - 1 = x - 8**. So this is not correct.\n\n**B.** 1 ג€\" x - 7\n\nJohn's age last year should be **x - 8**. This expression does not match that result, so it is not correct.\n\n**C.** x + 8\n\nThis is greater than **x**, but John's age last year must be **less than** his age in 7 years. The correct expression is **x - 8**, so this is not correct.\n\n**D.** x - 8\n\nThis is correct. If John will be **x** in 7 years, then now he is **x - 7**. Last year he was **x - 8**.\n\n**E.** 7x\n\nMultiplying 7 by **x** does not represent going backward 8 years from **x**. The correct age last year is **x - 8**.\n\n---\n\n## 3. Overall Explanation\n\nLet John's current age be **c**.\n\nIf in 7 years he will be **x**, then:\n\n**c + 7 = x**\n\nSo:\n\n**c = x - 7**\n\nLast year, he was:\n\n**(x - 7) - 1 = x - 8**\n\nSo the correct answer is **D**.","revealAnswer":{"schemaVersion":"mcq_option_analysis_v1","correctOptionPositions":[3],"isMultiSelect":false,"overallExplanationHtml":"

Let John's current age be c.

If in 7 years he will be x, then:

c + 7 = x

So:

c = x - 7

Last year, he was:

(x - 7) - 1 = x - 8

So the correct answer is D.

","options":[{"position":0,"label":"A","explanationHtml":"

If John will be x in 7 years, then his current age is x - 7. Last year, he would have been (x - 7) - 1 = x - 8. So this is not correct.

","isCorrect":false},{"position":1,"label":"B","explanationHtml":"

John's age last year should be x - 8. This expression does not match that result, so it is not correct.

","isCorrect":false},{"position":2,"label":"C","explanationHtml":"

This is greater than x, but John's age last year must be less than his age in 7 years. The correct expression is x - 8, so this is not correct.

","isCorrect":false},{"position":3,"label":"D","explanationHtml":"

This is correct. If John will be x in 7 years, then now he is x - 7. Last year he was x - 8.

","isCorrect":true},{"position":4,"label":"E","explanationHtml":"

Multiplying 7 by x does not represent going backward 8 years from x. The correct age last year is x - 8.

","isCorrect":false}]},"images":null},{"id":368110,"sortOrder":5,"type":"multiple_choice","domain":null,"visibility":"full","questionText":"

\n\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\tFind the slope: 4x `\" 5y = 20 -
\n

","questionPreview":null,"options":[{"id":1441628,"position":0,"text":"5/4","imageUrl":null},{"id":1441629,"position":1,"text":"4/5","imageUrl":null},{"id":1441630,"position":2,"text":"- 4/5","imageUrl":null},{"id":1441631,"position":3,"text":"- 5/4","imageUrl":null},{"id":1441632,"position":4,"text":"- 4","imageUrl":null}],"correctOptions":[1],"correctAnswerHtml":null,"explanation":"The equation form for slope is y = mx + b, in which m is slope.","aiExplanation":"$38","revealAnswer":{"schemaVersion":"mcq_option_analysis_v1","correctOptionPositions":[1],"isMultiSelect":false,"overallExplanationHtml":"

The equation is best interpreted as 4x - 5y = 20. Put it into slope-intercept form:

4x - 5y = 20

-5y = -4x + 20

y = (4/5)x - 4

In y = mx + b, the slope is m, so the slope is 4/5, which is B. The prompt appears slightly garbled, but the answer choices strongly support the minus-sign interpretation.

","options":[{"position":0,"label":"A","explanationHtml":"

This is the reciprocal of the slope. Rewriting the equation as y = (4/5)x - 4 shows the slope is 4/5, not 5/4.

","isCorrect":false},{"position":1,"label":"B","explanationHtml":"

Rewriting 4x - 5y = 20 in slope-intercept form gives y = (4/5)x - 4. The coefficient of x is the slope, so the slope is 4/5.

","isCorrect":true},{"position":2,"label":"C","explanationHtml":"

This would be the slope if the equation were 4x + 5y = 20. For 4x - 5y = 20, solving for y gives y = (4/5)x - 4, so the slope is positive 4/5.

","isCorrect":false},{"position":3,"label":"D","explanationHtml":"

This has both the wrong sign and the reciprocal. From y = (4/5)x - 4, the slope is 4/5.

","isCorrect":false},{"position":4,"label":"E","explanationHtml":"

This is the y-intercept, not the slope. In y = (4/5)x - 4, the slope is 4/5 and the intercept is -4.

","isCorrect":false}]},"images":null}],"exam":{"id":2223,"code":"PRAXIS-MATHEMATICS-SECTION","shortcode":"PRAXIS Mathematics Section","name":"Pre-Professional Skills Test (PPST) - Mathematics Section","slug":"praxis-mathematics-section","description":"This certification validates practical skills in system administration and infrastructure, including deployment, administration, troubleshooting, and resilience. It is intended for professionals operating dependable enterprise technology environments.","overviewSource":"baseline","overviewText":null,"overviewHtml":null,"rating":4.8,"updatedAt":"$D2026-08-15T19:10:34.261Z","anonFreeCount":5,"registeredFreeCount":10,"price30DayCents":1999,"price90DayCents":3999,"provider":{"name":"Test Prep","slug":"test-prep"}},"currentPage":1,"totalPages":10,"isLoggedIn":false,"bookmarkLoginHref":"/auth/login?redirect=%2Fexams%2Ftest-prep%2Fpraxis-mathematics-section"}],"$L39"]}],"$L3a",null]}]}]