Free Praxis 5003 Practice Test

Question 1

Each can of Brand A paint will cover 200 square feet. A building has two walls to be painted. One is a rectangle with length 30 feet and width 16.5 feet, and the other is a triangle with height 12 feet and base 16 feet. What is the least number of cans of Brand A paint that are needed to paint the two walls in their entirety?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

Three cans of Brand A paint are needed to cover the walls.

To determine the total coverage required, we first calculate the area of both walls and then divide by the coverage per can of paint. The areas of the rectangle and triangle combine to necessitate three cans of paint, given the coverage of 200 square feet per can.

A) 2
Choosing two cans would provide a total coverage of 400 square feet. However, the total area of the walls exceeds this coverage, so two cans are insufficient for complete coverage.

B) 3
This choice accurately reflects the total area calculation. The rectangle's area is 495 square feet (30 ft × 16.5 ft), and the triangle's area is 96 square feet (0.5 × 16 ft × 12 ft), giving a combined area of 591 square feet. Dividing this by the 200 square feet covered by each can shows that three cans are necessary to fully cover the walls.

C) 4
While four cans would provide 800 square feet of coverage, which exceeds the required area, it is unnecessary. The calculation confirms that only three cans are needed, making this choice excessive and incorrect.

D) 5
Five cans would cover 1000 square feet, which is significantly more than what is needed. This choice is not only excessive but also misrepresents the actual requirement based on the area to be painted.

Conclusion
To fully paint the two walls, calculating the areas and dividing by the coverage provided by each can leads to the conclusion that three cans of Brand A paint are necessary. Options A, C, and D do not accurately reflect the area calculations and thus do not serve as valid solutions. The choice of three cans is the most efficient and accurate for this painting task.

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Question 2

Which of the following statements is true about the number 90?

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Question 3

Which of the following is a decomposition of the number 1260?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

1 thousand, 2 hundreds, and 60 tens is a decomposition of the number 1260.

This decomposition breaks down 1260 into its constituent place values, clearly illustrating the contributions of each position (thousands, hundreds, and tens) to the overall number.

A) 12 hundreds and 6 tens
This choice represents a total of 1200 (12 hundreds) plus 60 (6 tens), which sums to 1260. However, it does not accurately depict the breakdown into thousands, hundreds, and tens as required by the decomposition format.

B) 11 hundreds and 60 tens
Calculating this option gives 1100 (11 hundreds) plus 600 (60 tens), resulting in a total of 1700. This exceeds the target number of 1260 and fails to correctly decompose it into the required components.

C) 1 thousand and 26 hundreds
This choice translates to 1000 (1 thousand) plus 2600 (26 hundreds), which totals 3600. Again, this exceeds the target number and does not reflect a valid decomposition of 1260.

D) 1 thousand, 2 hundreds, and 60 tens
This option accurately breaks down the number 1260 into its respective components: 1000 (1 thousand) + 200 (2 hundreds) + 60 (60 tens), which equals 1260. This decomposition correctly represents the number in terms of its place values.

Conclusion
The valid decomposition of the number 1260 is best represented by the breakdown of 1 thousand, 2 hundreds, and 60 tens. Other options either misrepresent the number or exceed the total, emphasizing the importance of accurate place value representation in numerical decomposition.

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Question 4

A high school schedules 288 students to take a math class during first period. If there are 12 math teachers, what is the student-to-teacher ratio for the math classes during first period?

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Question 5

Based on the preceding computation, what is the value of 1085 / 12?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

1085 divided by 12 equals 90.5.

The calculation of 1085 divided by 12 yields exactly 90.5. This result is derived from performing the division operation, which accurately reflects the quotient of these two numbers.

A) 90
This choice represents an integer value that is the approximate result of the division but fails to account for the decimal remainder. Since 1085 divided by 12 does not result in a whole number, this answer is incorrect.

B) 90{5/1085}
This option mistakenly suggests a \fraction that implies a very small addition to 90, which does not correctly represent the actual decimal result of the division. The notation used here is confusing and does not properly express the outcome of the division, making it incorrect.

C) 90{5/12}
While this choice correctly indicates a \fraction, it misrepresents the division result. The term "90{5/12}" suggests that the remainder is expressed in terms of 12 rather than accurately reflecting the decimal representation of the quotient from the division of 1085 by 12. Thus, this choice is also incorrect.

D) 90.5
This is the correct answer as it accurately reflects the result of dividing 1085 by 12. The calculation confirms that 90.5 is the exact quotient, including both the integer part and the decimal \fraction.

Conclusion
The division of 1085 by 12 results in 90.5, which is the only choice that correctly captures the complete value of the quotient. The other options either provide inaccurate approximations or misrepresent the mathematical computation involved. Understanding the correct result is critical for accurate calculations in various mathematical and real-world applications.

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Three cans of Brand A paint are needed to cover the walls.

1 thousand, 2 hundreds, and 60 tens is a decomposition of the number 1260.

1085 divided by 12 equals 90.5.

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